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August 2
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Events
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Events
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August 2
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Pre-1600
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Pre-1600
338 BC – A Macedonian army led by Philip II defeated the combined forces of Athens and Thebes in the Battle of Chaeronea, securing Macedonian hegemony in Greece and the Aegean.
216 BC – The Carthaginian army led by Hannibal defeats a numerically superior Roman army at the Battle of Cannae.
49 BC – Caesar, who marched to Spain earlier in the year, leaving Marcus Antonius in charge of Italy, defeats Pompey's general Afranius and Petreius in Ilerda (Lerida) north of the Ebro river.
461 – Majorian is arrested near Tortona (northern Italy) and deposed by the Suebian general Ricimer as puppet emperor.
932 – After a two-year siege, the city of Toledo, in Spain, surrenders to the forces of the Caliph of Córdoba Abd al-Rahman III, assuming an important victory in his campaign to subjugate the Central March.
1274 – Edward I of England returns from the Ninth Crusade and is crowned King seventeen days later.
1343 – After the execution of her husband, Jeanne de Clisson sells her estates and raises a force of men with which to attack French shipping and ports.
1377 – Russian troops are defeated by forces of the Blue Horde Khan Arapsha in the Battle on Pyana River.
1415 – Thomas Grey is executed for participating in the Southampton Plot.
1492 – The Jews are expelled from Spain: 40,000–200,000 leave. Sultan Bayezid II of the Ottoman Empire, learning of this, dispatches the Ottoman Navy to bring the Jews safely to Ottoman lands, mainly to the cities of Thessaloniki (in modern-day Greece) and İzmir (in modern-day Turkey).
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August 2
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1601–1900
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1601–1900
1610 – During Henry Hudson's search for the Northwest Passage, he sails into what is now known as Hudson Bay.
1776 – The signing of the United States Declaration of Independence took place.
1784 – The first British mail coach service ran from Bristol to London.
1790 – The first United States Census is conducted.
1798 – French Revolutionary Wars: The Battle of the Nile concludes in a British victory.
1830 – Charles X of France abdicates the throne in favor of his grandson Henri.
1858 – The Government of India Act 1858 replaces Company rule in India with that of the British Raj.
1869 – Japan's Edo society class system is abolished as part of the Meiji Restoration reforms.
1870 – Tower Subway, the world's first underground tube railway, opens in London, England, United Kingdom.
1873 – The Clay Street Hill Railroad begins operating the first cable car in San Francisco's famous cable car system.
1897 – Anglo-Afghan War: The Siege of Malakand ends when a relief column is able to reach the British garrison in the Malakand states.
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August 2
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1901–present
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1901–present
1903 – The Ilinden–Preobrazhenie Uprising against the Ottoman Empire begins.
1914 – The German occupation of Luxembourg during World War I begins.
1916 – World War I: Austrian sabotage causes the sinking of the Italian battleship Leonardo da Vinci in Taranto.
1918 – The first general strike in Canadian history takes place in Vancouver.
1922 – A typhoon hits Shantou, Republic of China, killing more than 50,000 people.
1923 – Vice President Calvin Coolidge becomes U.S. President upon the death of President Warren G. Harding.
1932 – The positron (antiparticle of the electron) is discovered by Carl D. Anderson.
1934 – Reichskanzler Adolf Hitler becomes Führer of Germany following the death of President Paul von Hindenburg.
1937 – The Marihuana Tax Act of 1937 is passed in America, the effect of which is to render marijuana and all its by-products illegal.
1939 – Albert Einstein and Leo Szilard write a letter to Franklin D. Roosevelt, urging him to begin the Manhattan Project to develop a nuclear weapon.
1943 – The Holocaust: Jewish prisoners stage a revolt at Treblinka, one of the deadliest of Nazi death camps where approximately 900,000 persons were murdered in less than 18 months.
1943 – World War II: The Motor Torpedo Boat PT-109 is rammed by the Japanese destroyer Amagiri and sinks. Lt. John F. Kennedy, future U.S. president, saves all but two of his crew.
1944 – ASNOM: Birth of the Socialist Republic of Macedonia, celebrated as Day of the Republic in North Macedonia.
1944 – World War II: The largest trade convoy of the world wars arrives safely in the Western Approaches.
1945 – World War II: End of the Potsdam Conference.
1947 – A British South American Airways Avro Lancastrian airliner crashes into a mountain during a flight from Buenos Aires, Argentina to Santiago, Chile. The wreckage would not be found until 1998.
1968 – An earthquake hits Casiguran, Aurora, Philippines killing more than 270 people and wounding 261.
1973 – A flash fire kills 50 people at the Summerland amusement centre at Douglas, Isle of Man.
1980 – A bomb explodes at the railway station in Bologna, Italy, killing 85 people and wounding more than 200.
1982 – The Helsinki Metro, the first rapid transit system of Finland, is opened to the general public.
1985 – Delta Air Lines Flight 191, a Lockheed L-1011 TriStar, crashes at Dallas/Fort Worth International Airport killing 137.
1989 – Pakistan is re-admitted to the Commonwealth of Nations after having restored democracy for the first time since 1972.
1989 – A massacre is carried out by an Indian Peace Keeping Force in Sri Lanka killing 64 ethnic Tamil civilians.
1990 – Iraq invades Kuwait, eventually leading to the Gulf War.
1991 – Space Shuttle Atlantis is launched on STS-43 to deploy the TDRS-5 satellite.
1999 – The Gaisal train disaster claims 285 lives in Assam, India.
2005 – Air France Flight 358 lands at Toronto Pearson International Airport and runs off the runway, causing the plane to burst into flames, leaving 12 injuries and no fatalities.
2014 – At least 146 people were killed and more than 114 injured in a factory explosion in Kunshan, Jiangsu, China.
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August 2
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Births
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Births
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August 2
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Pre-1600
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Pre-1600
1260 – Kyawswa of Pagan, last ruler of the Pagan Kingdom (d. 1299)
1455 – John Cicero, Elector of Brandenburg (d. 1499)
1533 – Theodor Zwinger, Swiss physician and scholar (d. 1588)
1549 – Mikołaj Krzysztof "the Orphan" Radziwiłł, Polish nobleman (d. 1616)
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August 2
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1601–1900
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1601–1900
1612 – Saskia van Uylenburgh, Dutch model and wife of Rembrandt van Rijn (d. 1642)
1627 – Samuel Dirksz van Hoogstraten, Dutch painter (d. 1678)
1630 – Estephan El Douaihy, Maronite patriarch (d. 1704)
1646 – Jean-Baptiste du Casse, French admiral and buccaneer (d. 1715)
1672 – Johann Jakob Scheuchzer, Swiss paleontologist and scholar (d. 1733)
1674 – Philippe II, Duke of Orléans (d. 1723)
1696 – Mahmud I, Ottoman sultan (d. 1754)
1702 – Dietrich of Anhalt-Dessau (d. 1769)
1703 – Lorenzo Ricci, Italian religious leader, 18th Superior General of the Society of Jesus (d. 1775)
1740 – Jean Baptiste Camille Canclaux, French general (d. 1817)
1754 – Pierre Charles L'Enfant, French-American architect and engineer, designed Washington, D.C. (d. 1825)
1788 – Leopold Gmelin, German chemist and academic (d. 1853)
1815 – Adolf Friedrich von Schack, German poet and historian (d. 1894)
1820 – John Tyndall, Irish-English physicist and mountaineer (d. 1893)
1828 – Manuel Pavía y Rodríguez de Alburquerque, Spanish general (d. 1895)
1834 – Frédéric Auguste Bartholdi, French sculptor, designed the Statue of Liberty (d. 1904)
1835 – Elisha Gray, American businessman, co-founded Western Electric (d. 1901)
1861 – Prafulla Chandra Ray, Indian chemist and academic (d. 1944)
1865 – Irving Babbitt, American academic and critic (d. 1933)
1865 – John Radecki, Australian stained glass artist (d. 1955)
1867 – Ernest Dowson, English poet, novelist, and short story writer (d. 1900)
1868 – Constantine I of Greece (d. 1923)
1870 – Marianne Weber, German sociologist and suffragist (d. 1954)
1871 – John French Sloan, American painter and illustrator (d. 1951)
1872 – George E. Stewart, Australian-American colonel, Medal of Honor recipient (d. 1946)
1876 – Pingali Venkayya, Indian geologist, designed the Flag of India (d. 1963)
1877 – Ravishankar Shukla, Indian lawyer and politician, 1st Chief Minister of Madhya Pradesh (d. 1956)
1878 – Aino Kallas, Finnish-Estonian author (d. 1956)
1880 – Arthur Dove, American painter and educator (d. 1946)
1882 – Red Ames, American baseball player and manager (d. 1936)
1882 – Albert Bloch, American painter and academic (d. 1961)
1884 – Rómulo Gallegos, Venezuelan author and politician, 46th President of Venezuela (d. 1969)
1886 – John Alexander Douglas McCurdy, Canadian pilot and politician, 20th Lieutenant Governor of Nova Scotia (d. 1961)
1887 – Oskar Anderson, Bulgarian-German mathematician and statistician (d. 1960)
1889 – Margaret Lawrence, American stage actress (d. 1929)
1891 – Arthur Bliss, English composer and conductor (d. 1975)
1891 – Viktor Zhirmunsky, Russian linguist and historian (d. 1971)
1892 – Jack L. Warner, Canadian-born American production manager and producer, co-founded Warner Bros. (d. 1978)
1894 – Bertha Lutz, Brazilian feminist and scientist (d. 1976)
1895 – Matt Henderson, New Zealand cricketer (d. 1970)
1897 – Karl-Otto Koch, German SS officer (d. 1945)
1897 – Max Weber, Swiss lawyer and politician (d. 1974)
1898 – Ernő Nagy, Hungarian fencer (d. 1977)
1899 – Charles Bennett, English director and screenwriter (d. 1995)
1900 – Holling C. Holling, American author and illustrator (d. 1973)
1900 – Helen Morgan, American actress and singer (d. 1941)
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August 2
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1901–present
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1901–present
1902 – Pope Cyril VI of Alexandria (d. 1971)
1902 – Mina Rees, American mathematician (d. 1997)
1905 – Karl Amadeus Hartmann, German composer (d. 1963)
1905 – Myrna Loy, American actress (d. 1993)
1905 – Ruth Nelson, American actress (d. 1992)"Ruth Nelson". IBDb. Retrieved November 1, 2022.Haun, Harry (2000). The Cinematic Century: An Intimate Diary of America's Affair with the Movies. New York: Applause. .
1907 – Mary Hamman, American journalist and author (d. 1984)
1910 – Roger MacDougall, Scottish director, playwright, and screenwriter (d. 1993)
1911 – Ann Dvorak, American actress (d. 1979)
1912 – Palle Huld, Danish actor (d. 2010)
1912 – Håkon Stenstadvold, Norwegian painter, illustrator, and critic (d. 1977)
1912 – Vladimir Žerjavić, Croatian economist and author (d. 2001)
1913 – Xavier Thaninayagam, Sri Lankan scholar and academic (d. 1980)
1914 – Félix Leclerc, Canadian singer-songwriter, actor, and poet (d. 1988)
1914 – Big Walter Price, American singer-songwriter and pianist (d. 2012)
1914 – Beatrice Straight, American actress (d. 2001)
1915 – Gary Merrill, American actor (d. 1990)
1916 – Alfonso A. Ossorio, Filipino-American painter and sculptor (d. 1990)
1917 – Wah Chang, Chinese-American artist and designer (d. 2003)
1919 – Nehemiah Persoff, Israeli-American actor (d. 2022)
1920 – Louis Pauwels, French journalist and author (d. 1997)
1920 – Augustus Rowe, Canadian physician and politician (d. 2013)
1922 – Betsy Bloomingdale, American philanthropist and socialite (d. 2016)
1922 – Geoffrey Dutton, Australian historian and author (d. 1998)
1922 – Len Murray, British trade union leader (d. 2004)
1923 – Shimon Peres, Polish-Israeli lawyer and politician, 9th President of Israel (d. 2016)
1923 – Ike Williams, American boxer (d. 1994)
1924 – James Baldwin, American novelist, poet, and critic (d. 1987)
1924 – Joe Harnell, American pianist and composer (d. 2005)
1924 – Carroll O'Connor, American actor, director, producer, and screenwriter (d. 2001)
1925 – K. Arulanandan, Ceylon-American engineer and academic (d. 2004)
1925 – John Dexter, English director and producer (d. 1990)
1925 – John McCormack, Canadian ice hockey player (d. 2017)
1925 – Jorge Rafael Videla, Argentinian general and politician, 43rd President of Argentina (d. 2013)
1925 – Alan Whicker, Egyptian-born British journalist and broadcaster (d. 2013)
1927 – Peter Swinnerton-Dyer, English mathematician and academic (d. 2018)
1928 – Malcolm Hilton, English cricketer (d. 1990)
1929 – Roy Crimmins, English trombonist and composer (d. 2014)
1929 – John Gale, English director and producer
1929 – Vidya Charan Shukla, Indian politician, Indian Minister of External Affairs (d. 2013)
1929 – David Waddington, Baron Waddington, English lawyer and politician, Governor of Bermuda (d. 2017)
1929 – K. M. Peyton, British children's author (d. 2023)
1930 – Vali Myers, Australian painter and dancer (d. 2003)
1931 – Pierre DuMaine, American bishop and academic (d. 2019)
1931 – Eddie Fuller, South African cricketer (d. 2008)
1931 – Karl Miller, English journalist and critic (d. 2014)
1931 – Viliam Schrojf, Czech footballer (d. 2007)
1932 – Lamar Hunt, American businessman, co-founded the American Football League and World Championship Tennis (d. 2006)
1932 – Peter O'Toole, British-Irish actor and producer (d. 2013)
1933 – Ioannis Varvitsiotis, Greek politician, Greek Minister of Defence
1934 – Valery Bykovsky, Russian general and cosmonaut (d. 2019)
1935 – Hank Cochran, American singer-songwriter and guitarist (d. 2010)
1936 – Anthony Payne, English composer and author (d. 2021)
1937 – Ron Brierley, New Zealand businessman
1937 – Billy Cannon, American football player and dentist (d. 2018)
1937 – María Duval, Mexican actress and singer
1937 – Garth Hudson, Canadian keyboard player, songwriter, and producer (d. 2025)
1937 – Tim Bowden, Australian historian and television presenter (d. 2024)
1938 – Dave Balon, Canadian ice hockey player and coach (d. 2007)
1938 – Pierre de Bané, Israeli-Canadian lawyer and politician (d. 2019)
1938 – Terry Peck, Falkland Islander soldier (d. 2006)
1939 – Benjamin Barber, American theorist, author, and academic (d. 2017)
1939 – Wes Craven, American director, producer, and screenwriter (d. 2015)
1939 – John W. Snow, American businessman and politician, 73rd United States Secretary of the Treasury
1940 – Angel Lagdameo, Filipino archbishop (d. 2022)
1940 – Beko Ransome-Kuti, Nigerian physician and activist (d. 2006)
1940 – Will Tura, Belgian singer-songwriter and guitarist
1941 – Doris Coley, American singer (d. 2000)
1941 – Jules A. Hoffmann, Luxembourgish-French biologist and academic, Nobel Prize laureate
1941 – François Weyergans, Belgian director and screenwriter (d. 2022)
1942 – Isabel Allende, Chilean-American novelist, essayist, essayist
1942 – Leo Beenhakker, Dutch football manager (d. 2025)
1942 – Juan Formell, Cuban singer-songwriter and bass player (d. 2014)
1942 – Nell Irvin Painter, American author and historian
1943 – Herbert M. Allison, American lieutenant and businessman (d. 2013)
1943 – Tom Burgmeier, American baseball player and coach
1943 – Jon R. Cavaiani, English-American sergeant, Medal of Honor recipient (d. 2014)
1943 – Rose Tremain, English novelist and short story writer
1944 – Jim Capaldi, English drummer and singer-songwriter (d. 2005)
1944 – Naná Vasconcelos, Brazilian singer and berimbau player (d. 2016)
1945 – Joanna Cassidy, American actress
1945 – Alex Jesaulenko, Austrian-Australian footballer and coach
1945 – Bunker Roy, Indian educator and activist
1945 – Eric Simms, Australian rugby league player and coach
1946 – James Howe, American journalist and author
1947 – Ruth Bakke, Norwegian organist and composer
1947 – Lawrence Wright, American journalist, author, and screenwriter
1948 – Andy Fairweather Low, Welsh singer-songwriter, guitarist, and producer
1948 – Dennis Prager, American radio host and author
1948 – Tapan Kumar Sarkar, Indian-American electrical engineer and academic (d. 2021)
1948 – James Street, American football and baseball player (d. 2013)
1948 – Snoo Wilson, English playwright and screenwriter (d. 2013)
1949 – James Fallows, American journalist and author
1949 – Bertalan Farkas, Hungarian general and cosmonaut
1950 – Jussi Adler-Olsen, Danish author and publisher
1950 – Ted Turner, British guitarist
1951 – Andrew Gold, American singer-songwriter and producer (d. 2011)
1951 – Steve Hillage, English singer-songwriter and guitarist
1951 – Burgess Owens, American football player and politician
1951 – Joe Lynn Turner, American singer-songwriter and guitarist
1951 – Per Westerberg, Swedish businessman and politician, Speaker of the Parliament of Sweden
1952 – Alain Giresse, French footballer and manager
1953 – Donnie Munro, Scottish singer and guitarist
1953 – Butch Patrick, American actor
1953 – Anthony Seldon, English historian and author
1954 – Sammy McIlroy, Northern Irish footballer and manager
1955 – Caleb Carr, American historian and author (d. 2024)
1955 – Tony Godden, English footballer and manager
1955 – Butch Vig, American drummer, songwriter, and record producer
1956 – Fulvio Melia, Italian-American physicist, astrophysicist, and author
1957 – Jacky Rosen, United States senator
1959 – Jim Doughan, American actor
1959 – Victoria Jackson, American actress and singer
1959 – Johnny Kemp, Bahamian singer-songwriter and producer (d. 2015)
1959 – Apollonia Kotero, American singer and actress
1960 – Linda Fratianne, American figure skater
1960 – Neal Morse, American singer and keyboard player
1960 – David Yow, American singer-songwriter
1961 – Pete de Freitas, Trinidadian-British drummer and producer (d. 1989)
1962 – Lee Mavers, English singer, songwriter and guitarist
1962 – Cynthia Stevenson, American actress
1963 – Laura Bennett, American architect and fashion designer
1963 – Uğur Tütüneker, Turkish footballer and manager
1964 – Frank Biela, German race car driver
1964 – Mary-Louise Parker, American actress
1965 – Joe Hockey, Australian lawyer and politician, 38th Treasurer of Australia
1965 – Hisanobu Watanabe, Japanese baseball player and coach
1966 – Takashi Iizuka, Japanese wrestler
1966 – Grainne Leahy, Irish cricketer
1966 – Tim Wakefield, American baseball player and sportscaster (d. 2023)
1967 – Aaron Krickstein, American tennis player
1967 – Aline Brosh McKenna, American screenwriter and producer
1968 – Stefan Effenberg, German footballer and sportscaster
1969 – Cedric Ceballos, American basketball player
1969 – Fernando Couto, Portuguese footballer and manager
1970 – Tony Amonte, American ice hockey player and coach
1970 – Kevin Smith, American actor, director, producer, and screenwriter Note: At least one source, Yahoo! Movies, gives birthplace as Highlands, New Jersey.
