The Clerk Who Wrote to Cambridge

In the town of Kumbakonam in southern India, at the end of the nineteenth century, a quiet boy was teaching himself mathematics from a book that was already out of date.

His name was Srinivasa Ramanujan. He was born in December 1887 in Erode, and he grew up in a modest household in Kumbakonam. As a teenager he got hold of a book by G. S. Carr called A Synopsis of Elementary Results in Pure and Applied Mathematics. It was not a textbook in the usual sense. It listed thousands of formulas and results, mostly without explaining how they had been proved.

For most students it would have been dry reading. For Ramanujan it was a door. He worked through it alone and then went far beyond it, filling notebooks with results of his own.

A brilliant student who failed

His gift was obvious, and it was also a problem. Ramanujan was so absorbed in mathematics that he neglected his other subjects. He won a scholarship to the Government College in Kumbakonam and then lost it after failing in other subjects. He tried again at a college in Madras (now Chennai) and again did not pass the examinations.

By his early twenties he had no degree, very little money and a family to support. He went looking for work, carrying his notebooks with him and showing them to anyone who might understand them.

A few people did see something remarkable. With their help, in 1912 he got a job as a clerk in the accounts section of the Madras Port Trust. It was steady work. In his spare moments he kept doing mathematics.

The letter

Ramanujan knew that his ideas needed experts who could judge them. He wrote to several mathematicians in England. According to his biographers, his first letters did not lead anywhere.

Then, in January 1913, he wrote to G. H. Hardy, a leading mathematician at Trinity College, Cambridge.

The letter was polite and modest. It described the writer as a clerk with no university training, and it went on to fill several pages with theorems and formulas. There were well over a hundred of them, given mostly without proofs.

Hardy could easily have put it aside. Unsolicited letters from people claiming great discoveries were not unusual, and many of them were nonsense. At first glance some of Ramanujan's results looked strange or even wrong.

But Hardy kept reading. With his colleague J. E. Littlewood, he went through the pages carefully. Some results were already known. A few were mistaken. Others were completely new, and some were so unusual that Hardy found it hard to imagine how anyone had arrived at them. In his later writings, Hardy made clear that he had quickly concluded he was dealing with a mathematician of the very highest class.

Cambridge

Hardy worked to bring Ramanujan to England. It was not a simple decision for Ramanujan, who faced religious and family concerns about crossing the sea. In 1914 he made the journey and arrived at Cambridge.

The collaboration between the two men became one of the most famous in the history of mathematics. Hardy was rigorous and believed in careful, complete proofs. Ramanujan relied on deep intuition and often reached results by routes he could not fully explain. Each pushed the other. Together they published important work, especially on partitions, which concern the number of ways a whole number can be written as a sum of smaller ones.

Recognition followed. In 1918 Ramanujan was elected a Fellow of the Royal Society, one of the youngest people ever to receive the honour at the time. The same year he became a Fellow of Trinity College.

Illness and legacy

England was hard on him. The climate, the food, the isolation and the strains of the First World War all took their toll. He fell seriously ill. In 1919 he returned to India, and he died in April 1920, at the age of just thirty-two.

His work did not die with him. Mathematicians spent decades proving the results in his notebooks. In 1976 the mathematician George Andrews came across a bundle of Ramanujan's later papers in the library at Trinity College. It became known as the "lost notebook", and it set off a new wave of research.

Today Ramanujan's ideas are used in areas that he could not have imagined, and his birthday, 22 December, is celebrated in India as National Mathematics Day.

Two acts of courage

It is easy to tell Ramanujan's story as one about genius alone. But it rests on two acts of courage.

The first was Ramanujan's. A clerk with no degree, who had been turned down more than once, sent his life's work to a stranger on the other side of the world.

The second was Hardy's. A busy, celebrated professor took a strange letter seriously enough to read it twice.

Both are worth remembering the next time we're tempted to hide our work, or to dismiss someone else's.