Srinivasa Ramanujan: Greatest Mathematical Genius of the Twentieth Century

In the last year of his life, dying of an illness no doctor in England or India had been able to name, Srinivasa Ramanujan lay in a rented house in Madras and did the only thing he had ever truly known how to do. He filled sheet after sheet with numbers. The man was failing; the mathematics was not. Some of those final pages would not be understood for another eighty years — and when they finally were, they turned out to describe the physics of black holes.

This is the strange shape of Ramanujan’s story. A clerk with no degree, no teacher, and no money saw further into the structure of numbers than almost anyone before or since — and then died at thirty-two, leaving the world a century of catching up to do. He did not study mathematics so much as inhabit it. To understand how that was possible, you have to go back to a small town in southern India, and a single letter that should never have been believed.

A Childhood in Kumbakonam: The Making of a Mathematical Mind

Srinivasa Ramanujan Iyengar was born on 22 December 1887 in Erode, a small town in Tamil Nadu, in southern India. His family soon moved to Kumbakonam, where his father worked as a clerk in a cloth merchant’s shop. They were Brahmin and devoutly religious, and Ramanujan would remain so all his life, attributing many of his insights to the goddess Namagiri of Namakkal, whom his family worshipped. He described her appearing to him in dreams, writing equations on his tongue. Whether this was metaphor, vision, or something else, no one can say.

His gifts were obvious before he was a teenager. By eleven he had absorbed the mathematics of the college students who boarded in the family home, exhausting their knowledge and asking them questions they could not answer. At sixteen he encountered the book that would shape everything: George Carr’s A Synopsis of Elementary Results in Pure and Applied Mathematics, a dense catalogue of thousands of theorems listed without proofs. For most students it was a revision guide. For Ramanujan it was a challenge. He worked through every theorem, reconstructing the proofs himself, then went beyond them — filling the margins with results Carr had never imagined.

That approach — working alone, rebuilding foundations, generating results by intuition — was both the making and the limiting of him. He proved extraordinary things, but often in ways that were invisible even to himself, by pattern-recognition he could not always translate into the formal language the Western tradition demanded.

Years of Struggle: Poverty, Failure, and Notebooks

His gifts did not translate into academic success. He won a scholarship to the Government College in Kumbakonam at fifteen, then failed his examinations the next year — not in mathematics, where he was untouchable, but in English and physiology, subjects he could not make himself care about. He lost the scholarship, tried college again, failed again, and dropped out.

For several years he lived in poverty in Madras, dependent on the charity of friends and a few occasional patrons. He filled notebooks with results, conjectures, and identities — without income, without recognition, without anyone nearby who could judge what he was producing. He married in 1909, in a marriage arranged by his mother, a girl named Janaki who was then about ten, as was the custom of the time.

The notebooks kept filling. Ramachandra Rao, a mathematician and official in Madras, gave him a stipend after hearing him explain work on hypergeometric series that Rao had no framework to evaluate but could plainly see was extraordinary. By 1912 Ramanujan had a clerkship at the Madras Port Trust. He was a competent clerk. The notebooks kept filling.

The Letter That Changed Everything

In January 1913, encouraged by colleagues at the Port Trust, Ramanujan wrote to G.H. Hardy at Trinity College, Cambridge — one of the most eminent mathematicians in Britain. The letter ran to pages of theorems, organised by topic, with no proofs and no account of method. Hardy almost dismissed it; every prominent mathematician received letters from cranks. But something stopped him. He showed it to his colleague J.E. Littlewood, and the two spent the evening working through the results. Some were already known and correctly stated.

Some were new and appeared to be true. Some seemed impossible, yet proved correct on careful analysis. A few were simply wrong — his intuition occasionally outpaced even his own accuracy. The overall impression was overwhelming.

“They must be true,” Hardy said of the formulas, “because if they were not true, no one would have had the imagination to invent them.”

Hardy arranged support at once. The University of Madras granted a scholarship. E.H. Neville, a colleague lecturing in India, worked to overcome Ramanujan’s deep reluctance to cross the sea — a serious obstacle, since orthodox Brahmin tradition forbade it. After prolonged persuasion, and reportedly the intervention of his goddess Namagiri in a dream, he agreed. He sailed from India on 17 March 1914.

Cambridge: The Great Collaboration

Ramanujan reached Trinity College in April 1914, aged 26. England was cold, grey, and alien. A strict vegetarian in a country that barely understood vegetarian food, he cooked for himself, struggled with the climate, and missed India with a homesickness those around him could see but not ease. He was not unhappy — his letters home were warm, sometimes funny — but he was out of his element in every way except the one that mattered most.

The partnership worked because each man held exactly what the other lacked. Hardy brought rigorous command of formal proof, a map of contemporary European mathematics, and the discipline to turn intuition into publishable work. Ramanujan brought an almost supernatural capacity to see patterns and relationships that no amount of training produces. Hardy later attempted a famous assessment of mathematical talent on a scale of 0 to 100. He gave himself 25. He gave Littlewood 30. He gave David Hilbert, the towering figure of the previous generation, 80. He gave Ramanujan 100.

Between 1914 and 1919 Ramanujan produced more than thirty research papers. The most celebrated was his 1918 work with Hardy on the partition function — which counts the ways a whole number can be written as a sum of positive integers. The number of partitions grows explosively and had no known formula; together they built the circle method, an elegant use of complex analysis, to produce an asymptotic formula of extraordinary accuracy. It founded analytic number theory, a field still active today. In 1918 Ramanujan was elected a Fellow of the Royal Society, among the youngest ever, and soon after a Fellow of Trinity. He had arrived with no degree and left as one of the most distinguished mathematicians alive.