1970 – Philo Wallace, Barbadian cricketer
1971 – Jason Bell, Australian rugby league player
1971 – Michael Hughes, Irish footballer and manager
1972 – Mohamed Al-Deayea, Saudi Arabian footballer
1972 – Muriel Bowser, American politician, Mayor of Washington, D.C.
1973 – Danie Keulder, Namibian cricketer
1973 – Miguel Mendonca, Zimbabwean journalist and author
1973 – Susie O'Neill, Australian swimmer
1974 – Phil Williams, English journalist and radio host
1975 – Mineiro, Brazilian footballer
1975 – Xu Huaiwen, Chinese-German badminton player and coach
1975 – Tamás Molnár, Hungarian water polo player
1976 – Reyes Estévez, Spanish runner
1976 – Jay Heaps, American soccer player and coach
1976 – Michael Weiss, American figure skater
1976 – Sam Worthington, English-Australian actor and producer
1976 – Mohammad Zahid, Pakistani cricketer
1977 – Edward Furlong, American actor
1978 – Goran Gavrančić, Serbian footballer
1978 – Matt Guerrier, American baseball player
1978 – Deividas Šemberas, Lithuanian footballer
1978 – Dragan Vukmir, Serbian footballer
1979 – Marco Bonura, Italian footballer
1979 – Reuben Kosgei, Kenyan runner
1980 – Ivica Banović, Croatian footballer
1981 – Alexander Emelianenko, Russian mixed martial artist and boxer
1981 – Tim Murtagh, English-Irish cricketer
1982 – Hélder Postiga, Portuguese footballer
1982 – Kerry Rhodes, American football player
1982 – Grady Sizemore, American baseball player
1983 – Michel Bastos, Brazilian footballer
1983 – Huston Street, American baseball player
1984 – Giampaolo Pazzini, Italian footballer
1984 – JD Vance, vice president of the United States
1985 – Stephen Ferris, Irish rugby player
1985 – David Hart Smith, Canadian wrestler
1985 – Britt Nicole, American Christian pop artist
1986 – Mathieu Razanakolona, Canadian skier
1986 – Lily Gladstone, American actress
1988 – Rob Kwiet, Canadian ice hockey player
1988 – Golden Tate, American football player
1989 – Nacer Chadli, Belgian footballer
1990 – Ima Bohush, Belarusian tennis player
1990 – Vitalia Diatchenko, Russian tennis player
1990 – Skylar Diggins-Smith, American basketball player
1991 – Evander Kane, Canadian ice hockey player
1992 – Charli XCX, English singer-songwriter
1993 – Gael Bussa, Congolese politician
1994 – Cr1TiKaL, American YouTuber and streamer
1994 – Laura Pigossi, Brazilian tennis player
1994 – Laremy Tunsil, American football player
1995 – Kristaps Porziņģis, Latvian basketball player
1995 – Vikkstar123, English internet personality
1996 – Keston Hiura, American baseball player
1996 – Simone Manuel, American swimmer
1997 – Austin Theory, American wrestler
1999 – Mark Lee, Korean-Canadian singer
2000 – Varvara Gracheva, Russian tennis player
2000 – Mohammed Kudus, Ghanaian footballer
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August 2
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Deaths
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Deaths
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August 2
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Pre-1600
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Pre-1600
216 BC – Gnaeus Servilius Geminus, Roman consul
216 BC – Lucius Aemilius Paullus, Roman consul and general
216 BC – Marcus Minucius Rufus, Roman consul
257 – Pope Stephen I
575 – Ahudemmeh, Syriac Orthodox Grand Metropolitan of the East.
640 – Pope Severinus
686 – Pope John V
855 – Ahmad ibn Hanbal, Arab theologian and jurist (b. 780)
924 – Ælfweard of Wessex (b. 904)
1075 – Patriarch John VIII of Constantinople
1100 – William II of England (b. 1056)
1222 – Raymond VI, Count of Toulouse (b. 1156)
1277 – Mu'in al-Din Sulaiman Pervane, Chancellor and Regent of the Sultanate of Rum
1316 – Louis of Burgundy (b. 1297)
1330 – Yolande of Dreux, Queen consort of Scotland and Duchess consort of Brittany (b. 1263)
1332 – King Christopher II of Denmark (b. 1276)
1415 – Thomas Grey, English conspirator (b. 1384)
1445 – Oswald von Wolkenstein, Austrian poet and composer (b. 1376)
1451 – Elizabeth of Görlitz (b. 1390)
1511 – Andrew Barton, Scottish admiral (b. 1466)
1512 – Alessandro Achillini, Italian physician and philosopher (b. 1463)
1589 – Henry III of France (b. 1551)
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August 2
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1601–1900
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1601–1900
1605 – Richard Leveson, English admiral (b. c. 1570)
1611 – Katō Kiyomasa, Japanese daimyō (b. 1562)
1667 – Francesco Borromini, Swiss architect, designed San Carlo alle Quattro Fontane and Sant'Agnese in Agone (b. 1599)
1696 – Robert Campbell of Glenlyon (b. 1630)
1769 – Daniel Finch, 8th Earl of Winchilsea, English politician, Lord President of the Council (b. 1689)
1788 – Thomas Gainsborough, English painter (b. 1727)
1799 – Jacques-Étienne Montgolfier, French inventor, co-invented the hot air balloon (b. 1745)
1815 – Guillaume Brune, French general and politician (b. 1763)
1823 – Lazare Carnot, French mathematician, general, and politician, president of the National Convention (b. 1753)
1834 – Harriet Arbuthnot, English diarist (b. 1793)
1849 – Muhammad Ali of Egypt, Ottoman Albanian commander (b. 1769)
1854 – Heinrich Clauren, German author (b. 1771)
1859 – Horace Mann, American educator and politician (b. 1796)
1876 – "Wild Bill" Hickok, American sheriff (b. 1837)
1889 – Eduardo Gutiérrez, Argentinian author (b. 1851)
1890 – Louise-Victorine Ackermann, French poet and author (b. 1813)
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August 2
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1901–present
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1901–present
1903 – Eduard Magnus Jakobson, Estonian missionary and engraver (b. 1847)
1903 – Edmond Nocard, French veterinarian and microbiologist (b. 1850)
1911 – Ioryi Mucitano, Aromanian revolutionary
1913 – Ferenc Pfaff, Hungarian architect and academic, designed Zagreb Central Station (b. 1851)
1915 – John Downer, Australian politician, 16th premier of South Australia (b. 1843)
1917 – Jaan Mahlapuu, Estonian military pilot (b. 1894)
1921 – Enrico Caruso, Italian tenor and actor (b. 1873)
1922 – Alexander Graham Bell, Scottish-Canadian engineer, invented the telephone (b. 1847)
1923 – Warren G. Harding, American journalist and politician, 29th president of the United States (b. 1865)
1923 – Joseph Whitty, Irish Republican died on hunger strike during the 1923 Irish Hunger Strikes (b. 1904)The Civil War". rootsireland.ie. roots ireland. Retrieved 29 August 2021. Joe Whitty aged 19 who died on hunger-strike
1934 – Paul von Hindenburg, German field marshal and politician, 2nd president of Germany (b. 1847)
1937 – Artur Sirk, Estonian soldier, lawyer, and politician (b. 1900)
1939 – Harvey Spencer Lewis, American mystic and author (b. 1883)
1945 – Pietro Mascagni, Italian composer and educator (b. 1863)
1955 – Alfred Lépine, Canadian ice hockey player and coach (b. 1901)
1955 – Wallace Stevens, American poet and educator (b. 1879)
1963 – Oliver La Farge, American anthropologist and author (b. 1901)
1967 – Walter Terence Stace, English-American epistemologist, philosopher, and academic (b. 1886)
1970 – Angus MacFarlane-Grieve, English academic, mathematician, rower, and soldier (b. 1891)
1972 – Brian Cole, American bass player (b. 1942)
1972 – Paul Goodman, American psychotherapist and author (b. 1911)
1972 – Helen Hoyt, American poet and author (b. 1887)
1973 – Ismail Abdul Rahman, Former Deputy Prime Minister of Malaysia (b. 1915)
1973 – Jean-Pierre Melville, French actor, director, producer, and screenwriter (b. 1917)
1974 – Douglas Hawkes, English race car driver and businessman (b. 1893)
1976 – László Kalmár, Hungarian mathematician and academic (b. 1905)
1976 – Fritz Lang, Austrian-American director, producer, and screenwriter (b. 1890)
1978 – Carlos Chávez, Mexican composer and conductor (b. 1899)
1978 – Antony Noghès, French businessman, founded the Monaco Grand Prix (b. 1890)
1979 – Thurman Munson, American baseball player (b. 1947)
1981 – Kieran Doherty, Irish hunger striker and politician (b. 1955)
1981 – Stefanie Clausen, Danish diver (b. 1900)
1983 – James Jamerson, American bass player (b. 1936)
1986 – Roy Cohn, American lawyer and politician (b. 1927)
1988 – Joe Carcione, American activist and author (b. 1914)
1988 – Raymond Carver, American short story writer and poet (b. 1938)
1990 – Norman Maclean, American short story writer and essayist (b. 1902)
1990 – Edwin Richfield, English actor and screenwriter (b. 1921)
1992 – Michel Berger, French singer-songwriter and producer (b. 1947)
1996 – Michel Debré, French lawyer and politician, 150th prime minister of France (b. 1912)
1996 – Obdulio Varela, Uruguayan footballer and manager (b. 1917)
1996 – Mohamed Farrah Aidid, Somalian general and politician, 5th president of Somalia (b. 1934)
1996 – Sergey Golovkin, Russian serial killer and rapist, last person executed by Russia (b. 1959)
1997 – William S. Burroughs, American novelist, short story writer, and essayist (b. 1914)
1997 – Harald Kihle, Norwegian painter and illustrator (b. 1905)
1997 – Fela Kuti, Nigerian singer-songwriter and activist (b. 1938)
1998 – Shari Lewis, American television host and puppeteer (b. 1933)
1999 – Willie Morris, American writer (b. 1934)
2003 – Peter Safar, Austrian-American physician and academic (b. 1924)
2004 – Ferenc Berényi, Hungarian painter and academic (b. 1929)
2004 – François Craenhals, Belgian illustrator (b. 1926)
2004 – Heinrich Mark, Estonian lawyer and politician, 5th prime minister of Estonia in exile (b. 1911)
2005 – Steven Vincent, American journalist and author (b. 1955)
2007 – Chauncey Bailey, American journalist (b. 1950)
2008 – Fujio Akatsuka, Japanese illustrator (b. 1935)
2011 – José Sanchis Grau, Spanish author and illustrator (b. 1932)
2012 – Gabriel Horn, English biologist and academic (b. 1927)
2012 – Magnus Isacsson, Canadian director and producer (b. 1948)
2012 – Jimmy Jones, American singer-songwriter (b. 1930)
2012 – John Keegan, English historian and journalist (b. 1934)
2012 – Bernd Meier, German footballer (b. 1972)
2012 – Marguerite Piazza, American soprano (b. 1920)
2013 – Julius L. Chambers, American lawyer and activist (b. 1936)
2013 – Richard E. Dauch, American businessman, co-founded American Axle (b. 1942)
2013 – Alla Kushnir, Russian–Israeli chess player (b. 1941)
2014 – Ed Joyce, American journalist (b. 1932)
2014 – Billie Letts, American author and educator (b. 1938)
2014 – Barbara Prammer, Austrian social worker and politician (b. 1954)
2014 – James Thompson, American-Finnish author (b. 1964)
2015 – Forrest Bird, American pilot and engineer (b. 1921)
2015 – Giovanni Conso, Italian jurist and politician, Italian Minister of Justice (b. 1922)
2015 – Piet Fransen, Dutch footballer (b. 1936)
2015 – Jack Spring, American baseball player (b. 1933)
2016 – Terence Bayler, New Zealand actor (b. 1930)
2016 – David Huddleston, American actor (b. 1930)
2016 – Franciszek Macharski, Polish cardinal (b. 1927)
2016 – Ahmed Zewail, Egyptian-American chemist and academic, Nobel Prize laureate (b. 1946)
2017 – Judith Jones, American literary and cookbook editor (b. 1924)
2020 – Suzanne Perlman, Hungarian-Dutch visual artist (b. 1922)
2022 – Vin Scully, American sportscaster and game show host (b. 1927)
2023 – Nitin Chandrakant Desai, Indian art director, production designer, and film and television producer (b. 1965)
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August 2
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Holidays and observances
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Holidays and observances
Christian feast day:
Ahudemmeh (Syriac Orthodox Church).
