query: field_of_work victor kolyvagin
supports: Sir Henry Peter Francis Swinnerton-Dyer, 16th Baronet (born 2 August 1927), commonly known as Peter Swinnerton-Dyer, is an English mathematician specialising in number theory at University of Cambridge. As a mathematician he is best known for his part in the Birch and Swinnerton-Dyer conjecture relating algebraic properties of elliptic curves to special values of L-functions, which was developed with Bryan Birch during the first half of the 1960s with the help of machine computation, and for his work on the Titan operating system. Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers). Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States. CMI's scientific activities are managed from the President's office in Oxford, United Kingdom. The institute is "dedicated to increasing and disseminating mathematical knowledge." It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the sponsorship of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI.  Sir Andrew John Wiles (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is most notable for proving Fermat's Last Theorem, for which he received the 2016 Abel Prize. Wiles has received numerous other honours. Victor Alexandrovich Kolyvagin ( Russian :    ) is a Russian mathematician who wrote a series of papers on Euler systems , leading to breakthroughs on the Birch and Swinnerton - Dyer conjecture , and Iwasawa 's conjecture for cyclotomic fields . His work also influenced Andrew Wiles 's work on Fermat 's Last Theorem . Kolyvagin received his Ph.D. in Mathematics in 1981 from Moscow State University , where his advisor was Yuri I. Manin . He then worked at Steklov Institute of Mathematics in Moscow until 1994 . In 1990 he received the Chebyshev Prize of the USSR Academy of Sciences . Since 1994 he has been a professor of mathematics in the United States . He was a professor at Johns Hopkins University until 2002 when he became the first person to hold the Mina Rees Chair in mathematics at the Graduate Center Faculty at The City University of New York . In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper and the work of . Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product. The University of Oxford (informally Oxford University or simply Oxford) is a collegiate research university located in Oxford, England, United Kingdom. While having no known date of foundation, there is evidence of teaching as far back as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in continuous operation. It grew rapidly from 1167 when Henry II banned English students from attending the University of Paris. After disputes between students and Oxford townsfolk in 1209, some academics fled northeast to Cambridge where they established what became the University of Cambridge. The two "ancient universities" are frequently jointly referred to as "Oxbridge". Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer who made important and influential discoveries in many branches of mathematics like infinitesimal calculus and graph theory while also making pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been known to have infinitely many solutions since antiquity. The President, Council and Fellows of the Royal Society of London for Improving Natural Knowledge, commonly known as the Royal Society, is a learned society for science and is possibly the oldest such society still in existence. Founded in November 1660, it was granted a royal charter by King Charles II as "The Royal Society". The Society is the United Kingdom's and Commonwealth of Nations' Academy of Sciences and fulfills a number of roles; promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, fostering international and global cooperation, education and public engagement. 
  The society is governed by its Council, which is chaired by the Society's President, according to a set of statutes and standing orders. The members of Council and the President are elected from and by its Fellows, the basic members of the society, who are themselves elected by existing Fellows. As of 2016, there are about 1,600 fellows, allowed to use the postnominal title FRS (Fellow of the Royal Society), with up to 52 new fellows appointed each year. There are also royal fellows, honorary fellows and foreign members, the last of which are allowed to use the postnominal title ForMemRS (Foreign Member of the Royal Society). The Royal Society President is Venkatraman Ramakrishnan, who took up the post on November 30, 2015. In mathematics, the Birch and Swinnerton-Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. The conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, which has offered a $1,000,000 prize for the first correct proof. It is named after mathematicians Bryan Birch and Peter Swinnerton-Dyer who developed the conjecture during the first half of the 1960s with the help of machine computation. , only special cases of the conjecture have been proved.
candidates: education english mathematician mathematics number theory research science
answer: number theory