FRS (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians. When his skills became apparent to the wider mathematical community, centered in Europe at the time, he began a famous partnership with the English mathematician G. H. Hardy. He rediscovered previously known theorems in addition to producing new work.
During his short life, Ramanujan independently compiled nearly 3900 results (mostly identities and equations). Nearly all his claims have now been proven correct, although a small number of these results were actually false and some were already known. He stated results that were both original and highly unconventional, such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research. The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work.
Although Ramanujan secured a first class in mathematics in the matriculation examination and was awarded the Subramanyan Scholarship, he failed twice in his first year arts examination in college, as he neglected other subjects such as history, English and physiology. This disappointed his father. When he found the boy always scribbling numbers and not doing much else, he thought Ramanujan had gone mad. “To set him right”, he forced his son to marry. The girl chosen was eight-year-old Janaki.
A few months earlier, Ramanujan had sent a letter to the great mathematician G.H. Hardy, of Cambridge University, in which he set out 120 theorems and formulae. Among them was what is known as the Reimann series, a topic in the definite integral of calculus. But Ramanujan was ignorant of the work of the German mathematician, George F. Reimann, who had earlier arrived at the series, a rare achievement. Also included was Ramanujan’s conjecture about the kind of questions called “modular”. Pierre Deligne subsequently proved this conjecture to be correct. He also gave a key formula in the hypergeometric series, which came to be named after him.
In Ramanujan Hardy found an unsystematic mathematician, similar to one who knows the Pythagoras theorem but does not know that a congruent triangle means. Several discrepancies in his research could be attributed to his lack of formal education. Ramanujan played with numbers, as a child would with a toy. It was sheer genius that led him to mathematical “truths”. The task of proving them, so important in science, he left to lesser mortals.
Besides being a mathematician, Ramanujan was an astrologer of repute and a good speaker. He used to give lectures on subjects like “God, Zero and Infinity.
1729 is the natural number following 1728 and preceding 1730. 1729 is known as the Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see the Indian mathematician Srinivasa Ramanujan. In Hardy's words.
“ I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
91 = 63 + (−5)3 = 43 + 33 Of course, equating "smallest" with "most negative", as opposed to "closest to zero" gives rise to solutions like −91, −189, −1729, and further negative numbers. This ambiguity is eliminated by the term "positive cubes".
Numbers that are the smallest number that can be expressed as the sum of two cubes in n distinct ways have been dubbed "taxicab numbers". The number was also found in one of Ramanujan's notebooks dated years before the incident, and was noted by Frénicle de Bessy in 1657.
The same expression defines 1729 as the first in the sequence of "Fermat near misses" (sequence A050794 in OEIS) defined as numbers of the form 1 + z3 which are also expressible as the sum of two other cubes.
1729 is also the third Carmichael number and the first absolute Euler pseudoprime. It is also a sphenic number.1729 is a Zeisel number. It is a centered cube number, as well as a dodecagonal number, a 24-gonal and 84-gonal number.
Investigating pairs of distinct integer-valued quadratic forms that represent every integer the same number of times, Schiemann found that such quadratic forms must be in four or more variables, and the least possible discriminant of a four-variable pair is 1729 (Guy 2004).
1729 has another mildly interesting property: the 1729th decimal place is the beginning of the first occurrence of all ten digits consecutively in the decimal representation of the transcendental number e.
1 + 7 + 2 + 9 = 1919 × 91 = 1729 It suffices only to check sums congruent to 0 or 1 (mod 9) up to 19.