Basil Fool for Christ (Russian Orthodox Church)
Justin Russolillo
Eusebius of Vercelli
Peter Faber
Peter Julian Eymard
Plegmund
Pope Stephen I
Portiuncola Indulgence ("Pardon of Assisi"), the plenary indulgence related to St. Francis of Assisi (Catholic Church).
Samuel David Ferguson (Episcopal Church)
August 2 (Eastern Orthodox liturgics)
Day of Azerbaijani cinema (Azerbaijan)
Our Lady of the Angels Day (Costa Rica)
Paratroopers Day (Russia)
Republic Day (North Macedonia)
Romani genocide-related observances, including:
Roma Holocaust Memorial Day (Council of Europe, European Parliament)
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August 2
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References
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References
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August 2
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External links
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External links
Category:Days of August
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August 2
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Table of Content
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About, Events, Pre-1600, 1601–1900, 1901–present, Births, Pre-1600, 1601–1900, 1901–present, Deaths, Pre-1600, 1601–1900, 1901–present, Holidays and observances, References, External links
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Atlantic (disambiguation)
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Wiktionary
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The Atlantic Ocean is the second largest of the world's oceans, that separates the old world from the new world.
Atlantic may also refer to:
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Atlantic (disambiguation)
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Places
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Places
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Atlantic (disambiguation)
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In Canada
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In Canada
Atlantic, Nova Scotia
Atlantic Canada
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Atlantic (disambiguation)
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In the United States
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In the United States
Atlantic, Iowa
Atlantic, Massachusetts
Atlantic, North Carolina, an unincorporated community in eastern Carteret County
Atlantic, Pennsylvania
Atlantic, Seattle, a neighborhood in Washington state
Atlantic, Virginia
Atlantic City, New Jersey
Atlantic County, New Jersey
Atlantic Peak (Colorado), a mountain
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Atlantic (disambiguation)
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Art, entertainment, and media
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Art, entertainment, and media
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Atlantic (disambiguation)
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Companies and labels
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Companies and labels
Atlantic Books, an independent British publishing house
Atlantic Monthly Press, an American publishing house
Atlantic Entertainment Group, a defunct movie studio company
Atlantic FM, a former radio station serving Cornwall, United Kingdom
Atlantic Records, a record company
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Atlantic (disambiguation)
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Music
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Music
The Atlantics, an Australian surf rock band formed in the early 1960s
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Atlantic (disambiguation)
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Albums
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Albums
Atlantic (Dufresne album)
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Atlantic (disambiguation)
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Songs
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Songs
"Atlantic" (song), by Keane
"Atlantic", a song by Björk from Vessel (DVD)
"Atlantic", a song by Thrice from Vheissu
"Atlantic", a song by Sleep Token from This Place Will Become Your Tomb
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Atlantic (disambiguation)
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Other art, entertainment, and media
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Other art, entertainment, and media
Atlantic (film), a 1929 black and white British film
The Atlantic, an American magazine founded as The Atlantic Monthly in 1857
Atlantic., a 2014 Dutch film
Atlantic (2015 film), an Irish documentary film, awarded Best Irish Documentary at the 2016 Dublin International Film Festival
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Atlantic (disambiguation)
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Enterprises and organizations
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Enterprises and organizations
Atlantic (cinema), a movie theater in Warsaw, Poland
Atlantic (toy company), a defunct Italian toy manufacturer
Atlantic (supermarkets), a defunct supermarket chain in Greece
Atlantic Broadband, a cable company in Massachusetts
Atlantic City Electric, a division of Elexon supplying electricity in New Jersey
Atlantic LNG, a liquefied natural gas producing company based in Trinidad and Tobago
Atlantic Petroleum, a former oil company in the United States
Atlantic Petroleum (Faroe Islands), an oil and gas production company
Atlantic Philanthropies, a defunct private foundation
Atlantic Technological University, north-western Ireland
Atlantic University, Virginia Beach, Virginia
Groupe Atlantic, a French climate control engineering company
Real Atlantic Superstore, a Canadian supermarket chain
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Atlantic (disambiguation)
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Sports
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Sports
Atlantic Championship Series, developmental open-wheel racing series in North America
Atlantic League of Professional Baseball, an American professional baseball league
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Atlantic (disambiguation)
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Structures
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Structures
Atlantic Building or Edificio Atlantic, a condominium building in Havana, Cuba
The Atlantic (Atlanta), a skyscraper in Atlanta, Georgia, United States
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Atlantic (disambiguation)
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Transportation
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Transportation
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Atlantic (disambiguation)
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Airlines
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Airlines
Air Atlantic, a Canadian airline
Atlantic Airways, a Faroese airline company
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Atlantic (disambiguation)
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Aircraft
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Aircraft
Breguet Atlantic, a French long-range maritime patrol aircraft (1961)
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Atlantic (disambiguation)
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Motor vehicles
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Motor vehicles
Atlantic (1921 automobile), a defunct automobile company
Austin Atlantic, a British car produced by the Austin Motor Company from 1949 to 1952
Fisker Atlantic, a 2012 plug-in electric concept car
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Atlantic (disambiguation)
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Railroads and trains
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Railroads and trains
Atlantic (locomotive), name of an early steam-powered locomotive of the Baltimore and Ohio Railroad
Atlantic station (Los Angeles Metro)
Atlantic station (Staten Island Railway)
Atlantic (train), a named passenger train operated by Canadian Pacific Railway and later Via Rail
Atlantic, a type of steam locomotive with a 4-4-2 wheel arrangement (UIC classification 2B1)
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Atlantic (disambiguation)
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Ships
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Ships
, any one of several vessels by that name
Atlantic (yacht), a three-masted gaff-rigged schooner
Atlantic 85-class lifeboats, lifeboats that serve the shores of the United Kingdom and Ireland as a part of the RNLI inshore fleet
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Atlantic (disambiguation)
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Other uses
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Other uses
Atlantic (period) of palaeoclimatology
Atlantic languages (formerly West Atlantic), a language family in West Africa
Atlantic (horse), British-bred Thoroughbred racehorse of the 1870s
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Atlantic (disambiguation)
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See also
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See also
Atlantik (disambiguation)
Atlantique (disambiguation)
Atlantic Beach (disambiguation)
Atlantic Bridge (disambiguation)
Atlantic City (disambiguation)
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Atlantic (disambiguation)
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Table of Content
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Wiktionary, Places, In Canada, In the United States, Art, entertainment, and media, Companies and labels, Music, Albums, Songs, Other art, entertainment, and media, Enterprises and organizations, Sports, Structures, Transportation, Airlines, Aircraft, Motor vehicles, Railroads and trains, Ships, Other uses, See also
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Algebraic number
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Short description
|
thumb|200px|The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1.
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial . That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number is algebraic because it is a root of .
All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as and , are called transcendental numbers.
The set of algebraic (complex) numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental. Similarly, the set of algebraic (real) numbers is countably infinite and has Lebesgue measure zero as a subset of the real numbers, and in that sense almost all real numbers are transcendental.
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Algebraic number
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Examples
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Examples
All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer and a (non-zero) natural number , satisfies the above definition, because is the root of a non-zero polynomial, namely .Some of the following examples come from
Quadratic irrational numbers, irrational solutions of a quadratic polynomial with integer coefficients , , and , are algebraic numbers. If the quadratic polynomial is monic (), the roots are further qualified as quadratic integers.
Gaussian integers, complex numbers for which both and are integers, are also quadratic integers. This is because and are the two roots of the quadratic .
A constructible number can be constructed from a given unit length using a straightedge and compass. It includes all quadratic irrational roots, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots. (By designating cardinal directions for +1, −1, +, and −, complex numbers such as are considered constructible.)
Any expression formed from algebraic numbers using any finite combination of the basic arithmetic operations and extraction of th roots gives another algebraic number.
Polynomial roots that cannot be expressed in terms of the basic arithmetic operations and extraction of th roots (such as the roots of ). That happens with many but not all polynomials of degree 5 or higher.
Values of trigonometric functions of rational multiples of (except when undefined): for example, , , and satisfy . This polynomial is irreducible over the rationals and so the three cosines are conjugate algebraic numbers. Likewise, , , , and satisfy the irreducible polynomial , and so are conjugate algebraic integers. This is the equivalent of angles which, when measured in degrees, have rational numbers.
Some but not all irrational numbers are algebraic:
The numbers and are algebraic since they are roots of polynomials and , respectively.
The golden ratio is algebraic since it is a root of the polynomial .
The numbers and e are not algebraic numbers (see the Lindemann–Weierstrass theorem).Also, Liouville's theorem can be used to "produce as many examples of transcendental numbers as we please," cf.
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Algebraic number
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<span class="anchor" id="Degree of an algebraic number"></span> Properties
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Properties
thumb|Algebraic numbers on the complex plane colored by degree (bright orange/red = 1, green = 2, blue = 3, yellow = 4). The larger points come from polynomials with smaller integer coefficients.
If a polynomial with rational coefficients is multiplied through by the least common denominator, the resulting polynomial with integer coefficients has the same roots. This shows that an algebraic number can be equivalently defined as a root of a polynomial with either integer or rational coefficients.
Given an algebraic number, there is a unique monic polynomial with rational coefficients of least degree that has the number as a root. This polynomial is called its minimal polynomial. If its minimal polynomial has degree , then the algebraic number is said to be of degree . For example, all rational numbers have degree 1, and an algebraic number of degree 2 is a quadratic irrational.
The algebraic numbers are dense in the reals. This follows from the fact they contain the rational numbers, which are dense in the reals themselves.
The set of algebraic numbers is countable, and therefore its Lebesgue measure as a subset of the complex numbers is 0 (essentially, the algebraic numbers take up no space in the complex numbers). That is to say, "almost all" real and complex numbers are transcendental.
All algebraic numbers are computable and therefore definable and arithmetical.
For real numbers and , the complex number is algebraic if and only if both and are algebraic.
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Algebraic number
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Degree of simple extensions of the rationals as a criterion to algebraicity
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Degree of simple extensions of the rationals as a criterion to algebraicity
For any , the simple extension of the rationals by , denoted by , is of finite degree if and only if is an algebraic number.
The condition of finite degree means that there is a finite set in such that ; that is, every member in can be written as for some rational numbers (note that the set is fixed).
Indeed, since the are themselves members of , each can be expressed as sums of products of rational numbers and powers of , and therefore this condition is equivalent to the requirement that for some finite , .
The latter condition is equivalent to , itself a member of , being expressible as for some rationals , so or, equivalently, is a root of ; that is, an algebraic number with a minimal polynomial of degree not larger than .
It can similarly be proven that for any finite set of algebraic numbers , ... , the field extension has a finite degree.
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Algebraic number
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Field
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Field
thumb|Algebraic numbers colored by degree (blue = 4, cyan = 3, red = 2, green = 1). The unit circle is black.
The sum, difference, product, and quotient (if the denominator is nonzero) of two algebraic numbers is again algebraic:
For any two algebraic numbers , , this follows directly from the fact that the simple extension , for being either , , or (for ) , is a linear subspace of the finite-degree field extension , and therefore has a finite degree itself, from which it follows (as shown above) that is algebraic.
An alternative way of showing this is constructively, by using the resultant.
Algebraic numbers thus form a field (sometimes denoted by , but that usually denotes the adele ring).
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Algebraic number
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Algebraic closure
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Algebraic closure
Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic. That can be rephrased by saying that the field of algebraic numbers is algebraically closed. In fact, it is the smallest algebraically closed field containing the rationals and so it is called the algebraic closure of the rationals.
That the field of algebraic numbers is algebraically closed can be proven as follows: Let be a root of a polynomial with coefficients that are algebraic numbers , , ... . The field extension then has a finite degree with respect to . The simple extension then has a finite degree with respect to (since all powers of can be expressed by powers of up to ). Therefore, also has a finite degree with respect to . Since is a linear subspace of , it must also have a finite degree with respect to , so must be an algebraic number.
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Algebraic number
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Related fields
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Related fields
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Algebraic number
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Numbers defined by radicals
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Numbers defined by radicals
Any number that can be obtained from the integers using a finite number of additions, subtractions, multiplications, divisions, and taking (possibly complex) th roots where is a positive integer are algebraic. The converse, however, is not true: there are algebraic numbers that cannot be obtained in this manner. These numbers are roots of polynomials of degree 5 or higher, a result of Galois theory (see Quintic equations and the Abel–Ruffini theorem). For example, the equation:
has a unique real root, ≈ 1.1673, that cannot be expressed in terms of only radicals and arithmetic operations.
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Algebraic number
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Closed-form number
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Closed-form number
Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers. One may generalize this to "closed-form numbers", which may be defined in various ways. Most broadly, all numbers that can be defined explicitly or implicitly in terms of polynomials, exponentials, and logarithms are called "elementary numbers", and these include the algebraic numbers, plus some transcendental numbers. Most narrowly, one may consider numbers explicitly defined in terms of polynomials, exponentials, and logarithms – this does not include all algebraic numbers, but does include some simple transcendental numbers such as or ln 2.
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Algebraic number
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Algebraic integers
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Algebraic integers
thumb|Visualisation of the (countable) field of algebraic numbers in the complex plane. Colours indicate the leading integer coefficient of the polynomial the number is a root of (red = 1 i.e. the algebraic integers, green = 2, blue = 3, yellow = 4...). Points becomes smaller as the other coefficients and number of terms in the polynomial become larger. View shows integers 0,1 and 2 at bottom right, +i near top.
An algebraic integer is an algebraic number that is a root of a polynomial with integer coefficients with leading coefficient 1 (a monic polynomial). Examples of algebraic integers are and Therefore, the algebraic integers constitute a proper superset of the integers, as the latter are the roots of monic polynomials for all . In this sense, algebraic integers are to algebraic numbers what integers are to rational numbers.
The sum, difference and product of algebraic integers are again algebraic integers, which means that the algebraic integers form a ring. The name algebraic integer comes from the fact that the only rational numbers that are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers. If is a number field, its ring of integers is the subring of algebraic integers in , and is frequently denoted as . These are the prototypical examples of Dedekind domains.
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Algebraic number
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Special classes
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Special classes
Algebraic solution
Gaussian integer
Eisenstein integer
Quadratic irrational number
Fundamental unit
Root of unity
Gaussian period
Pisot–Vijayaraghavan number
Salem number
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Algebraic number
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Notes
|
Notes
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Algebraic number
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References
|
References
|
Algebraic number
|
Table of Content
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Short description, Examples, <span class="anchor" id="Degree of an algebraic number"></span> Properties, Degree of simple extensions of the rationals as a criterion to algebraicity, Field, Algebraic closure, Related fields, Numbers defined by radicals, Closed-form number, Algebraic integers, Special classes, Notes, References
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Automorphism
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Short description
|
thumb|right|400px|An automorphism of the Klein four-group shown as a mapping between two Cayley graphs, a permutation in cycle notation, and a mapping between two Cayley tables.
