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  • Topic: David Hilbert, Srinivasa Ramanujan, Mathematics
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Srinivasa Ramanujan|
BIO-DATA| Born| (1887-12-22)22 December 1887
Erode, Madras Presidency|
Died| 26 April 1920(1920-04-26) (aged 32)
Chetput, Madras, Madras Presidency|
Residence| Kumbakonam|
Nationality| Indian|
Fields| Mathematics|
Alma mater| Government Arts College
Pachaiyappa's College|
Academic advisors| G. H. Hardy
J. E. Littlewood|
Known for| Landau–Ramanujan constant
Mock theta functions
Ramanujan conjecture
Ramanujan prime
Ramanujan–Soldner constant
Ramanujan theta function
Ramanujan's sum
Rogers–Ramanujan identities
Ramanujan's master theorem|
Influences| G. H. Hardy|

Srinivasa Ramanujan (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. Living in India with no access to the larger mathematical community, which was centered in Europe at the time, Ramanujan developed his own mathematical research in isolation. As a result, he sometimes rediscovered known theorems in addition to producing new work. Ramanujan was said to be a natural genius by the English mathematician G.H. Hardy, in the same league as mathematicians like Euler and Gauss.

Born in a poor Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered by the age of 12; he even discovered theorems of his own, and re-discovered Euler's identity independently. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan had conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. Ramanujan received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself. In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. G. H. Hardy, recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge. Srinivasa died of illness, malnutrition, and possibly liver infection in 1920 at the age of 32. During his short lifetime, Ramanujan independently compiled nearly 3900 results (mostly identities and equations). Most of 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. However, the mathematical mainstream has been rather slow in absorbing some of his major discoveries. The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work. In December 2011, in recognition of his contribution to mathematics, the Government of India declared that Ramanujan's birthday (22 December) should be celebrated every year as National Mathematics Day, and also declared 2012 the National Mathematical Year. Ramanujan–Hardy number 1729

Main article: 1729 (number)

The number 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see Ramanujan. In Hardy's words:[91] “| I remember once going to see him when he was ill at Putney. I had ridden in taxi cab...
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