The Man Who Knew Infinity

Hardy received the letter in January 1913 and spent the evening with it, at first suspicious, then increasingly disturbed in the best way. He showed it to his close collaborator J.E. Littlewood, and the two of them sat over it late into the night. Some of the theorems they recognized. Some they could prove only with effort. And some, Hardy admitted, he had never seen and could not begin to derive — formulas so strange that, as he famously put it, they must be true, because no one would have had the imagination to invent them if they were false.

The decision that followed was not automatic. Bringing an unknown, uncredentialed Indian to Cambridge meant vouching for him against every assumption of the place. Hardy did it. He arranged a fellowship and set about persuading Ramanujan to make the journey. That, too, was not simple. Ramanujan was an orthodox Brahmin for whom crossing the sea was a religious transgression, and his mother resisted fiercely. In the end a dream, a vision attributed to the family goddess Namagiri, cleared the way. In the spring of 1914 he boarded a ship for England.

The partnership that unfolded at Trinity between 1914 and 1919 was one of the strangest in the history of science, and Kanigel treats it as the heart of the book. Hardy was rigorous to the point of severity, a man who believed a result meant nothing without proof, that mathematics was a chain of logic every link of which had to hold. Ramanujan simply saw things. He produced conclusions the way other people remember faces, and grew impatient when asked to justify what seemed to him plainly true. Hardy's task became partly to teach proof to a man whose gift ran ahead of it — without breaking the gift in the process.

It was a delicate, sometimes painful negotiation. Push too hard on formal rigor and Hardy risked smothering the intuition that made Ramanujan valuable; push too little and the work could not enter mathematics as knowledge others could trust. The collaboration produced landmark papers all the same, most famously their work on the partition function — the number of ways a whole number can be broken into sums — where Ramanujan's instinct and Hardy's method fused into something neither could have reached alone. Together they built results that still anchor the field.

Step back from the illness and the awards, and Ramanujan's story keeps posing a question that mathematics has never fully answered: where do the results come from? He arrived at truths without the scaffolding of proof, sometimes without any visible reasoning at all, and a striking number of them turned out to be correct — including some that were only verified, or fully understood, decades after his death. His notebooks are still mined today; his formulas turn up in places he could not have foreseen, from the study of black holes to the behavior of certain crystals. A mind that worked by pure pattern left problems that rigorous minds are still catching up to.

Ramanujan attributed his insight to divine intervention, to the goddess Namagiri writing on his tongue. Hardy, an atheist, could not accept the explanation and had no better one. Kanigel does not try to settle it. What the book does instead is treat the mystery honestly: here was a way of doing mathematics so different from the trained Western method that the trained Western method could barely describe it, only confirm, after the fact, that it worked.

Ramanujan sailed home to India in 1919, already gravely ill, and died in April 1920 at the age of thirty-two, still working — the last notebook, the one now called the lost notebook, was found and studied only decades later, and its results confirmed his powers had not dimmed. Hardy outlived him by nearly thirty years and never stopped measuring himself against the friend he had summoned from Madras. He once ranked mathematicians on a scale of natural talent, put himself modestly, David Hilbert high, and Ramanujan at a hundred.