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.
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Automorphism
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Definition
|
Definition
In an algebraic structure such as a group, a ring, or vector space, an automorphism is simply a bijective homomorphism of an object into itself. (The definition of a homomorphism depends on the type of algebraic structure; see, for example, group homomorphism, ring homomorphism, and linear operator.)
More generally, for an object in some category, an automorphism is a morphism of the object to itself that has an inverse morphism; that is, a morphism is an automorphism if there is a morphism such that where is the identity morphism of . For algebraic structures, the two definitions are equivalent; in this case, the identity morphism is simply the identity function, and is often called the trivial automorphism.
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Automorphism
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Automorphism group
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Automorphism group
The automorphisms of an object form a group under composition of morphisms, which is called the automorphism group of . This results straightforwardly from the definition of a category.
The automorphism group of an object in a category is often denoted , or simply Aut(X) if the category is clear from context.
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Automorphism
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Examples
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Examples
In set theory, an arbitrary permutation of the elements of a set X is an automorphism. The automorphism group of X is also called the symmetric group on X.
In elementary arithmetic, the set of integers, , considered as a group under addition, has a unique nontrivial automorphism: negation. Considered as a ring, however, it has only the trivial automorphism. Generally speaking, negation is an automorphism of any abelian group, but not of a ring or field.
A group automorphism is a group isomorphism from a group to itself. Informally, it is a permutation of the group elements such that the structure remains unchanged. For every group G there is a natural group homomorphism G → Aut(G) whose image is the group Inn(G) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.
In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL(V). (The algebraic structure of all endomorphisms of V is itself an algebra over the same base field as V, whose invertible elements precisely consist of GL(V).)
A field automorphism is a bijective ring homomorphism from a field to itself.
The field of the rational numbers has no other automorphism than the identity, since an automorphism must fix the additive identity and the multiplicative identity ; the sum of a finite number of must be fixed, as well as the additive inverses of these sums (that is, the automorphism fixes all integers); finally, since every rational number is the quotient of two integers, all rational numbers must be fixed by any automorphism.
The field of the real numbers has no automorphisms other than the identity. Indeed, the rational numbers must be fixed by every automorphism, per above; an automorphism must preserve inequalities since is equivalent to and the latter property is preserved by every automorphism; finally every real number must be fixed since it is the least upper bound of a sequence of rational numbers.
The field of the complex numbers has a unique nontrivial automorphism that fixes the real numbers. It is the complex conjugation, which maps to The axiom of choice implies the existence of uncountably many automorphisms that do not fix the real numbers.
The study of automorphisms of algebraic field extensions is the starting point and the main object of Galois theory.
The automorphism group of the quaternions () as a ring are the inner automorphisms, by the Skolem–Noether theorem: maps of the form . This group is isomorphic to SO(3), the group of rotations in 3-dimensional space.
The automorphism group of the octonions () is the exceptional Lie group G2.
In graph theory an automorphism of a graph is a permutation of the nodes that preserves edges and non-edges. In particular, if two nodes are joined by an edge, so are their images under the permutation.
In geometry, an automorphism may be called a motion of the space. Specialized terminology is also used:
In metric geometry an automorphism is a self-isometry. The automorphism group is also called the isometry group.
In the category of Riemann surfaces, an automorphism is a biholomorphic map (also called a conformal map), from a surface to itself. For example, the automorphisms of the Riemann sphere are Möbius transformations.
An automorphism of a differentiable manifold M is a diffeomorphism from M to itself. The automorphism group is sometimes denoted Diff(M).
In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism (see homeomorphism group). In this example it is not sufficient for a morphism to be bijective to be an isomorphism.
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Automorphism
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History
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History
One of the earliest group automorphisms (automorphism of a group, not simply a group of automorphisms of points) was given by the Irish mathematician William Rowan Hamilton in 1856, in his icosian calculus, where he discovered an order two automorphism, writing:
so that is a new fifth root of unity, connected with the former fifth root by relations of perfect reciprocity.
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Automorphism
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Inner and outer automorphisms
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Inner and outer automorphisms
In some categories—notably groups, rings, and Lie algebras—it is possible to separate automorphisms into two types, called "inner" and "outer" automorphisms.
In the case of groups, the inner automorphisms are the conjugations by the elements of the group itself. For each element a of a group G, conjugation by a is the operation given by (or a−1ga; usage varies). One can easily check that conjugation by a is a group automorphism. The inner automorphisms form a normal subgroup of Aut(G), denoted by Inn(G); this is called Goursat's lemma.
The other automorphisms are called outer automorphisms. The quotient group is usually denoted by Out(G); the non-trivial elements are the cosets that contain the outer automorphisms.
The same definition holds in any unital ring or algebra where a is any invertible element. For Lie algebras the definition is slightly different.
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Automorphism
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See also
|
See also
Antiautomorphism
Automorphism (in Sudoku puzzles)
Characteristic subgroup
Endomorphism ring
Frobenius automorphism
Morphism
Order automorphism (in order theory).
Relation-preserving automorphism
Fractional Fourier transform
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Automorphism
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References
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References
|
Automorphism
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External links
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External links
Automorphism at Encyclopaedia of Mathematics
Category:Morphisms
Category:Abstract algebra
Category:Symmetry
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Automorphism
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Table of Content
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Short description, Definition, Automorphism group, Examples, History, Inner and outer automorphisms, See also, References, External links
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Accordion
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short description
|
thumb|upright=1.2|An accordionist
Accordions (from 19th-century German , from —"musical chord, concord of sounds")accordion, entry in Online Etymology Dictionary are a family of box-shaped musical instruments of the bellows-driven free reed aerophone type (producing sound as air flows past a reed in a frame). The essential characteristic of the accordion is to combine in one instrument a melody section, also called the diskant, usually on the right-hand keyboard, with an accompaniment or Basso continuo functionality on the left-hand. The musician normally plays the melody on buttons or keys on the right-hand side (referred to as the keyboard or sometimes the manual), and the accompaniment on bass or pre-set chord buttons on the left-hand side. A person who plays the accordion is called an accordionist.
The accordion belongs to the free-reed aerophone family. Other instruments in this family include the concertina, harmonica, and bandoneon. The concertina and bandoneon do not have the melody–accompaniment duality. The harmoneon is also related and, while having the descant vs. melody dualism, tries to make it less pronounced. The harmonium and American reed organ are in the same family, but are typically larger than an accordion and sit on a surface or the floor.
The accordion is played by compressing or expanding the bellows while pressing buttons or keys, causing pallets to open, which allow air to flow across strips of brass or steel, called reeds. These vibrate to produce sound inside the body. Valves on opposing reeds of each note are used to make the instrument's reeds sound louder without air leaking from each reed block.For the accordion's place among the families of musical instruments, see Henry Doktorski's Taxonomy of Musical Instruments (The Classical Free-Reed, Inc.) Also on this page is Diarmuid Pigott's The Free-Reed Family of Aerophones
The accordion is widely spread across the world because of the waves of migration from Europe to the Americas and other regions. In some countries (for example: Argentina, Brazil, Colombia, the Dominican Republic, Mexico, and Panama) it is used in popular music (for example: Chamamé in Argentina; gaucho, forró, and sertanejo in Brazil; vallenato in Colombia; merengue in the Dominican Republic; and norteño in Mexico), whereas in other regions (such as Europe, North America, and other countries in South America) it tends to be more used for dance-pop and folk music.
In Europe and North America, some popular music acts also make use of the instrument. Additionally, the accordion is used in cajun, zydeco, jazz, and klezmer music, and in both solo and orchestral performances of classical music. Many conservatories in Europe have classical accordion departments. The oldest name for this group of instruments is harmonika, from the Greek , meaning "harmonic, musical". Today, native versions of the name accordion are more common. These names refer to the type of accordion patented by Cyrill Demian, which concerned "automatically coupled chords on the bass side".Dyremose, Jeanette & Lars, Det levende bælgspil (2003), p. 133
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Accordion
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History
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History
thumb|left|Eight-key bisonoric diatonic accordion (c. 1830)
The accordion's basic form is believed to have been invented in Berlin, in 1822, by Christian Friedrich Ludwig Buschmann,There is not a single document to back up this belief. Christian Friedrich Ludwig Buschmann was 16 years old at that time; handwritten evidence of C.F. Buschschmann and his father exists, but without any related notice within. The first mention of an aeoline was in a text dated 1829. although one instrument was discovered in 2006 that appears to have been built earlier.This is the accordion owned by Fredrik Dillner of Sweden, which has the name F. Löhner Nürnberg engraved (stamped) on it. The instrument was given to Johannes Dillner in 1830 or earlier"Interview with Fredrik DillnerThe Owner of What May Be the World's Oldest Accordion". The Free-Reed Journal, 22 June 2006Müller, Mette & Lisbet Torp (red.) Musikkens tjenere. Forsker, Instrument, Musiker – Musikhistorisk Museums 100 års Jubilæumsskrift 1998, 297 s., indb rigt illustreret Serie: Meddelelser fra Musikhistorisk Museum og Carl Claudius Samling
The earliest history of the accordion in Russia is poorly documented. Nevertheless, according to Russian researchers, the earliest known simple accordions were made in Tula, Russia, by Ivan Sizov and Timofey Vorontsov around 1830, after they received an early accordion from Germany.Mirek, Alfred. Garmonika. Proshloe i nastoiashchee. Nauchno-istoricheskaia entsyklopedicheskaia kniga. Moscow, 1994. p. 50 By the late 1840s, the instrument was already very widespread;<ref>[http://publ.lib.ru/ARCHIVES/__Raritetnye_knigi/IRGO_Etnograficheskij_sbornik_02_1854.pdf Etnograficheskii sbornik Russkogo geograficheskogo obshchestva. Vol. 2] , Saint Petersburg, 1854. pp. 26, 162.</ref> together the factories of the two masters were producing 10,000 instruments a year. By 1866, over 50,000 instruments were being produced yearly by Tula and neighbouring villages, and by 1874 the yearly production was over 700,000.Mirek, Alfred. Iz istorii akkordeona i baiana. Moscow, 1967. pp. 43–45 By the 1860s, Novgorod, Vyatka and Saratov governorates also had significant accordion production. By the 1880s, the list included Oryol, Ryazan, Moscow, Tver, Vologda, Kostroma, Nizhny Novgorod and Simbirsk, and many of these places created their own varieties of the instrument.
The accordion is one of several European inventions of the early 19th century that use free reeds driven by a bellows. An instrument called accordion was first patented in 1829 by Cyrill Demian in Vienna.A summary and pictures of this patent can be found at www.ksanti.net/free-reed/history/demian.html (Version of 20 Okt 4 – 19 Jun 9 Using Way Back Machine to Display: The Classical Free-Reed, Inc.) Demian's instrument bore little resemblance to modern instruments. It only had a left-hand buttonboard, with the right hand simply operating the bellows. One key feature for which Demian sought the patent was the sounding of an entire chord by depressing one key. His instrument could also sound two chords with the same key, one for each bellow direction (a bisonoric action). At that time in Vienna, mouth harmonicas with Kanzellen (chambers) had already been available for many years, along with bigger instruments driven by hand bellows. The diatonic key arrangement was also already used on mouth-blown instruments. Demian's patent thus covered an accompanying instrument: an accordion played with the left hand, opposite to how contemporary chromatic hand harmonicas were played, small and light enough for travelers to take with them and used to accompany singing. The patent also described instruments with both bass and treble sections, although Demian preferred the bass-only instrument owing to its cost and weight advantages.German Text: "Mit den Dekel des Balges, läßt sich das ganze Instrument verdoppeln, so daß man dadurch die Accorde vermehrt, oder auch mit einzelne Töne spielen kann, in diesem Fall, muß ein zweyter Einsatz mit Federn, und auch eine 2te Claviatur dazu kommen, der Blasebalg bleibt in der Mitte, jede Hand dirigirt abwechselnd, entweder die Claves, oder den Balg. Durch eine obengenannte Verdoplung des Instruments oder durch Vermehrung der Accorde, würde niemand etwas verbessern, oder was neues liefern, weil nur die Bestandtheile dadurch vermehrt, das Instrument theurer und schwerer wird."
Translation of this snip: With the Cover of the bellows the instrument can be duplicated, so the number of Chords or single notes can be enlarged, or one can sound single notes, in this case, a second part with springs (free reeds) and also a second keyboard must be added, the bellows are in between these two parts, both hands push buttons and push and pull the bellows at the same time or alternatively. Through this doubling or increasing of chords within the instrument nothing new is invented or improved by someone else, because only the amount of similar parts is increased and the Instrument is heavier and more expensive.German full text
The accordion was introduced from Germany into Britain in about the year 1828.The National Cyclopaedia of Useful Knowledge, Vol I, A–Arcesilaus, London, George Woodfall and Son, 1847, p. 107. The instrument was noted in The Times in 1831 as one new to British audiencesThe Times, Thursday 9 June 1831; p. 5; Issue 14560; col A: (Review of a performance by a flautist, Mr. Sedlatzek) "At the close of the concert Mr. Sedlatzek performed on a new instrument called the Accordion or Aeolian, which, however, has little beside its novelty to recommend it." and was not favourably reviewed, but nevertheless it soon became popular.The Times, Wednesday, 26 April 1837; p. 5; Issue 16400; col C : "Great Concert-room – King's Theatre ...There was also a novelty in the shape of an instrument called "a concertina", an improvement on the accordion, which has been such a favourite musical toy for the last two or three years". It had also become popular with New Yorkers by the mid-1840s.New York Times, 19 May 1907: 'The Lay of the Last of the Old Minstrels: Interesting Reminiscences of Isaac Odell, Who Was A Burnt Cork Artist Sixty Years Ago': "While we were drawing big crowds to the Palmer House on Chambers Street Charley White was making a great hit playing an accordion in Thalia Hall on Grand Street. In those days" (i.e. mid-1840s) "accordions were the real attraction to the public".
After Demian's invention, other accordions appeared, some featuring only the right-handed keyboard for playing melodies. It took English inventor Charles Wheatstone to bring both chords and keyboard together in one squeezebox. His 1844 patent for what he called a concertina also featured the ability to easily tune the reeds from the outside with a simple tool.
thumb|The first pages in Adolf Müller's accordion book
The Austrian musician Adolf Müller described a great variety of instruments in his 1854 book . At the time, Vienna and London had a close musical relationship, with musicians often performing in both cities in the same year, so it is possible that Wheatstone was aware of this type of instrument and may have used them to put his key-arrangement ideas into practice.
Jeune's flutina resembles Wheatstone's concertina in internal construction and tone colour, but it appears to complement Demian's accordion functionally. The flutina is a one-sided bisonoric melody-only instrument whose keys are operated with the right hand while the bellows are operated with the left. When the two instruments are combined, the result is quite similar to diatonic button accordions still manufactured today.
Further innovations followed and continue to the present. Various buttonboard and keyboard systems have been developed, as well as voicings (the combination of multiple tones at different octaves), with mechanisms to switch between different voices during performance, and different methods of internal construction to improve tone, stability, and durability. Modern accordions may incorporate electronics such as condenser microphones and tone and volume controls so that the accordion can be plugged into a PA system or keyboard amplifier for live shows. Some 2010s-era accordions may incorporate MIDI sensors and circuitry, enabling the accordion to be plugged into a synth module and produce accordion sounds or other synthesized instrument sounds, such as piano or organ.
Construction
thumb|A diatonic button accordion being played
Accordions have many configurations and types. What may be easy to do with one type of accordion could be technically challenging or impossible with another, and proficiency with one layout may not translate to another.
