Know Srinivasa Ramanujan birthday, speech, facts and history
Contd from previous issue
He brought his notebooks from India which were filled with thousands of identities, equations, and theorems that he discovered for himself in the years 1903 to 1914. Some were discovered by earlier mathematicians; some through inexperience, were mistaken, and many were entirely new.
He had very little formal training in mathematics. He spent around 5 years in Cambridge collaborating with Hardy and Littlewood and published part of his findings there.
Srinivasa Ramanujan: Major Works
He worked in several areas including the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series, in which he discovered a value for the sum of such series using a technique he invented and came to be known as Ramanujan summation.
He also made several advances in England, mainly in the partition of numbers (the various ways that a positive integer can be expressed as the sum of positive integers; e.g. 4 can be expressed as 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1).
His papers were published in English and European Journals. He was elected to the Royal Society of London in 1918 and became the second Indian. He was also elected "for his investigation in elliptic functions and the Theory of Numbers."
In October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge.
He is also known for Landau–Ramanujan constant, Mock theta functions, Rama-nujan conjecture, Ramanujan prime, Ramanujan–Soldner constant, Ramanujan theta function, Ramanujan's sum, Rogers–Ramanujan identities, Ramanujan's master theorem, and Ramanujan–Sato series.
1729 is famous as Hardy-Ramanujan number and generalisation of this idea have generated the notion of "Taxicab numbers".
Srinivasa Ramanujan: Illness and Death
He contracted tuberculosis in 1917. His condition improved so that he could return to India in 1919. He died the following year. He left behind three notebooks and some pages, also known as the "lost notebook" that contained various unpublished results. Mathematicians continued to verify these results after his death.