The Illness That Could Not Be Named

By 1917 Ramanujan was seriously ill. The diagnosis shifted over the years — tuberculosis was the main one, though other conditions were suggested — and the damp English climate did not help. He was admitted to several sanatoriums and lost a great deal of weight. There were periods when those around him feared the worst.

He returned to India in 1919 as his health slightly improved. He was thirty-one. Even bedridden and weakening, he kept filling pages with new mathematics — including the results that would later become the lost notebook. He died on 26 April 1920 in Kumbakonam, aged thirty-two, having worked almost until the end.

The Three Notebooks and the Lost One

Ramanujan left three notebooks recording roughly 3,900 results, most without proofs. Verifying them occupied mathematicians for decades; Bruce Berndt of the University of Illinois spent more than twenty years working through them, publishing his findings in five volumes. Most results proved correct, and the act of proving them generated entirely new mathematics.

The most dramatic story belongs to the fourth — the lost notebook. When Ramanujan returned to India in 1919 he carried a manuscript of about 138 pages from his final months: work on mock theta functions, q-series, and more. After his death it passed through several hands, became tangled with the papers of the mathematician G.N. Watson, and was nearly incinerated after Watson died in 1965 before surviving by chance and reaching the Wren Library at Trinity. There it sat, unsorted, until the spring of 1976, when the American mathematician George Andrews — who had written his doctorate on mock theta functions, precisely this subject — examined the Watson papers and recognised at once what he was holding.

The discovery was later described as the mathematical equivalent of finding Beethoven’s tenth symphony. The notebook held over 600 formulas, none published, and many among the most profound things he ever wrote — produced in his last year, while dying.

What Ramanujan Actually Discovered

He worked across several areas of mathematics. A brief tour gives a sense of what the achievement actually was — and how long the rest of the world took to catch up.

The mock theta functions were perhaps his deepest work, described in his last letter to Hardy. What they actually were went unexplained until 2002, when Sander Zwegers proved they were the holomorphic parts of objects called harmonic weak Maass forms. That breakthrough revealed connections to modular forms now found in the entropy of black holes and in string theory. Ramanujan had reached these objects by intuition eighty years before the framework to understand them existed.

The Source of His Genius: What We Know and Don’t

Hardy wrestled all his life with how Ramanujan did what he did. The standard account of discovery — deep study, formal training, gradual extension of known methods — described him not at all. Cut off from most of the mathematics of his era, he was forced to rediscover and reinvent from first principles. That isolation cost him effort on results already known in Europe. But it also meant he approached problems from directions no trained mathematician would have tried, and sometimes those directions led somewhere genuinely new.

It is a useful contrast with how machines search for answers today. An evolutionary algorithm explores a vast space of possibilities by brute trial, mutation, and selection. Ramanujan seemed to skip the search entirely — to arrive at the answer without visibly traversing the space at all. Hardy, who distrusted mystical explanations, never found a framework that fully accounted for what he had witnessed. The source of Ramanujan’s intuition remained, by his own admission, beyond his power to explain.

The Legacy: Why Ramanujan Still Matters

A century after his death, his work is not a historical curiosity but active mathematics. His mock theta functions, understood through Zwegers’ 2002 framework, are now central to the physics of black holes: the entropy of certain black holes can be expressed in terms of them. In string theory, the structures he identified appear in calculations of the quantum properties of strings.

He was doing physics he did not know he was doing, a century before the physics existed. His congruences seeded a whole field linking partitions to modular forms, and his circle method remains a working tool at the frontier of analytic number theory. The Rogers–Ramanujan identities — which he found independently in India — turned out in the 1980s to describe exactly solvable models in statistical mechanics, for reasons still not fully understood.

Ken Ono, who has spent decades working on Ramanujan’s legacy, is among many mathematicians still finding new paths through it. The enduring image is Freeman Dyson’s, from a 1987 lecture he titled “A Walk in Ramanujan’s Garden”: “The seeds from Ramanujan’s garden have been blowing on the wind and have been sprouting all over the landscape.”

Hardy’s Grief and the Question He Could Never Answer

Hardy outlived Ramanujan by twenty-seven years and never fully recovered from the loss. In his 1940 book A Mathematician’s Apology he returned again and again to Ramanujan as the measure of genuine greatness. Years later, when the young Paul Erdős asked Hardy what his greatest contribution to mathematics had been, Hardy answered without hesitation: the discovery of Ramanujan. In a lecture he described their collaboration as “the one romantic incident in my life” — and he meant it in the deepest sense, an encounter with something that exceeded the categories available for understanding it.

Ramanujan’s wife Janaki survived until 1994, living quietly in Madras. In her later years she spoke of a husband she had barely known — they had lived together only a few years in all — yet whose devotion she never forgot. In his final days, she recalled, even in great pain he would not stop, filling sheet after sheet with numbers. The image with which his story began is also the one with which it ends.

His story sits alongside other self-taught minds whose solitary intensity reshaped science — among them Paul Dirac, the strangest man in physics, and Richard Feynman, who made curiosity his instrument. Different temperaments, the same refusal to see the world the way they were told to.

Frequently Asked Questions

Sources

• Encyclopaedia Britannica — Srinivasa Ramanujan
• MacTutor History of Mathematics — Ramanujan
• Quanta Magazine — Ramanujan Was a Genius. Math Is Still Catching Up (2024)
• Wikipedia — Ramanujan’s Lost Notebook
• Wikipedia — Srinivasa Ramanujan
• George Andrews — Uncovering Ramanujan’s Lost Notebook (oral history)
• Springer — Ramanujan’s Lost Notebook, Part I (Andrews & Berndt)

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