The most obvious difference between accordions is their right-hand sides. Piano accordions use a piano-style musical keyboard; button accordions use a buttonboard. Button accordions are furthermore differentiated by their usage of a chromatic or diatonic buttonboard for the right-hand side.
Accordions may be either bisonoric, producing different pitches depending on the direction of bellows movement, or unisonoric, producing the same pitch in both directions. Piano accordions are unisonoric. Chromatic button accordions also tend to be unisonoric, while diatonic button accordions tend to be bisonoric, though notable exceptions exist.
Accordion size is not standardized, and may vary significantly from model to model. Accordions vary not only in their dimensions and weight, but also in the number of buttons or keys present in the right- and left-hand keyboards. For example, piano accordions may have as few as 8 bass buttons (two rows of four), or up to 140 (seven rows of twenty) or beyond. Accordions also vary by their available registers and by their specific tuning and voicing.
Despite these differences, all accordions share several common components.
Universal components
Bellows
thumb|265px|Bellows-driven instruments
The bellows is the most recognizable part of the instrument, and the primary means of articulation. The production of sound in an accordion is in direct proportion to the motion of the bellows by the player. In a sense, the role of the bellows can be compared to the role of moving a violin's bow on bowed strings. For a more direct analogy, the bellows can be compared to the role of breathing for a singer. The bellows is located between the right- and left-hand keyboards, and is made from pleated layers of cloth and cardboard, with added leather and metal.How To Repair Bellows Ike's Accordion It is used to create pressure and vacuum, driving air across the internal reeds and producing sound by their vibrations, applied pressure increases the volume.
The keyboard touch is not expressive and does not affect dynamics: all expression is effected through the bellows. Bellows effects include:
Volume control, including swells and fades
Repeated short, rapid changes of direction ("bellows shake"), which has been popularized by musicians such as Renato Borghetti (gaucho music) and Luiz Gonzaga, and extensively used in Forró, called resfulego in Brazil
Constant bellows motion while applying pressure at intervals
Constant bellows motion to produce clear tones with no resonance
Subtly changing the intonation to mimic the expressiveness of a singer
Using the bellows with the silent air button gives the sound of air moving ("whooshing"), which is sometimes used in contemporary compositions for this instrument
Body
thumb|left|Showroom of accordions (Petosa Accordions, Seattle, Washington)
The accordion's body consists of two boxes, commonly made of wood, joined by the bellows. These boxes house reed chambers for the right- and left-hand keyboards. Each side has grilles in order to facilitate the transmission of air in and out of the instrument and to allow the sound to project. The grille at the right-hand side is usually larger and is often shaped for decorative purposes. The right-hand keyboard is normally used for playing the melody and the left-hand one for playing the accompaniment; however, skilled players can reverse these roles and play melodies with the left hand.Guido Deiro claimed he was the first accordionist to play a solo with the left hand: Sharpshooter's March (1908) Guido Deiro, Guido Deiro's Own Story of Sharpshooters March, The Pietro Musicordion, Volume 6, Number 2 (May–June 1948)
The size and weight of an accordion varies depending on its type, layout and playing range, which can be as small as to have only one or two rows of basses and a single octave on the right-hand keyboard, to the most common 120-bass accordion and through to large and heavy 160-bass free-bass converter models.
Pallet mechanism
The accordion is an aerophone. The keyboard mechanisms of the instrument either enable the air flow, or disable it:Illustration made with reference from a similar illustration that can be found in both Det levende bælgspil (p. 9) by Jeanette & Lars Dyremose (2003), and Harmonikaens historie (p. 35a) by Bjarne Glenstrup (1972, The University of Copenhagen, Faculty of Music)
upright=3.4|thumb|center|A side view of the pallet mechanism in a piano accordion. As the key is pressed down the pallet is lifted, allowing for air to enter the tone chamber in either direction and excite the reeds; air flow direction depends on the direction of bellows movement. A similar mechanical pallet movement is used in button accordions, as well as for bass mechanisms such as the Stradella bass machine that translates a single button press into multiple pallet openings for the notes of a chord.|alt=Accordion; cross-sectional view
Variable components
The term accordion covers a wide range of instruments, with varying components. All instruments have reed ranks of some format, apart from reedless digital accordions. Not all have switches to change registers or ranks, as some have only one treble register and one bass register. The most typical accordion is the piano accordion, which is used for many musical genres. Another type of accordion is the button accordion, which is used in musical traditions including Cajun, Conjunto and Tejano music, Swiss and Slovenian-Austro-German Alpine music, and Argentinian tango music. The Helikon-style accordion has multiple flared horns projecting out of the left side to strengthen the bass tone. The word "Helikon" refers to a deep-pitched tuba.
Right-hand keyboard systems
Different systems exist for the right-hand keyboard of an accordion, which is normally used for playing the melody (while it can also play chords). Some use a button layout arranged in one way or another, while others use a piano-style keyboard. Each system has different claimed benefits by those who prefer it. They are also used to define one accordion or another as a different "type":
Chromatic button accordions and the bayan, a Russian variant, use a buttonboard where notes are arranged chromatically. Two major systems exist, referred to as the B-system and the C-system (there are also regional variants). Rarely, some chromatic button accordions have a decorative right-hand keyboard in addition to the rows of buttons, an approach used by the virtuoso accordionist Pietro Frosini.
Diatonic button accordions use a buttonboard designed around the notes of diatonic scales in a small number of keys. The keys are often arranged in one row for each key available. Chromatic scales may be available by combining notes from different rows. The adjective "diatonic" is also commonly used to describe bisonic or bisonoric accordions—that is, instruments whose right-hand (and in some instances even bass) keys each sound two different notes depending on the direction of the bellows (for instance, producing major triad sequences while closing the bellows and dominant seventh or 7–9 while opening). Such is the case, for instance, with the Argentinian bandoneon, the Slovenian-Austro-German Steirische Harmonika, the Czech Heligonka Harmonika, the Italian organetto, the Swiss Schwyzerörgeli and the Anglo concertina.
Piano accordions use a musical keyboard similar to a piano, at right angles to the cabinet, the tops of the keys inward toward the bellows.
The rarely used bass accordion has only a right-hand keyboard, with ranks of 8', 16', and 32' reeds, with the lowest note being the deepest pitch on a pipe organ pedal keyboard (pedal C). It is intended for performing basslines in accordion orchestras.
The rarely used piccolo accordion also has only a right-hand keyboard.
6-plus-6 accordions use a buttonboard with three rows of buttons in a "uniform" or "whole-tone" arrangement, generally known as a Jankó keyboard. The chromatic scale consists of two rows. The third row is a repetition of the first row, so there is the same fingering in all twelve scales. These accordions are produced only in special editions e.g. the logicordion produced by Harmona.
Left-hand keyboard systems
thumb|right|300px|Typical 120-button Stradella bass system. This is the left-hand keyboard system found on most unisonoric accordions today.
Different systems are also in use for the left-hand keyboard, which is normally used for playing the accompaniment. These usually use distinct bass buttons and often have buttons with concavities or studs to help the player navigate the layout despite not being able to see the buttons while playing. There are three general categories:
thumb|right|200px|The bass buttons trigger a complex mechanism of wires, rods, and levers, which is normally hidden inside the instrument.
The Stradella bass system, also called standard bass, is arranged in a circle of fifths and uses single buttons for bass notes and additional rows of single buttons for preset major, minor, dominant seventh, and diminished chords. The dominant seventh and diminished chords are three-note chord voicings that omit the fifths of the chords.
The Belgian bass system is a variation used in Belgian chromatic accordions. It is also arranged in a circle of fifths but in reverse order. This system has three rows of basses, three rows of chord buttons allowing easier fingering for playing melodies, combined chords, better use of fingers one and five, and more space between the buttons. This system was rarely used outside of its native Belgium.
Various free-bass systems for greater access to playing melodies and complex basslines on the left-hand keyboard and to forming one's own chords note-by-note. These are often chosen for playing jazz and classical music. Some models can convert between free-bass and Stradella bass; this is called converter bass. The free-bass left hand notes are arranged chromatically in three rows with one additional duplicate row of buttons.
Luttbeg double-keyboard piano accordions have a piano keyboard layout on both the treble and bass sides. This allows pianists, most notably Duke Ellington, to double up on the accordion without difficulty. The Bercandeon is an improved version of that instrument, also making it a "keyboard bandoneon".
In 2021, a patent was published by Valerio Chiovarelli for a new bass system called the "Chiovarelli Jazz System". This system is a variation of the Stradella bass system where, instead of triads, the chordal buttons of this system produce bichords (chords with only 2 pitches instead of 3). The "Chiovarellia Jazz System" (or "CJS" for short) prioritizes the effectiveness of left hand accordion in jazz music, hence the name of the system, but according to the inventor, these chords can be useful when playing many varieties of music.
Reed ranks and switches
upright=0.75|thumb|right|Accordion reed ranks with closeup of reeds
Inside the accordion are the reeds that generate the instrument tones. These are organized in different sounding banks, which can be further combined into registers producing differing timbres. All but the smaller accordions are equipped with switches that control which combination of reed banks operate, organized from high to low registers. Each register stop produces a separate sound timbre, many of which also differ in octaves or in how different octaves are combined. See the accordion reed ranks and switches article for further explanation and audio samples. All but the smaller accordions usually have treble switches. The larger and more expensive accordions often also have bass switches to give options for the reed bank on the bass side.
Classification of chromatic and piano type accordions
In describing or pricing an accordion, the first factor is size, expressed in number of keys on either side. For a piano type, this could for one example be 37/96, meaning 37 treble keys (three octaves plus one note) on the treble side and 96 bass keys. A second aspect of size is the width of the white keys, which means that even accordions with the same number of keys have keyboards of different lengths, ranging from for a child's accordion to for an adult-sized instrument. After size, the price and weight of an accordion is largely dependent on the number of reed ranks on either side, either on a cassotto or not, and to a lesser degree on the number of combinations available through register switches. The next, but important, factor is the quality of the reeds, the highest grade called "a mano" (meaning "hand-made"), the next "tipo a mano" ("like hand-made"), lower grades including "export" and several more.
Price is also affected by the use of costly woods, luxury decorations, and features such as a palm switch, grille mute, and so on. Some accordion makers sell a range of different models, from a less-expensive base model to a more costly luxury model. Typically, the register switches are described as Reeds: 5 + 3, meaning five reeds on the treble side and three on the bass, and Registers: 13 + M, 7, meaning 13 register buttons on the treble side plus a special "master" that activates all ranks, like the "tutti" or "full organ" switch on an organ, and seven register switches on the bass side. Another factor affecting the price is the presence of electronics, such as condenser microphones, volume and tone controls, or MIDI sensors and connections.
thumb|Accordion player on a street in the historic centre of Quito, Ecuador
Straps
The larger piano and chromatic button accordions are usually heavier than other smaller squeezeboxes, and are equipped with two shoulder straps to make it easier to balance the weight and increase bellows control while sitting, and avoid dropping the instrument while standing. Other accordions, such as the diatonic button accordion, have only a single shoulder strap and a right hand thumb strap. All accordions have a (mostly adjustable) leather strap on the left-hand side to keep the player's hand in position while drawing the bellows. There are also straps above and below the bellows to keep it securely closed when the instrument is not being played.
Electronic and digital
thumb|right|200px|Rainer von Vielen playing a Roland digital V-Accordion. The bank of electronic switches can change the accordion's sound, tone and volume.
In the 2010s, a range of electronic and digital accordions were introduced. They have an electronic sound module which creates the accordion sound, and most use MIDI systems to encode the keypresses and transmit them to the sound module. A digital accordion can have hundreds of sounds, which can include different types of accordions and even non-accordion sounds, such as pipe organ, piano, or guitar. Sensors are used on the buttons and keys, such as magnetic reed switches. Sensors are also used on the bellows to transmit the pushing and pulling of the bellows to the sound module. Digital accordions may have features not found in acoustic instruments, such as a piano-style sustain pedal, a modulation control for changing keys, and a portamento effect.
As an electronic instrument, these types of accordions are plugged into a PA system or keyboard amplifier to produce sound. Some digital accordions have a small internal speaker and amplifier, so they can be used without a PA system or keyboard amplifier, at least for practicing and small venues like coffeehouses. One benefit of electronic accordions is that they can be practiced with headphones, making them inaudible to other people nearby. On a digital accordion, the volume of the right-hand keyboard and the left-hand buttons can be independently adjusted.
Acoustic-digital hybrid accordions also exist. They are acoustic accordions (with reeds, bellows, and so on), but they also contain sensors, electronics, and MIDI connections, which provides a wider range of sound options. An acoustic-digital hybrid may be manufactured in this form, or it may be an acoustic accordion which has had aftermarket electronics sensors and connections added. Several companies sell aftermarket electronics kits, but they are typically installed by professional accordion technicians, because of the complex and delicate nature of the internal parts of an accordion.
Unusual accordions
Various hybrid accordions have been created between instruments of different buttonboards and actions. Many remain curiosities – only a few have remained in use:
The Schrammel accordion, used in Viennese chamber music and klezmer, which has the treble buttonboard of a chromatic button accordion and a bisonoric bass buttonboard, similar to an expanded diatonic button accordion
The Steirische Harmonika, a type of bisonoric diatonic button accordion particular to the Alpine folk music of Slovenia, Austria, the Czech Republic, the German state of Bavaria, and the Italian South Tyrol
The schwyzerörgeli or Swiss organ, which usually has a three-row diatonic treble and 18 unisonoric bass buttons in a bass/chord arrangement – a subset of the Stradella system in reverse order like the Belgian bass – that travel parallel to the bellows motion
The trikitixa of the Basque people, which has a two-row diatonic, bisonoric treble and a 12-button diatonic unisonoric bass
The British chromatic accordion, the favoured diatonic accordion in Scotland. While the right hand is bisonoric, the left hand follows the Stradella system. The elite form of this instrument is generally considered the German manufactured Shand Morino, produced by Hohner with the input of Sir Jimmy Shand
Pedal harmony, a type of accordion used sometimes in Polish folk music, which has a pair of pump organ-like bellows attached.
The Finnish composer and accordionist Veli Kujala developed a quarter tone accordion together with the Italian accordion manufacturer Pigini in 2005, and has written works for it. It deploys the same system as the concert accordion, with a scale of five octaves, each divided into 24 quarter tones. Other notable composers who have written concertos for the quarter tone accordion include Jukka Tiensuu and Sampo Haapamäki.
Manufacturing process
The most expensive accordions are typically fully hand-made, particularly the reeds; completely hand-made reeds have a better tonal quality than even the best automatically manufactured ones. Some accordions have been modified by individuals striving to bring a more pure sound out of low-end instruments, such as the ones improved by Yutaka Usui,Yutaka Usuai, Japanese-born accordion craftsman. a Japanese craftsman.
The manufacture of an accordion is only a partly automated process. In a sense, all accordions are handmade, since there is always some hand assembly of the small parts required. The general process involves making the individual parts, assembling the subsections, assembling the entire instrument, and final decorating and packaging.
Notable centres of production are the Italian cities of Stradella and Castelfidardo, with many small and medium size manufacturers especially at the latter. Castelfidardo honours the memory of Paolo Soprani who was one of the first large-scale producers. has built accordions in the French town of Tulle since 1919, and the company is now the last complete-process manufacturer of accordions in France. German companies such as Hohner and Weltmeister made large numbers of accordions, but production diminished by the end of the 20th century. Hohner still manufactures its top-end models in Germany, and Weltmeister instruments are still handmade by HARMONA Akkordeon GmbH in Klingenthal.
