Srinivasa Ramanujan

Srinivasa Ramanujan (1887 to 1920) was an Indian mathematician who made major contributions to the analytic theory of numbers, elliptic functions, continued fractions and infinite series. He had little formal training in advanced mathematics, yet he left behind about 4,000 original results. His collaboration with the English mathematician G. H. Hardy at Cambridge brought his work to the world.

Early life of Srinivasa Ramanujan

Ramanujan was born on December 22, 1887, in his grandmother’s house in Erode, in what is now Tamil Nadu, India. He was the third of five children of Kuppuswamy Srinivasa, a clerk in a shop, and Komalatammal. When he was about a year old the family moved to Kumbakonam, and his family was poor.

He contracted smallpox in December 1889. He entered the Town High School in Kumbakonam in January 1898 and showed marked mathematical ability from early on. In 1900 he began working on his own on series, and he learned to solve cubic equations in 1902 and found his own method for the quartic.

At about sixteen he was shown a copy of G. S. Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics, a book with some 5,000 theorems. He set out to prove them and soon went beyond the book. With a scholarship he entered the Government College in Kumbakonam in 1904, but he lost interest in other subjects and failed them. He later attended Pachaiyappa’s College in Madras, and he began keeping notebooks of his results.

Career and major work of Srinivasa Ramanujan

Ramanujan married Janaki on July 14, 1909, in an arranged marriage when she was still a child. He then looked for work or a patron, and in 1911 his research paper on Bernoulli numbers appeared in the Journal of the Indian Mathematical Society and gained him recognition. On March 1, 1912, he began work as a clerk at the Madras Port Trust. The Chief Accountant there, S. N. Aiyar, was trained as a mathematician and published a paper in 1913 on Ramanujan’s work on the distribution of primes.

In January 1913 he wrote to Hardy at Trinity College, Cambridge, enclosing about 100 theorems. Hardy responded warmly, and the University of Madras gave Ramanujan its first research scholarship in May 1913. It later offered him 250 pounds a year for five years so that he could travel to England. Hardy then brought him to Cambridge, and Ramanujan sailed from India on March 17, 1914, and reached London on April 14.

He graduated from Cambridge on March 16, 1916, with a Bachelor of Arts by research. He fell seriously ill in 1917. In February 1918 he was elected a Fellow of the Cambridge Philosophical Society and was proposed for the Royal Society, and his election as a Fellow of the Royal Society was confirmed on May 2, 1918. In October 1918 he became a Fellow of Trinity College.

He sailed back to India on February 27, 1919, arriving on March 13. His health was very poor, and he died on April 26, 1920. MacTutor gives Kumbakonam as the place of death and the Institute of Mathematical Sciences gives Madras.

Ideas and contributions of Srinivasa Ramanujan

Ramanujan worked on elliptic integrals, hypergeometric series and the zeta function. He independently found results that mathematicians such as Gauss and Kummer had already obtained on hypergeometric series. His work on partial sums and products of these series has led to later developments in the field.

Perhaps his best-known work concerns the number of partitions of an integer, meaning the number of ways to write it as a sum of smaller whole numbers. Using tables of values for small numbers, he conjectured remarkable properties and proved some of them with elliptic functions. In a joint paper with Hardy he gave an asymptotic formula for the partition function that gave very accurate values, and the mathematician Hans Rademacher later proved the result.

His results on infinite series connect to calculus, where series are used to represent functions and to evaluate difficult quantities.

He also worked on prime numbers, although the verdict on that work is mixed, as the next section explains. Many of his results were stated without proof, and mathematicians have spent decades filling in the details.

Strengths and limits of his work

MacTutor notes that Ramanujan had only a vague idea of what constitutes a mathematical proof. Some of his theorems about prime numbers were wrong, even though many of his other results were brilliant. Hardy and others had to check, correct and prove his claims, which is why his collaboration with Cambridge mathematicians mattered.

His formal training was limited, and he rediscovered a great deal of mathematics that was already known. The Oxford Dictionary of National Biography says that he reinvented large parts of Western mathematics while working alone. This explains why his notebooks mix new discoveries with known results.

Legacy of Srinivasa Ramanujan

Ramanujan left unpublished notebooks full of theorems that mathematicians have continued to study. G. N. Watson published 14 papers called Theorems stated by Ramanujan and nearly 30 papers inspired by his work. The Collected Papers of Ramanujan, edited by Hardy, P. V. Seshu Aiyar and B. M. Wilson, was published by Cambridge University Press in 1927.

In the spring of 1976 George Andrews of Pennsylvania State University found his so-called lost notebook among the papers of G. N. Watson, and a facsimile was published in 1987, the year of his birth centenary. The Institute of Mathematical Sciences describes his return from Cambridge as having earned a scientific reputation no Indian had enjoyed before.

He died at age 32. Because he often recorded results without showing how he reached them, readers of his notebooks must rebuild the reasoning, a task that has occupied scholars for generations. Ramanujan is now regarded as one of India’s greatest mathematicians. His life shows how talent can emerge without formal training when mentors and institutions give it a chance.

Editorially reviewed by Specialty Digest Editorial TeamLast reviewed November 4, 2026Researched and drafted with AI assistanceReport an issue