Srinivasa Ramanujan

Ramanujan was born on 22 December 1887 in Erode, in what is now Tamil Nadu, India, and grew up in Kumbakonam. He attended school and showed strong mathematical ability, but his interest increasingly centered on mathematics. A collection of results by George Shoobridge Carr became an important resource for his independent study: Ramanujan worked through its theorems and developed ideas of his own. His formal education did not follow the usual path into advanced mathematics, but he continued to pursue research while seeking employment. In 1912 he became a clerk at the Madras Port Trust, where colleagues and local mathematicians helped bring his work to wider notice.

Ramanujan published mathematical work in India before he became known internationally. In 1913 he sent a letter describing many of his results to the British mathematician G. H. Hardy at Cambridge. Hardy recognized the originality in the material and helped arrange for Ramanujan to come to England. Ramanujan arrived in 1914 and collaborated with Hardy during the First World War. He also studied at Cambridge, receiving a Bachelor of Arts by Research in 1916. Their collaboration brought his independent discoveries into sustained exchange with contemporary mathematical methods; it did not erase the substantial work he had already done in India.

Ramanujan made important contributions to number theory and analysis, including work on integer partitions, continued fractions, infinite series and elliptic functions. The partition function counts the different ways a positive integer can be written as a sum of positive integers; Ramanujan and Hardy developed an influential approximation for its values. Ramanujan's papers and notebooks also contain formulas and results that stimulated later mathematical research. His work often began from powerful intuition and calculation, while later mathematicians supplied proofs, placed results in broader theories and distinguished correct discoveries from claims that needed revision.

Ramanujan was elected a Fellow of the Royal Society on 2 May 1918 and a Fellow of Trinity College, Cambridge, later that year. His health had deteriorated during his time in England. He returned to India in 1919, but remained seriously ill and died in Kumbakonam on 26 April 1920, aged 32. Accounts differ in their descriptions of the illness, so his biography is more secure on the broad fact of his prolonged ill health than on a single simple diagnosis.

Ramanujan's notebooks and published papers preserve a wide range of mathematical ideas, some of which took later researchers decades to understand fully. His work remains part of research on number theory and related fields, while his career is also discussed in the history of mathematics as an example of how original insight can develop outside conventional academic routes. A balanced account recognizes both his extraordinary originality and the collaborative work through which his results were tested, proved and extended.