Use in various music genres
thumb|A street performer playing the accordion
The accordion has traditionally been used to perform folk or ethnic music, popular music, and transcriptions from the operatic and light-classical music repertoire.Henry Doktorski, CD booklet notes for "Guido Deiro: Complete Recorded Works, Vol. 1", Archeophone Records (2007) It was also used by the Kikuyu tribe in Kenya and is the main instrument in the traditional Mwomboko dance. Today the instrument is sometimes heard in contemporary pop styles, such as rock and pop-rock,Sometimes in modern pop music the accordion is not actually played, but its sound is heard by use of a MIDI instrument and sampled sound module. and occasionally even in serious classical music concerts, as well as advertisements.
Use in traditional music
right|thumb|A folk accordionist, 2009
The accordion's popularity spread rapidly: it has mostly been associated with the common people, and was propagated by Europeans who emigrated around the world. The accordion in both button and piano forms became a favorite of folk musiciansChristoph Wagner, "A Brief History of How the Accordion Changed the World", CD booklet notes for Planet Squeezebox, performed by various artists, (Roslyn, New York: Ellipsis Arts, 1995), 6 and has been integrated into traditional music styles all over the world: see the list of music styles that incorporate the accordion.
Use in jazz
Notable jazz accordionists
Early jazz accordionists include Charles Melrose, who recorded Wailing Blues/Barrel House Stomp (1930, Voc. 1503) with the Cellar Boys; Buster Moten, who played second piano and accordion in the Bennie Moten orchestra; and Jack Cornell, who did recordings with Irving Mills. Later jazz accordionists from the United States include Steve Bach, Milton DeLugg, Orlando DiGirolamo, Angelo Di Pippo,The Biographical Encyclopedia of Jazz. Feather, Leonard. Gitler, Ira Eds. Oxford University Press. 2007 ebook ISBN 9780195320008 Angelo Di Pippo Biography on Google BooksAngelo Di Pippo Biography on allmusic.comAngelo Di Pippo Biography on imbdAngelo Di Pippo Biography on angelodipippo.com Dominic Frontiere, Guy Klucevsek, Yuri Lemeshev, Frank Marocco, Dr. William Schimmel, John Serry Sr.,Discography of American Historical Recordings: University of California Santa Barbara – Audio recordings online of John Serry and the Shep Fields Rippling Rhythm Jazz Orchestra 1937–1938 Lee Tomboulian, and Art Van Damme. French jazz accordionists include Richard Galliano, Bernard Lubat, and Vincent Peirani. Norwegian jazz accordionists include Asmund Bjørken, Stian Carstensen, Gabriel Fliflet, Frode Haltli, and Eivin One Pedersen.
Left hand techniques
The constraints of the Stradella bass system, limiting the left hand to preset chord buttons, is a barrier to some jazz chord conventions. Jazz accordionists expand the range of chord possibilities by using more than one chord button simultaneously, or by using combinations of a chord button and a bass note other than the typical root of the chord. An example of the former technique is used to play a minor seventh chord. To play an Am7(add9) chord, the Am and Em preset buttons are pressed simultaneously, along with an A bassnote. An example of the latter technique is used to play the half-diminished chord. To play an Eø7, a Gm preset button is pressed along with an E bassnote.
For the left hand, the free-bass system is used in jazz as a means of creating complex chord voicings. Jazz harmony that would otherwise be difficult to replicate with the Stradella bass system, such as tritone substitutions, become more accessible using a free-bass accordion.Jacobson, M. [Squeeze This – A Cultural History of the Accordion in America]. University of Illinois Press.
Use in popular music
thumb|John Linnell of They Might Be Giants playing a Main Squeeze 911
The accordion appeared in popular music from the 1900s to the 1960s. This half-century is often called the "golden age of the accordion". Five players, Pietro Frosini, the two brothers Count Guido Deiro and Pietro Deiro and Slovenian brothers Vilko Ovsenik and Slavko Avsenik, Charles Magnante were major influences at this time.
Most vaudeville theaters closed during the Great Depression, but accordionists during the 1930s–1950s taught and performed for radio. Included among this group was the concert virtuoso John Serry, Sr.The Los Angeles Examiner 9 October 1938, p. 1Jacobson, Marion (2012). Squeeze This: A Cultural History of the Accordion in America. University of Illinois Press, Chicago, p. 61. During the 1950s through the 1980s the accordion received significant exposure on television with performances by Myron Floren on The Lawrence Welk Show.Myron Floren and Randee Floren, Accordion Man, with a foreword by Lawrence Welk (The Stephen Greene Press, Brattleboro, Vermont: 1981) In the late 1950s and early 1960s, the accordion declined in popularity because of the rise of rock and roll. The first accordionist to appear and perform at the Newport Jazz Festival was Angelo DiPippo. He can be seen playing his accordion in the motion picture The Godfather. He also composed and performed with his accordion on part of the soundtrack of Woody Allen's movie To Rome With Love. He was featured twice on The Tonight Show with Johnny Carson.
Richard Galliano is an internationally known accordionist whose repertoire covers jazz, tango nuevo, Latin, and classical. Some popular bands use the instrument to create distinctive sounds. A notable example is Grammy Award–winning parodist "Weird Al" Yankovic, who plays the accordion on many of his musical tracks, particularly his polkas. Yankovic was trained in the accordion as a child.
The accordion has also been used in the rock genre, most notably by John Linnell of They Might Be Giants, featuring more prominently in the band's earlier works. The instrument is still frequently used during live performances, and continues to make appearances in their studio albums. Accordion is also used in the music of the Dropkick Murphys and Gogol Bordello. Tom Waits used the accordion extensively (often played by Dr. William Schimmel) on his album Rain Dogs and Franks Wild Years. The folk metal subgenre also employs accordionists, but they are otherwise generally rare in other genres. Full-time accordionists in folk metal seem even rarer, but they are still utilized for studio work, as flexible keyboardists are usually more accessible for live performances. The Finnish symphonic folk-metal band Turisas used to have a full-time accordionist, employing classical and polka sensibilities alongside a violinist. One of their accordionists, Netta Skog, is now a member of Ensiferum, another folk-metal band. Another Finnish metal band, Korpiklaani, invokes a type of Finnish polka called humppa, and also has a full-time accordionist. Sarah Kiener, the former hurdy-gurdy player for the Swiss melodic-death-folk metal band Eluveitie, played a Helvetic accordion known as a zugerörgeli.
Use in classical music
Although best known as a folk instrument, it has grown in popularity among classical composers. The earliest surviving concert piece is , written in 1836 by Louise Reisner of Paris. Other composers, including the Russian Pyotr Ilyich Tchaikovsky, the Italian Umberto Giordano, and the American Charles Ives, wrote works for the diatonic button accordion.
thumb|Finnish accordionist Esa Pakarinen (Feeliks Esaias Pakarinen, 1911–1989)
The first composer to write specifically for the chromatic accordion was Paul Hindemith.Accordion Composers in German Accordion Online In 1922, the Austrian Alban Berg included an accordion in Wozzeck, Op. 7. In 1937, the first accordion concerto was composed in Russia. Other notable composers have written for the accordion during the first half of the 20th century.Henry Doktorski, "The Classical Squeezebox: A Short History of the Accordion and Other Free-Reed Instruments in Classical Music", The Classical Free-Reed, Inc. (1997) Included among this group was the Italian-American John Serry Sr., whose Concerto for Free Bass Accordion was completed in 1964.Library of Congress Copyright Office, "Concerto in C Major for Bassetti Accordion", Composer: John Serry, 4 June 1968, Copyright # EP247602.Eastman School of Music - University of Rochester - Sibley Music Library: John J. Serry Sr. Collection score "Concerto in C Major (1967) for Free Bass Accordion", Folder 15 & 16 p. 10 archived at the University of Rochester Eastman School of Music Sibley Music Library Special collections on esm.rochester.eduAccordion World, Bedford Hills, NY, 1968. In addition, the American accordionist Robert Davine composed his Divertimento for Flute, Clarinet, Bassoon and Accordion as a work for chamber orchestra. American composer William P. Perry featured the accordion in his orchestral suite Six Title Themes in Search of a Movie (2008). The experimental composer Howard Skempton began his musical career as an accordionist, and has written numerous solo works for it. In his work Drang (1999), British composer John Palmer pushed the expressive possibilities of the accordion/bayan. Luciano Berio wrote Sequenza XIII (1995) for accordionist Teodoro Anzellotti. Accordionists like Mogens Ellegaard, Joseph Macerollo, Nick Ariondo, Friedrich Lips, Hugo Noth, Dr. William Schimmel (also a composer), Stefan Hussong, Teodoro Anzellotti, and Geir Draugsvoll, encouraged composers to write new music for the accordion (solo and chamber music) and also started playing baroque music on the free bass accordion.
French composer Henri Dutilleux used an accordion in both his late song cycles Correspondences (2003) and Le Temps L'Horloge (2009). Russian-born composer Sofia Gubaidulina has composed solos, concertos, and chamber works for accordion. Astor Piazzolla's concert tangos are performed widely. Piazzolla performed on the bandoneon, but his works are also performed on or accordion. Dr. William schimmel and "The Tango Project" recorded a number of hit recordings and appeared in the movie Scent of a Woman with Al Pacino which earned Pacino an Oscar. Their recordings were used in many films.
Australia
The earliest mention of the novel accordion instrument in Australian music occurs in the 1830s.
The accordion initially competed against cheaper and more convenient reed instruments such as mouth organ, concertina and melodeon.
Frank Fracchia was an Australian accordion composer and copies of his works "My dear, can you come out tonight" and "Dancing with you" are preserved in Australian libraries.
Other Australian composers who arranged music for accordion include Reginald Stoneham.
The popularity of the accordion peaked in the late 1930s and continued until the 1950s.
The accordion was particularly favoured by buskers.
Bosnia and Herzegovina
The accordion is a traditional instrument in Bosnia and Herzegovina. It is the dominant instrument used in sevdalinka, a traditional genre of folk music from Bosnia and Herzegovina.
Brazil
thumb|right|150px|Brazilian accordionist Dominguinhos (José Domingos de Morais, 1941–2013)
The accordion was brought to Brazil by settlers and immigrants from Europe, especially from Italy and Germany, who mainly settled in the south (Rio Grande do Sul, Santa Catarina and Paraná). The first instrument brought was a "Concertina" (a 120 button chromatic accordion). The instrument was popular in the 1950s, and it was common to find several accordions in the same house. There are many different configurations and tunes which were adapted from the cultures that came from Europe.
Accordion is the official symbol instrument of the Rio Grande do Sul state, where was voted by unanimity in the deputy chamber.
During the boom of accordions there were around 65 factories in Brazil, where most of them (52) in the south, in Rio Grande do Sul state, with only 7 outside the south. One of the most famous and genuinely Brazilian brands was Accordeões Todeschini from Bento Gonçalves-RS, closed in 1973. The Todeschini accordion is very appreciated today and survives with very few maintainers. The most notable musicians of button accordions are Renato Borghetti, Adelar Bertussi, Albino Manique and Edson Dutra.
Compared to many other countries, the instrument is very popular in mainstream pop music. In some parts of the country, such as the northeast it is the most popular melodic instrument. As opposed to most European folk accordions, a very dry tuning is usually used in Brazil. Outside the south, the accordion (predominantly the piano accordion) is used in almost all styles of Forró (in particular in the subgenres of Xote and Baião) as the principal instrument, Luiz Gonzaga (the "King of the Baião") and Dominguinhos being among the notable musicians in this style from the northeast. In this musical style the typical combination is a trio of accordion, triangle and zabumba (a type of drum).
This style has gained popularity recently, in particular among the student population of the southeast of the country (in the Forró Universitário genre, with important exponents today being Falamansa, and trios such as Trio Dona Zefa, Trio Virgulino and Trio Alvorada). Moreover, the accordion is the principal instrument in Junina music (music of the São João Festival), with Mario Zan having been a very important exponent of this music. It is an important instrument in Sertanejo (and Caipira) music, which originated in the midwest and southeast of Brazil, and subsequently has gained popularity throughout the country.
China
The number of accordionists in China exceeds every other country in the world, and possibly every country combined. Introduced in 1926, the accordion has risen to popularity in China throughout the years, thanks to Russian teachers and its being a popular instrument in the People's Liberation Army, and remains popular.
In the late 20th century, the development of high performance standards for the accordion within China's halls of academe was also influenced by several American virtuosos including Robert Davine, who was invited by the Ministry of Culture of the People's Republic to present Master Classes and to broaden its national program of music for the accordion in 1984.
Colombia
The accordion is also a traditional instrument in Colombia, commonly associated with the vallenato and cumbia genres. The accordion has been used by tropipop musicians such as Carlos Vives, Andrés Cabas, Fonseca (singer) and Bacilos, as well as rock musicians such as Juanes and pop musicians as Shakira. Vallenato, who emerged in the early twentieth century in Valledupar, and have come to symbolize the folk music of Colombia.
Every year in April, Colombia holds one of the most important musical festivals in the country: the Vallenato Legend Festival. The festival holds contests for best accordion player. Once every decade, the "King of Kings" accordion competition takes place, where winners of the previous festivals compete for the highest possible award for a vallenato accordion player: the Pilonera Mayor prize.Smithsonian Channel, "The Accordion Kings", 15 August 2010. This is the world's largest competitive accordion festival.
Czech Republic
thumb|At U Flekú, Prague
Accordion is often played at traditional Czech pubs, such as U Flekú, Prague.
Mexico
thumb|right|200px|A Norteño band, including an accordion
Norteño heavily relies on the accordion; it is a genre related to polka. Ramón Ayala, known in Mexico as the "King of the Accordion", is a norteño musician. Cumbia, which features the accordion, is also popular with musicians such as Celso Piña, creating a more contemporary style. U.S.-born Mexican musician Julieta Venegas incorporates the sound of the instrument into rock, pop and folk. She was influenced by her fellow Chicanos Los Lobos who also use the music of the accordion.
North Korea
According to Barbara Demick in Nothing to Envy, the accordion is known as "the people's instrument" and all North Korean teachers were expected to learn the accordion.
United States
Accordions are played in Tejano music, Cajun and Creole music, zydeco, klezmer, and polka.
