Srinivasa Ramanujan (1887 - 1920) was an Indian mathematician who, with almost no formal training in the subject, produced deep and original results in number theory, infinite series, and continued fractions. [1] Working in isolation in southern India, he independently rediscovered established theorems and devised entirely new ones before his talent was recognised by the English mathematician G. H. Hardy, with whom he collaborated at the University of Cambridge. [2] In 1918 he became one of the youngest Fellows of the Royal Society, but his career was cut short by illness and he died at the age of 32. [3]
Early life and education
Ramanujan was born on 22 December 1887 in Erode, in the Madras Presidency of British India, and grew up in the town of Kumbakonam. [1] As a boy he showed an extraordinary aptitude for mathematics, mastering advanced material on his own. A pivotal influence was G. S. Carr's A Synopsis of Elementary Results in Pure and Applied Mathematics, a compilation of thousands of theorems that Ramanujan worked through and extended. [2] His single-minded devotion to mathematics came at the expense of his other studies, and he twice failed to secure a college degree, losing a scholarship after neglecting non-mathematical subjects. [1]
Correspondence and Cambridge
Unable to find academic employment, Ramanujan took a clerical post at the Madras Port Trust while continuing his research. In 1913 he wrote to several English mathematicians, enclosing samples of his results; the letter to G. H. Hardy at Trinity College, Cambridge, contained formulas so unusual that Hardy judged them the work of a mathematician of the highest class. [2] With Hardy's support, Ramanujan travelled to England in 1914 and began a remarkable collaboration, publishing a series of joint and individual papers over the following years. [4]
Mathematical work
Ramanujan's output ranged across the theory of partitions, highly composite numbers, mock theta functions, modular equations, and rapidly converging infinite series for the constant pi. [1] Working with Hardy, he developed the circle method and an asymptotic formula for the partition function. [2] Much of his mathematics was recorded in notebooks as identities stated without proof, reflecting a highly intuitive style; verifying and extending these results has occupied mathematicians for a century. A famous anecdote concerns the number 1729, which Ramanujan instantly identified as the smallest number expressible as a sum of two cubes in two different ways. [4]
Later life and legacy
In 1918 Ramanujan was elected a Fellow of the Royal Society and a Fellow of Trinity College, honours rarely granted to someone so young. [3] His health, however, deteriorated in the English climate, and in 1919 he returned to India, where he died on 26 April 1920. [1] In his final year he produced the results of what became known as the "lost notebook," rediscovered decades later. [2] Ramanujan is remembered as one of the most gifted mathematicians in history, and his conjectures continue to influence number theory, combinatorics, and mathematical physics. [4]
