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Srinivasa Ramanujan FRS
Born	22 December 1887 Erode, Madras Presidency, British India
Died	26 April 1920 (aged 32) Kumbakonam, Madras Presidency, British India
Nationality	British India
Other names	Srinivasa Ramanujan Aiyangar
Education	Government Arts College (no degree) Pachaiyappa's College (no degree) Trinity College, Cambridge (BSc, 1916)
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 Ramanujan–Sato series
Awards	Fellow of the Royal Society
Scientific career
Fields	Mathematics
Institutions	Trinity College, Cambridge
Thesis	Highly Composite Numbers (1916)
Academic advisors	G. H. Hardy J. E. Littlewood
Influences	G. S. Carr
Influenced	G. H. Hardy
Signature

Srinivasa Ramanujan FRS (/ˈsrɪnɪvɑːs rɑːˈmɑːnʊdʒən/; born Srinivasa Ramanujan Aiyangar, 22 December 1887 – 26 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Hardy commented that Ramanujan had produced groundbreaking new theorems, including some that "defeated me completely; I had never seen anything in the least like them before", and some recently proven but highly advanced results.

During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Nearly all his claims have now been proven correct. The Ramanujan Journal, a scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan, and his notebooks—containing summaries of his published and unpublished results—have been analyzed and studied for decades since his death as a source of new mathematical ideas. As late as 2011 and again in 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death. He became one of the youngest Fellows of the Royal Society and only the second Indian member, and the first Indian to be elected a Fellow of Trinity College, Cambridge. Of his original letters, Hardy stated that a single look was enough to show they could only have been written by a mathematician of the highest calibre, comparing Ramanujan to mathematical geniuses such as Euler and Jacobi.

In 1919, ill health—now believed to have been hepatic amoebiasis (a complication from episodes of dysentery many years previously)—compelled Ramanujan's return to India, where he died in 1920 at the age of 32. His last letters to Hardy, written in January 1920, show that he was still continuing to produce new mathematical ideas and theorems. His "lost notebook", containing discoveries from the last year of his life, caused great excitement among mathematicians when it was rediscovered in 1976.

A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess Namagiri Thayar. He once said, "An equation for me has no meaning unless it expresses a thought of God."

1. Some properties of Bernoulli's numbers
   Journal of the Indian Mathematical Society, III, 1911, 219 – 234
2. On question 330 of Professor Sanjana
   Journal of the Indian Mathematical Society, IV, 1912, 59 – 61
3. Note on a set of simultaneous equations
   Journal of the Indian Mathematical Society, IV, 1912, 94 – 96
4. Irregular numbers
   Journal of the Indian Mathematical Society, V, 1913, 105 – 106
5. Squaring the circle
   Journal of the Indian Mathematical Society, V, 1913, 132
6. Modular equations and approximations to π
   Quarterly Journal of Mathematics, XLV, 1914, 350 – 372
7. On the integral
   Journal of the Indian Mathematical Society, VII,1915, 93 – 96
8. On the number of divisors of a number
   Journal of the Indian Mathematical Society, VII, 1915, 131 – 133
9. On the sum of the square roots of the first n natural numbers
   Journal of the Indian Mathematical Society, VII, 1915, 173 – 175
10. On the product
    Journal of the Indian Mathematical Society, VII, 1915, 209 – 211
11. Some definite integrals
    Messenger of Mathematics, XLIV, 1915, 10 – 18
12. Some definite integrals connected with Gauss's sums
    Messenger of Mathematics, XLIV, 1915, 75 – 85
13. Summation of a certain series
    Messenger of Mathematics, XLIV, 1915, 157 – 160
14. New expressions for Riemann's functions ξ(s) and Ξ(t)
    Quarterly Journal of Mathematics, XLVI, 1915, 253 – 260
15. Highly composite numbers
    Proceedings of the London Mathematical Society, 2, XIV, 1915, 347 – 409
16. On certain infinite series
    Messenger of Mathematics, XLV, 1916, 11 – 15
17. Some formulæ in the analytic theory of numbers
    Messenger of Mathematics, XLV, 1916, 81 – 84
18. On certain arithmetical functions
    Transactions of the Cambridge Philosophical Society, XXII, No.9, 1916, 159 – 184
19. A series for Euler's constant γ
    Messenger of Mathematics, XLVI, 1917, 73 – 80
20. On the expression of a number in the form ax² + by² + cz² + du²
    Proceedings of the Cambridge Philosophical Society, XIX, 1917, 11 – 21
21. On certain trigonometrical sums and their applications in the theory of numbers
    Transactions of the Cambridge Philosophical Society, XXII, No.13, 1918, 259 – 276
22. Some definite integrals
    Proceedings of the London Mathematical Society, 2, XVII, 1918,Records for 17 Jan. 1918
23. Some definite integrals
    Journal of the Indian Mathematical Society, XI, 1919, 81 – 87
24. A proof of Bertrand's postulate
    Journal of the Indian Mathematical Society, XI, 1919, 181 – 182
25. Some properties of p(n), the number of partitions of n
    Proceedings of the Cambridge Philosophical Society, XIX, 1919, 207 – 210
26. Proof of certain identities in combinatory analysis
    Proceedings of the Cambridge Philosophical Society, XIX, 1919,214 – 216
27. A class of definite integrals
    Quarterly Journal of Mathematics, XLVIII, 1920, 294 – 310
28. Congruence properties of partitions
    Proceedings of the London Mathematical Society, 2, XVIII, 1920, Records for 13 March 1919
29. Algebraic relations between certain infinite products
    Proceedings of the London Mathematical Society, 2, XVIII, 1920, Records for 13 March 1919
30. Congruence properties of partitions
    Mathematische Zeitschrift, IX, 1921, 147 – 153
31. Une formule asymptotique pour le nombre des partitions de n
    (written in collaboration with G. H. Hardy)
    Comptes Rendus, 2 Jan. 1917
32. Proof that almost all numbers n are composed of about log log n prime factors
    (written in collaboration with G. H. Hardy)
    Proceedings of the London Mathematical Society, 2, XVI,1917,Records for 14 Dec. 1916
33. Asymptotic formulæ in combinatory analysis
    (written in collaboration with G. H. Hardy)
    Proceedings of the London Mathematical Society, 2, XVI, 1917, Records for 1 March 1917
34. Asymptotic formulæ for the distribution of integers of various types
    (written in collaboration with G. H. Hardy)
    Proceedings of the London Mathematical Society, 2, XVI, 1917, 112 – 132
35. The normal number of prime factors of a number n
    (written in collaboration with G. H. Hardy)
    Quarterly Journal of Mathematics, XLVIII, 1917, 76 – 92
36. Asymptotic formulæ in combinatory analysis
    (written in collaboration with G. H. Hardy)
    Proceedings of the London Mathematical Society, 2, XVII, 1918, 75 – 115
37. On the coefficients in the expansions of certain modular functions
    (written in collaboration with G. H. Hardy)
    Proceedings of the Royal Society, A, XCV, 1919, 144 – 155