During the post-World War II era from the 1940s to the 1960s, accordions were widely used in the United States for performances of traditional Western classical music within the configuration of large free-reed symphonic orchestras both in live performances on the concert hall stage and in phonograph recordings.Squeese This! A Cultural History of the Accordion in America. Jacobson, Marion. University of Illinois Press. 2012. p. 78-80 ebook ISBN 9780252093852Accordion Orchestra Joe Biviano on Google Books on Google BooksMusic Trades: "Accordion Orchestra Featured on New Coral 12" Record" Vol. 109, 1961 p. 84 John Serry on Google Books"Pietro Deiro Presents The Accordion Orchestra - Under Direction of Joe Biviano" Coral Records (CRL-57323, 1960) See album cover for performers credits including John Serry, Eugene Ettore, Carmen Carrozza and Angelo Di Pippo. Pietro Deiro on Discogs.comPietro The Billboard- Reviews and Ratings of New albums: "Pietro Deiro Presents The Accordion Orchestra" (Coral, CRL-57323), 27 June 1960 p. 33 Pietro Deiro Presents the Accordion Orchestra on Google BooksThe Coral Album Discography. Edwards, David. Callahan, Mike. Eyrles, Patrice. Watts, Randy. Neely, Timothy. April 27, 2014. CRL-57323 "Pietro Deiro Presents the Accordion Orchestra" (1960) on bsnpubs.com Included among the leading accordion orchestras were: The New York Accordion Symphony in New York City, The Springfield Accordion Orchestra in Massachusetts, The Houston Accordion Symphony in Houston, Texas and The Philadelphia Accordion Orchestra in Philadelphia, Pennsylvania.Squeeze This! A Cultural History of the Accordion in America. Jacobson, Marion. University of Illinois Press. 2012, pp. 78-79 ebook ISBN 978-0-252-09385-2 Accordion Orchestra on Google Books Prominent orchestra members included: Joe Biviano (President of the American Accordionists Association)"American Accordionists Association: Joe Biviano and Charles Magnante - A Lifetime Commitment to the American Accordionists Association". Joe Biviano BBiography on ameraccord.com"Squeeze This! A Cultural History of the Accordion in the United States". Jacobson, Marion. University of Illinois Press 2012 p. 93 ISBN 9780252093852 Joe Biviano on google books Carmen Carrozza,"Squeeze This! A Cultural History of the Accordion in the United States". Jacobson, Marion. University of Illinois Press 2012 p. 85 ISBN 9780252093852 Carmen Carrozza on google books"Accordion World" Gerstner Publications 1957 Vol. 22 p. 55 Pietro Deiro and Carmen Carrozza on Google Books Orlando Di Girolamo (President of the American Symphony Society),"Music Trades", Music Trades Corporation, "Accordion Orchestra Featured On New Coral 12" Record" 1961 Vol. 109, p. 84 Orlando Girolamo on Google books( Tony Mecca (who collaborated with Leonard Bernstein),"Accordion Journal" Vol 12-13 p. 21 Tony Mecca on Google Books"The Accordion in all its Guises". Miller, Malcom. Harwood Academic Publishers 2010 p. 88 Tony Mecca on google books Angelo Di Pippo (jazz accordionist and arranger for Robert Merrill),"The Biographical Encyclopedia of Jazz" Feather, Leonard. Gitler, Ira. Ed. Oxford University Prress 2007 p. 181 ISBN 9780195074185 Angelo Di Pippo Biography on Google Books John Serry Sr."Music Trades", Music Trades Corporation, "Accordion Orchestra Featured On New Coral 12" Record" 1961 Vol. 109, p. 84 John Serry on Google booksInternational Musician – "Accordion Instrument Played with A Smile", Hope Stoddard, May 1951, pp. 10-11 Contributing authors: Charles Nunzio and Sergei Matsusewitch – Photographs of John Serry, Joe Biviano and Anthony Mecca in the article published by the American Federation of Musicians' magazine "International Musician" on worldradiohistory.com and Alfonso Veltri (Director of the National Conservatory of Music)."Accordion Journal - Pietro Deiro Presents the Accordion Orchestra - under the Direction of Joe Biviano" Vol 12-13 p. 21 Alfonso Veltri on Google Books By the 1960s recordings by such orchestras were even praised for their high level of musicality in The Billboard'' magazine.Pietro The Billboard- Reviews and Ratings of New albums: "Pietro Deiro Presents The Accordion Orchestra" (Coral, CRL-57323), 27 June 1960 p. 33 "Pietro Deiro Presents the Accordion Orchestra" album review on Google BooksAmerican Music - "Searching for the Rockordion: The Changing Image of the Accordion in America". Jacobson, Marion S. University of Illinois Press Vol. 25, No. 2 (Sommer 2007) pp.216-247, See pp. 220-225 on https://www.jstor.org/stable/40071656
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Accordion
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Other audio samples
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Other audio samples
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Accordion
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See also
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See also
List of accordionists
Steirische Harmonika
Confédération internationale des accordéonistes
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Accordion
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Notes
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Notes
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Accordion
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References
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References
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Accordion
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External links
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External links
Category:Folk music instruments
Category:Articles containing video clips
Category:German inventions
Category:19th-century inventions
Category:Symbols of Rio Grande do Sul
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Accordion
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Table of Content
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short description, History, Other audio samples, See also, Notes, References, External links
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Artificial intelligence
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Short description
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Artificial intelligence (AI) refers to the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. Such machines may be called AIs.
High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Alexa); autonomous vehicles (e.g., Waymo); generative and creative tools (e.g., ChatGPT and AI art); and superhuman play and analysis in strategy games (e.g., chess and Go). However, many AI applications are not perceived as AI: "A lot of cutting edge AI has filtered into general applications, often without being called AI because once something becomes useful enough and common enough it's not labeled AI anymore."AI set to exceed human brain power CNN.com (July 26, 2006)
Various subfields of AI research are centered around particular goals and the use of particular tools. The traditional goals of AI research include learning, reasoning, knowledge representation, planning, natural language processing, perception, and support for robotics. General intelligence—the ability to complete any task performed by a human on an at least equal level—is among the field's long-term goals. To reach these goals, AI researchers have adapted and integrated a wide range of techniques, including search and mathematical optimization, formal logic, artificial neural networks, and methods based on statistics, operations research, and economics. AI also draws upon psychology, linguistics, philosophy, neuroscience, and other fields..
Artificial intelligence was founded as an academic discipline in 1956, and the field went through multiple cycles of optimism throughout its history, followed by periods of disappointment and loss of funding, known as AI winters. Funding and interest vastly increased after 2012 when deep learning outperformed previous AI techniques. This growth accelerated further after 2017 with the transformer architecture, and by the early 2020s many billions of dollars were being invested in AI and the field experienced rapid ongoing progress in what has become known as the AI boom. The emergence of advanced generative AI in the midst of the AI boom and its ability to create and modify content exposed several unintended consequences and harms in the present and raised concerns about the risks of AI and its long-term effects in the future, prompting discussions about regulatory policies to ensure the safety and benefits of the technology.
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Artificial intelligence
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Goals
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Goals
The general problem of simulating (or creating) intelligence has been broken into subproblems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below have received the most attention and cover the scope of AI research.
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Artificial intelligence
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Reasoning and problem-solving
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Reasoning and problem-solving
Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions.Problem-solving, puzzle solving, game playing, and deduction: , (constraint satisfaction), , , By the late 1980s and 1990s, methods were developed for dealing with uncertain or incomplete information, employing concepts from probability and economics.Uncertain reasoning: , , ,
Many of these algorithms are insufficient for solving large reasoning problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow.Intractability and efficiency and the combinatorial explosion: Even humans rarely use the step-by-step deduction that early AI research could model. They solve most of their problems using fast, intuitive judgments.Psychological evidence of the prevalence of sub-symbolic reasoning and knowledge: , , , Accurate and efficient reasoning is an unsolved problem.
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Artificial intelligence
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Knowledge representation
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Knowledge representation
thumb|upright=1.2|An ontology represents knowledge as a set of concepts within a domain and the relationships between those concepts.
Knowledge representation and knowledge engineeringKnowledge representation and knowledge engineering: , , , allow AI programs to answer questions intelligently and make deductions about real-world facts. Formal knowledge representations are used in content-based indexing and retrieval, scene interpretation, clinical decision support, knowledge discovery (mining "interesting" and actionable inferences from large databases), and other areas.
A knowledge base is a body of knowledge represented in a form that can be used by a program. An ontology is the set of objects, relations, concepts, and properties used by a particular domain of knowledge. Knowledge bases need to represent things such as objects, properties, categories, and relations between objects;Representing categories and relations: Semantic networks, description logics, inheritance (including frames, and scripts): , , , situations, events, states, and time;Representing events and time:Situation calculus, event calculus, fluent calculus (including solving the frame problem): , , causes and effects;Causal calculus: knowledge about knowledge (what we know about what other people know);Representing knowledge about knowledge: Belief calculus, modal logics: , default reasoning (things that humans assume are true until they are told differently and will remain true even when other facts are changing);Default reasoning, Frame problem, default logic, non-monotonic logics, circumscription, closed world assumption, abduction: , , ,
(Poole et al. places abduction under "default reasoning". Luger et al. places this under "uncertain reasoning"). and many other aspects and domains of knowledge.
Among the most difficult problems in knowledge representation are the breadth of commonsense knowledge (the set of atomic facts that the average person knows is enormous);Breadth of commonsense knowledge: , , , (qualification problem) and the sub-symbolic form of most commonsense knowledge (much of what people know is not represented as "facts" or "statements" that they could express verbally). There is also the difficulty of knowledge acquisition, the problem of obtaining knowledge for AI applications.
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Artificial intelligence
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Planning and decision-making
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Planning and decision-making
An "agent" is anything that perceives and takes actions in the world. A rational agent has goals or preferences and takes actions to make them happen. In automated planning, the agent has a specific goal.Automated planning: . In automated decision-making, the agent has preferences—there are some situations it would prefer to be in, and some situations it is trying to avoid. The decision-making agent assigns a number to each situation (called the "utility") that measures how much the agent prefers it. For each possible action, it can calculate the "expected utility": the utility of all possible outcomes of the action, weighted by the probability that the outcome will occur. It can then choose the action with the maximum expected utility.Automated decision making, Decision theory: .
In classical planning, the agent knows exactly what the effect of any action will be.Classical planning: . In most real-world problems, however, the agent may not be certain about the situation they are in (it is "unknown" or "unobservable") and it may not know for certain what will happen after each possible action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked.Sensorless or "conformant" planning, contingent planning, replanning (a.k.a online planning): .
In some problems, the agent's preferences may be uncertain, especially if there are other agents or humans involved. These can be learned (e.g., with inverse reinforcement learning), or the agent can seek information to improve its preferences.Uncertain preferences:
Inverse reinforcement learning: Information value theory can be used to weigh the value of exploratory or experimental actions.Information value theory: . The space of possible future actions and situations is typically intractably large, so the agents must take actions and evaluate situations while being uncertain of what the outcome will be.
A Markov decision process has a transition model that describes the probability that a particular action will change the state in a particular way and a reward function that supplies the utility of each state and the cost of each action. A policy associates a decision with each possible state. The policy could be calculated (e.g., by iteration), be heuristic, or it can be learned.Markov decision process: .
Game theory describes the rational behavior of multiple interacting agents and is used in AI programs that make decisions that involve other agents.Game theory and multi-agent decision theory: .
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Artificial intelligence
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Learning
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Learning
Machine learning is the study of programs that can improve their performance on a given task automatically.Learning: , , , It has been a part of AI from the beginning.
right|upright=1.4|frameless
There are several kinds of machine learning. Unsupervised learning analyzes a stream of data and finds patterns and makes predictions without any other guidance.Unsupervised learning: (definition), (cluster analysis), (word embedding) Supervised learning requires labeling the training data with the expected answers, and comes in two main varieties: classification (where the program must learn to predict what category the input belongs in) and regression (where the program must deduce a numeric function based on numeric input).Supervised learning: (Definition), (Techniques)
In reinforcement learning, the agent is rewarded for good responses and punished for bad ones. The agent learns to choose responses that are classified as "good".Reinforcement learning: , Transfer learning is when the knowledge gained from one problem is applied to a new problem.Transfer learning: , Deep learning is a type of machine learning that runs inputs through biologically inspired artificial neural networks for all of these types of learning.
Computational learning theory can assess learners by computational complexity, by sample complexity (how much data is required), or by other notions of optimization.Computational learning theory: ,
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Artificial intelligence
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Natural language processing
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Natural language processing
Natural language processing (NLP)Natural language processing (NLP): , , allows programs to read, write and communicate in human languages such as English. Specific problems include speech recognition, speech synthesis, machine translation, information extraction, information retrieval and question answering.Subproblems of NLP:
Early work, based on Noam Chomsky's generative grammar and semantic networks, had difficulty with word-sense disambiguation unless restricted to small domains called "micro-worlds" (due to the common sense knowledge problem). Margaret Masterman believed that it was meaning and not grammar that was the key to understanding languages, and that thesauri and not dictionaries should be the basis of computational language structure.
Modern deep learning techniques for NLP include word embedding (representing words, typically as vectors encoding their meaning), transformers (a deep learning architecture using an attention mechanism), and others.Modern statistical and deep learning approaches to NLP: , In 2019, generative pre-trained transformer (or "GPT") language models began to generate coherent text, and by 2023, these models were able to get human-level scores on the bar exam, SAT test, GRE test, and many other real-world applications.
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Artificial intelligence
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Perception
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Perception
Machine perception is the ability to use input from sensors (such as cameras, microphones, wireless signals, active lidar, sonar, radar, and tactile sensors) to deduce aspects of the world. Computer vision is the ability to analyze visual input.Computer vision: ,
The field includes speech recognition, image classification, facial recognition, object recognition,object tracking, and robotic perception.
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Artificial intelligence
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Social intelligence
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Social intelligence
thumb|Kismet, a robot head which was made in the 1990s; it is a machine that can recognize and simulate emotions.
Affective computing is a field that comprises systems that recognize, interpret, process, or simulate human feeling, emotion, and mood.Affective computing: , , , For example, some virtual assistants are programmed to speak conversationally or even to banter humorously; it makes them appear more sensitive to the emotional dynamics of human interaction, or to otherwise facilitate human–computer interaction.
However, this tends to give naïve users an unrealistic conception of the intelligence of existing computer agents. Moderate successes related to affective computing include textual sentiment analysis and, more recently, multimodal sentiment analysis, wherein AI classifies the effects displayed by a videotaped subject.
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Artificial intelligence
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General intelligence
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General intelligence
A machine with artificial general intelligence should be able to solve a wide variety of problems with breadth and versatility similar to human intelligence.Artificial general intelligence: Proposal for the modern version: Warnings of overspecialization in AI from leading researchers: , ,
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Artificial intelligence
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Techniques
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Techniques
AI research uses a wide variety of techniques to accomplish the goals above.
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Artificial intelligence
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Search and optimization
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Search and optimization
AI can solve many problems by intelligently searching through many possible solutions.Search algorithms: , , , There are two very different kinds of search used in AI: state space search and local search.
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Artificial intelligence
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State space search
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State space search
State space search searches through a tree of possible states to try to find a goal state.State space search: For example, planning algorithms search through trees of goals and subgoals, attempting to find a path to a target goal, a process called means-ends analysis.
Simple exhaustive searchesUninformed searches (breadth first search, depth-first search and general state space search): , , , are rarely sufficient for most real-world problems: the search space (the number of places to search) quickly grows to astronomical numbers. The result is a search that is too slow or never completes. "Heuristics" or "rules of thumb" can help prioritize choices that are more likely to reach a goal.Heuristic or informed searches (e.g., greedy best first and A*): , , ,
Adversarial search is used for game-playing programs, such as chess or Go. It searches through a tree of possible moves and countermoves, looking for a winning position.Adversarial search:
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Artificial intelligence
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Local search
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Local search
class=skin-invert-image|thumb|Illustration of gradient descent for 3 different starting points; two parameters (represented by the plan coordinates) are adjusted in order to minimize the loss function (the height) Local search uses mathematical optimization to find a solution to a problem. It begins with some form of guess and refines it incrementally.Local or "optimization" search:
Gradient descent is a type of local search that optimizes a set of numerical parameters by incrementally adjusting them to minimize a loss function. Variants of gradient descent are commonly used to train neural networks, through the backpropagation algorithm.
Another type of local search is evolutionary computation, which aims to iteratively improve a set of candidate solutions by "mutating" and "recombining" them, selecting only the fittest to survive each generation.Evolutionary computation:
Distributed search processes can coordinate via swarm intelligence algorithms. Two popular swarm algorithms used in search are particle swarm optimization (inspired by bird flocking) and ant colony optimization (inspired by ant trails).
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Artificial intelligence
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Logic
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Logic
Formal logic is used for reasoning and knowledge representation.Logic: , ,
Formal logic comes in two main forms: propositional logic (which operates on statements that are true or false and uses logical connectives such as "and", "or", "not" and "implies")Propositional logic: , , and predicate logic (which also operates on objects, predicates and relations and uses quantifiers such as "Every X is a Y" and "There are some Xs that are Ys").First-order logic and features such as equality: , , ,
Deductive reasoning in logic is the process of proving a new statement (conclusion) from other statements that are given and assumed to be true (the premises).Logical inference: Proofs can be structured as proof trees, in which nodes are labelled by sentences, and children nodes are connected to parent nodes by inference rules.
