He Taught Himself Mathematics From a Single Book. Then He Rewrote the Rules of the Subject Entirely.

Some of what he wrote down still hasn't been explained.

The Book

In 1903, a fifteen-year-old boy in the town of Kumbakonam in southern India borrowed a book from a local library. It was not a novel or a collection of stories. It was a dense, dry mathematics reference called A Synopsis of Elementary Results in Pure and Applied Mathematics — a textbook containing thousands of theorems, listed without explanation or proof, intended as a reference for university students who already understood the subject.

The boy’s name was Srinivasa Ramanujan. He had no university. He had no teacher. He had no one to explain what any of it meant. He sat with the book and worked through it alone — not just verifying the theorems but extending them, questioning them, generating new ones from scratch. Mathematics, which he had always loved instinctively, suddenly had a language he could read.

The problem was that it became the only language he wanted to speak. He neglected every other subject. He lost his scholarships. He failed out of college twice. He lived in poverty in a small house with his mother, filling notebooks with theorems that no one around him could evaluate or understand. He worked through hunger and illness and obscurity, driven by something he described as a kind of divine compulsion — he was a devout Hindu and attributed his mathematical insights to his family deity, the goddess Namagiri. “An equation for me has no meaning,” he once said, “unless it represents a thought of God.”

The Letter

By 1912, Ramanujan was twenty-four years old, working as a clerk at the Madras Port Trust Office — a clerical job that paid enough to survive and left his mind free to work on mathematics during every spare hour. He had been sending letters to prominent mathematicians in England, enclosing pages of his theorems. Most ignored him. A few responded politely but without interest.

On January 16, 1913, he sent a letter to G.H. Hardy — a mathematician at Trinity College, Cambridge, widely regarded as one of the finest in England. The letter contained nine pages of mathematical results. Hardy read the first few and set them aside, uncertain what to make of them. That evening, he sat down with his colleague J.E. Littlewood and went through the pages carefully.

What they found was unlike anything either of them had seen. Some of the theorems were already known — Hardy recognized them. But others were entirely new, unlike any mathematics being done anywhere in the world. And they were correct. Not approximately correct. Precisely, demonstrably, rigorously correct — derived by a man with no formal training, working alone in a small house in southern India, who had taught himself everything he knew from a single borrowed book.

Hardy later wrote that the letter was “in the same class as Gauss and Euler” — two of the greatest mathematicians in human history. He arranged for Ramanujan to come to Cambridge immediately.

The Years at Cambridge

Ramanujan arrived in England in April 1914. The culture shock was considerable — the climate, the food, the customs, the profound difference between colonial India and Edwardian Cambridge. He was a devout Brahmin vegetarian in a country that understood neither. He struggled. He was often ill. He was often lonely.

But the mathematics poured out of him. Working alongside Hardy, Ramanujan published paper after groundbreaking paper — on number theory, on infinite series, on partitions, on prime numbers. In 1918, he was elected a Fellow of the Royal Society, one of the most prestigious scientific honors in the world. He was thirty years old. He was only the second Indian ever to receive the distinction.

Hardy later described their collaboration as the most remarkable of his career. He developed what became known as the Hardy-Ramanujan number — 1729 — after a famous anecdote. Hardy had visited Ramanujan in a hospital, arriving in a taxi numbered 1729, and remarked that the number seemed unremarkable. Ramanujan immediately replied that 1729 was in fact the smallest number expressible as the sum of two cubes in two different ways. He was lying in a hospital bed, gravely ill, and doing that in his head.

The End

The English climate and diet were incompatible with Ramanujan’s health. He contracted tuberculosis. By 1919 he was too ill to continue and returned to India. He was thirty-one years old. He continued working on mathematics from his sickbed — his final notebooks, filled with theorems in what he called “mock theta functions,” would not be fully understood by mathematicians for decades.

Srinivasa Ramanujan died on April 26, 1920. He was thirty-two years old. He left behind three notebooks and a “lost notebook” — discovered in 1976 in a box at Trinity College Cambridge — containing thousands of results that mathematicians are still working to prove and understand today. A century after his death, papers are still being published verifying theorems he wrote down in a small house in southern India, alone, with no teacher, no institution, and one borrowed book.

The Record Shows

What makes Ramanujan’s story resist easy summary is the question it leaves unanswered: where did it come from? Hardy — one of the most rigorous mathematical minds of his era — never fully resolved it. He rated mathematicians on a scale of 0 to 100 and gave himself 25, giving Ramanujan 100. “Every positive integer,” Ramanujan once said, “is one of my personal friends.” He spoke about mathematics the way mystics speak about faith — as something revealed rather than derived. Whether his genius came from God, from that borrowed book, or from somewhere no one has yet been able to name, we are still using what he left behind. And still catching up.

Sources

· Britannica — Srinivasa Ramanujan (britannica.com/biography/Srinivasa-Ramanujan)

· Quanta Magazine — Srinivasa Ramanujan Was a Genius. Math Is Still Catching Up. (quantamagazine.org)

· Linda Hall Library — Srinivasa Ramanujan (lindahall.org)

· Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. Scribner, 1991.

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