Srinivasa Ramanujan

Srinivasa Ramanujan was born on December 22, 1887, in Erode, a town in the Madras Presidency of British India, into a Tamil Brahmin family of modest means. From an early age he displayed a consuming passion for mathematics that set him apart from his peers. By the age of twelve he had mastered advanced trigonometry, and by fifteen he had obtained a copy of George Shoobridge Carr's Synopsis of Elementary Results in Pure and Applied Mathematics — a dense compendium of thousands of mathematical theorems — and worked through it almost entirely on his own, independently proving and extending many of its results.

Early Struggles

Ramanujan's single-minded devotion to mathematics proved academically costly. He failed his college examinations at the Government Arts College in Kumbakonam and later at Pachaiyappa's College in Madras because he neglected every subject except mathematics. Without a degree, he found himself in financial hardship and spent years in near poverty, filling notebooks with mathematical discoveries that he had no formal framework to present to the world. He married Janaki Ammal in 1909 and worked as a clerk at the Madras Port Trust to survive, all while continuing to produce remarkable mathematical work in his spare time.

Partnership with G.H. Hardy

In 1913, Ramanujan took a bold step and wrote a now-famous letter to the Cambridge mathematician G.H. Hardy, enclosing a collection of his theorems without formal proofs. Hardy, initially skeptical, shared the letter with his colleague J.E. Littlewood. The two men were astounded — many of the results were utterly original, some were known but independently rediscovered, and some Hardy and Littlewood simply could not evaluate without further investigation. Hardy arranged for Ramanujan to travel to Cambridge, and the two formed one of the most celebrated collaborations in mathematical history. Together and separately, they published papers on highly composite numbers, partition functions, and the distribution of prime numbers, among many other topics.

Mathematical Contributions

Ramanujan's contributions were breathtaking in their scope and depth. He developed the Ramanujan prime, the Ramanujan theta function, and the Rogers–Ramanujan identities, and made foundational contributions to the theory of modular forms that would prove essential to twentieth-century mathematics and, remarkably, to string theory in theoretical physics decades after his death. His work on the partition function — counting the number of ways a positive integer can be expressed as a sum of positive integers — with Hardy produced the Hardy–Ramanujan asymptotic formula, a landmark result. Perhaps most famously, he compiled three notebooks filled with thousands of results, many of which mathematicians spent the rest of the twentieth century verifying and understanding.

Death and Legacy

Ramanujan's years in England, though intellectually triumphant — he was elected a Fellow of the Royal Society in 1918 and a Fellow of Trinity College Cambridge — were physically devastating. The cold climate, the difficulty of maintaining a vegetarian diet during World War I food shortages, and the stress of his circumstances worsened his health dramatically. He was diagnosed with tuberculosis and returned to India in 1919. He died on April 26, 1920, in Kumbakonam, aged only thirty-two. His legacy endures with extraordinary vitality: the Ramanujan Journal publishes research inspired by his work, and his story was told in the 2015 film The Man Who Knew Infinity. December 22, his birthday, is celebrated as National Mathematics Day in India.