Given a problem and a set of premises, problem-solving reduces to searching for a proof tree whose root node is labelled by a solution of the problem and whose leaf nodes are labelled by premises or axioms. In the case of Horn clauses, problem-solving search can be performed by reasoning forwards from the premises or backwards from the problem.logical deduction as search: , , , In the more general case of the clausal form of first-order logic, resolution is a single, axiom-free rule of inference, in which a problem is solved by proving a contradiction from premises that include the negation of the problem to be solved.Resolution and unification:
Inference in both Horn clause logic and first-order logic is undecidable, and therefore intractable. However, backward reasoning with Horn clauses, which underpins computation in the logic programming language Prolog, is Turing complete. Moreover, its efficiency is competitive with computation in other symbolic programming languages.
Fuzzy logic assigns a "degree of truth" between 0 and 1. It can therefore handle propositions that are vague and partially true.Fuzzy logic: ,
Non-monotonic logics, including logic programming with negation as failure, are designed to handle default reasoning. Other specialized versions of logic have been developed to describe many complex domains.
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Artificial intelligence
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Probabilistic methods for uncertain reasoning
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Probabilistic methods for uncertain reasoning
class=skin-invert-image|thumb|upright=1.7|A simple Bayesian network, with the associated conditional probability tables
Many problems in AI (including in reasoning, planning, learning, perception, and robotics) require the agent to operate with incomplete or uncertain information. AI researchers have devised a number of tools to solve these problems using methods from probability theory and economics.Stochastic methods for uncertain reasoning: , , , Precise mathematical tools have been developed that analyze how an agent can make choices and plan, using decision theory, decision analysis,decision theory and decision analysis: , and information value theory.Information value theory: These tools include models such as Markov decision processes,Markov decision processes and dynamic decision networks: dynamic decision networks, game theory and mechanism design.Game theory and mechanism design:
Bayesian networksBayesian networks: , , , are a tool that can be used for reasoning (using the Bayesian inference algorithm),Bayesian inference algorithm: , , , learning (using the expectation–maximization algorithm),Bayesian learning and the expectation–maximization algorithm: , , , planning (using decision networks)Bayesian decision theory and Bayesian decision networks: and perception (using dynamic Bayesian networks).
Probabilistic algorithms can also be used for filtering, prediction, smoothing, and finding explanations for streams of data, thus helping perception systems analyze processes that occur over time (e.g., hidden Markov models or Kalman filters).Stochastic temporal models:
Hidden Markov model:
Kalman filters:
Dynamic Bayesian networks:
thumb|upright=1.2|Expectation–maximization clustering of Old Faithful eruption data starts from a random guess but then successfully converges on an accurate clustering of the two physically distinct modes of eruption.
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Artificial intelligence
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Classifiers and statistical learning methods
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Classifiers and statistical learning methods
The simplest AI applications can be divided into two types: classifiers (e.g., "if shiny then diamond"), on one hand, and controllers (e.g., "if diamond then pick up"), on the other hand. ClassifiersStatistical learning methods and classifiers: , are functions that use pattern matching to determine the closest match. They can be fine-tuned based on chosen examples using supervised learning. Each pattern (also called an "observation") is labeled with a certain predefined class. All the observations combined with their class labels are known as a data set. When a new observation is received, that observation is classified based on previous experience.
There are many kinds of classifiers in use. The decision tree is the simplest and most widely used symbolic machine learning algorithm.Decision trees: , K-nearest neighbor algorithm was the most widely used analogical AI until the mid-1990s, and Kernel methods such as the support vector machine (SVM) displaced k-nearest neighbor in the 1990s.Non-parameteric learning models such as K-nearest neighbor and support vector machines: , (k-nearest neighbor)
(kernel methods)
The naive Bayes classifier is reportedly the "most widely used learner" at Google, due in part to its scalability.Naive Bayes classifier: ,
Neural networks are also used as classifiers.
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Artificial intelligence
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Artificial neural networks
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Artificial neural networks
right|thumb|A neural network is an interconnected group of nodes, akin to the vast network of neurons in the human brain.
An artificial neural network is based on a collection of nodes also known as artificial neurons, which loosely model the neurons in a biological brain. It is trained to recognise patterns; once trained, it can recognise those patterns in fresh data. There is an input, at least one hidden layer of nodes and an output. Each node applies a function and once the weight crosses its specified threshold, the data is transmitted to the next layer. A network is typically called a deep neural network if it has at least 2 hidden layers.Neural networks: ,
Learning algorithms for neural networks use local search to choose the weights that will get the right output for each input during training. The most common training technique is the backpropagation algorithm.Gradient calculation in computational graphs, backpropagation, automatic differentiation: , , Neural networks learn to model complex relationships between inputs and outputs and find patterns in data. In theory, a neural network can learn any function.Universal approximation theorem:
The theorem: ,
In feedforward neural networks the signal passes in only one direction.Feedforward neural networks: Recurrent neural networks feed the output signal back into the input, which allows short-term memories of previous input events. Long short term memory is the most successful network architecture for recurrent networks.Recurrent neural networks: PerceptronsPerceptrons: use only a single layer of neurons; deep learning uses multiple layers. Convolutional neural networks strengthen the connection between neurons that are "close" to each other—this is especially important in image processing, where a local set of neurons must identify an "edge" before the network can identify an object.Convolutional neural networks:
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Artificial intelligence
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Deep learning
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Deep learning
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Deep learningDeep learning: , , , uses several layers of neurons between the network's inputs and outputs. The multiple layers can progressively extract higher-level features from the raw input. For example, in image processing, lower layers may identify edges, while higher layers may identify the concepts relevant to a human such as digits, letters, or faces.
Deep learning has profoundly improved the performance of programs in many important subfields of artificial intelligence, including computer vision, speech recognition, natural language processing, image classification, and others. The reason that deep learning performs so well in so many applications is not known as of 2021. The sudden success of deep learning in 2012–2015 did not occur because of some new discovery or theoretical breakthrough (deep neural networks and backpropagation had been described by many people, as far back as the 1950s) but because of two factors: the incredible increase in computer power (including the hundred-fold increase in speed by switching to GPUs) and the availability of vast amounts of training data, especially the giant curated datasets used for benchmark testing, such as ImageNet.
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Artificial intelligence
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GPT
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GPT
Generative pre-trained transformers (GPT) are large language models (LLMs) that generate text based on the semantic relationships between words in sentences. Text-based GPT models are pretrained on a large corpus of text that can be from the Internet. The pretraining consists of predicting the next token (a token being usually a word, subword, or punctuation). Throughout this pretraining, GPT models accumulate knowledge about the world and can then generate human-like text by repeatedly predicting the next token. Typically, a subsequent training phase makes the model more truthful, useful, and harmless, usually with a technique called reinforcement learning from human feedback (RLHF). Current GPT models are prone to generating falsehoods called "hallucinations", although this can be reduced with RLHF and quality data. They are used in chatbots, which allow people to ask a question or request a task in simple text.
Current models and services include Gemini (formerly Bard), ChatGPT, Grok, Claude, Copilot, and LLaMA. Multimodal GPT models can process different types of data (modalities) such as images, videos, sound, and text.
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Artificial intelligence
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Hardware and software
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Hardware and software
In the late 2010s, graphics processing units (GPUs) that were increasingly designed with AI-specific enhancements and used with specialized TensorFlow software had replaced previously used central processing unit (CPUs) as the dominant means for large-scale (commercial and academic) machine learning models' training. Specialized programming languages such as Prolog were used in early AI research, but general-purpose programming languages like Python have become predominant.
The transistor density in integrated circuits has been observed to roughly double every 18 months—a trend known as Moore's law, named after the Intel co-founder Gordon Moore, who first identified it. Improvements in GPUs have been even faster, a trend sometimes called Huang's law, named after Nvidia co-founder and CEO Jensen Huang.
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Artificial intelligence
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Applications
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Applications
AI and machine learning technology is used in most of the essential applications of the 2020s, including: search engines (such as Google Search), targeting online advertisements, recommendation systems (offered by Netflix, YouTube or Amazon), driving internet traffic, targeted advertising (AdSense, Facebook), virtual assistants (such as Siri or Alexa), autonomous vehicles (including drones, ADAS and self-driving cars), automatic language translation (Microsoft Translator, Google Translate), facial recognition (Apple's Face ID or Microsoft's DeepFace and Google's FaceNet) and image labeling (used by Facebook, Apple's iPhoto and TikTok). The deployment of AI may be overseen by a Chief automation officer (CAO).
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Artificial intelligence
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Health and medicine
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Health and medicine
The application of AI in medicine and medical research has the potential to increase patient care and quality of life. Through the lens of the Hippocratic Oath, medical professionals are ethically compelled to use AI, if applications can more accurately diagnose and treat patients.
For medical research, AI is an important tool for processing and integrating big data. This is particularly important for organoid and tissue engineering development which use microscopy imaging as a key technique in fabrication. It has been suggested that AI can overcome discrepancies in funding allocated to different fields of research. New AI tools can deepen the understanding of biomedically relevant pathways. For example, AlphaFold 2 (2021) demonstrated the ability to approximate, in hours rather than months, the 3D structure of a protein. In 2023, it was reported that AI-guided drug discovery helped find a class of antibiotics capable of killing two different types of drug-resistant bacteria. In 2024, researchers used machine learning to accelerate the search for Parkinson's disease drug treatments. Their aim was to identify compounds that block the clumping, or aggregation, of alpha-synuclein (the protein that characterises Parkinson's disease). They were able to speed up the initial screening process ten-fold and reduce the cost by a thousand-fold.
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Artificial intelligence
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Games
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Games
Game playing programs have been used since the 1950s to demonstrate and test AI's most advanced techniques. Deep Blue became the first computer chess-playing system to beat a reigning world chess champion, Garry Kasparov, on 11 May 1997. In 2011, in a Jeopardy! quiz show exhibition match, IBM's question answering system, Watson, defeated the two greatest Jeopardy! champions, Brad Rutter and Ken Jennings, by a significant margin. In March 2016, AlphaGo won 4 out of 5 games of Go in a match with Go champion Lee Sedol, becoming the first computer Go-playing system to beat a professional Go player without handicaps. Then, in 2017, it defeated Ke Jie, who was the best Go player in the world. Other programs handle imperfect-information games, such as the poker-playing program Pluribus. DeepMind developed increasingly generalistic reinforcement learning models, such as with MuZero, which could be trained to play chess, Go, or Atari games. In 2019, DeepMind's AlphaStar achieved grandmaster level in StarCraft II, a particularly challenging real-time strategy game that involves incomplete knowledge of what happens on the map. In 2021, an AI agent competed in a PlayStation Gran Turismo competition, winning against four of the world's best Gran Turismo drivers using deep reinforcement learning. In 2024, Google DeepMind introduced SIMA, a type of AI capable of autonomously playing nine previously unseen open-world video games by observing screen output, as well as executing short, specific tasks in response to natural language instructions.
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Artificial intelligence
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Mathematics
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Mathematics
Large language models, such as GPT-4, Gemini, Claude, LLaMa or Mistral, are increasingly used in mathematics. These probabilistic models are versatile, but can also produce wrong answers in the form of hallucinations. They sometimes need a large database of mathematical problems to learn from, but also methods such as supervised fine-tuning or trained classifiers with human-annotated data to improve answers for new problems and learn from corrections. A February 2024 study showed that the performance of some language models for reasoning capabilities in solving math problems not included in their training data was low, even for problems with only minor deviations from trained data. One technique to improve their performance involves training the models to produce correct reasoning steps, rather than just the correct result. The Alibaba Group developed a version of its Qwen models called Qwen2-Math, that achieved state-of-the-art performance on several mathematical benchmarks, including 84% accuracy on the MATH dataset of competition mathematics problems. In January 2025, Microsoft proposed the technique rStar-Math that leverages Monte Carlo tree search and step-by-step reasoning, enabling a relatively small language model like Qwen-7B to solve 53% of the AIME 2024 and 90% of the MATH benchmark problems.
Alternatively, dedicated models for mathematical problem solving with higher precision for the outcome including proof of theorems have been developed such as AlphaTensor, AlphaGeometry and AlphaProof all from Google DeepMind, Llemma from EleutherAI or Julius.
When natural language is used to describe mathematical problems, converters can transform such prompts into a formal language such as Lean to define mathematical tasks.
Some models have been developed to solve challenging problems and reach good results in benchmark tests, others to serve as educational tools in mathematics.
Topological deep learning integrates various topological approaches.
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Artificial intelligence
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Finance
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Finance
Finance is one of the fastest growing sectors where applied AI tools are being deployed: from retail online banking to investment advice and insurance, where automated "robot advisers" have been in use for some years.Matthew Finio & Amanda Downie: IBM Think 2024 Primer, "What is Artificial Intelligence (AI) in Finance?" 8 Dec. 2023
According to Nicolas Firzli, director of the World Pensions & Investments Forum, it may be too early to see the emergence of highly innovative AI-informed financial products and services. He argues that "the deployment of AI tools will simply further automatise things: destroying tens of thousands of jobs in banking, financial planning, and pension advice in the process, but I'm not sure it will unleash a new wave of [e.g., sophisticated] pension innovation."M. Nicolas, J. Firzli: Pensions Age / European Pensions magazine, "Artificial Intelligence: Ask the Industry", May–June 2024. https://videovoice.org/ai-in-finance-innovation-entrepreneurship-vs-over-regulation-with-the-eus-artificial-intelligence-act-wont-work-as-intended/ .
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Artificial intelligence
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Military
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Military
Various countries are deploying AI military applications.PD-notice The main applications enhance command and control, communications, sensors, integration and interoperability. Research is targeting intelligence collection and analysis, logistics, cyber operations, information operations, and semiautonomous and autonomous vehicles. AI technologies enable coordination of sensors and effectors, threat detection and identification, marking of enemy positions, target acquisition, coordination and deconfliction of distributed Joint Fires between networked combat vehicles, both human operated and autonomous.
AI has been used in military operations in Iraq, Syria, Israel and Ukraine.
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Artificial intelligence
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Generative AI
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Generative AI
thumb|Vincent van Gogh in watercolour created by generative AI software
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Artificial intelligence
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Agents
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Agents
Artificial intelligent (AI) agents are software entities designed to perceive their environment, make decisions, and take actions autonomously to achieve specific goals. These agents can interact with users, their environment, or other agents. AI agents are used in various applications, including virtual assistants, chatbots, autonomous vehicles, game-playing systems, and industrial robotics. AI agents operate within the constraints of their programming, available computational resources, and hardware limitations. This means they are restricted to performing tasks within their defined scope and have finite memory and processing capabilities. In real-world applications, AI agents often face time constraints for decision-making and action execution. Many AI agents incorporate learning algorithms, enabling them to improve their performance over time through experience or training. Using machine learning, AI agents can adapt to new situations and optimise their behaviour for their designated tasks.
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Artificial intelligence
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Sexuality
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Sexuality
Applications of AI in this domain include AI-enabled menstruation and fertility trackers that analyze user data to offer prediction, AI-integrated sex toys (e.g., teledildonics), AI-generated sexual education content, and AI agents that simulate sexual and romantic partners (e.g., Replika). AI is also used for the production of non-consensual deepfake pornography, raising significant ethical and legal concerns.
AI technologies have also been used to attempt to identify online gender-based violence and online sexual grooming of minors.
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