The Man Who Knew Infinity: A Life of the Genius Ramanujan

They must be true because, if they were not true, no one would have the imagination to invent them.

Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package.

But what Ramanujan wanted more, more than anything, was simply the freedom to do as he wished, to be left alone to think, to dream, to create, to lose himself in a world of his own making.

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.

Don’t be so easy on yourself, it said.

His academic failure forced him to develop unconventionally, free of the social straightjacket that might have constrained his progress to well-worn paths.

Ramanujan’s refrain was always the same—that his parents had made him marry, that now he needed a job, that he had no degree but that he’d been conducting mathematical researches on his own. And here … well, why didn’t the good sir just examine his notebooks. His notebooks were his sole credential in a society where, even more than in the West, credentials mattered; where academic degrees usually appeared on letterheads and were mentioned as part of any introduction; where, when they were not, you’d take care to slip them into the conversation. “Like regiments we have to carry our drums, and tambourinage is as essential a thing to the march of our careers as it is to the march of soldiers in the West,” Indian novelist and critic Nirad C. Chaudhuri has written of his countrymen’s bent for self-promotion. “In our society, a man is always what his designation makes him.” Ramanujan’s only designations were unemployed, and flunk-out. Without his B.A., one prominent mathematics professor told him straight out, he would simply never amount to anything.

In the West, there was an old debate as to whether mathematical reality was made by mathematicians or, existing independently, was merely discovered by them. Ramanujan was squarely in the latter camp; for him, numbers and their mathematical relationships fairly threw off clues to how the universe fit together. Each new theorem was one more piece of the Infinite unfathomed. So he wasn’t being silly, or sly, or cute when later he told a friend, “An equation for me has no meaning unless it expresses a thought of God.

Ramanujan was not the first foreigner to retreat into his shell in a new country; indeed, his was the typical response, not the exceptional one. One later study of Asian and African students in Britain observed that a sense of exclusion “from the life of the community … constituted one of the most serious problems with which they were confronted … [and had] a serious psychological effect” upon them. Another study, this time of Indian students in particular, reported that while 83 percent of them saw friends more or less every day back in India, just 17 percent did while in England.

A pure mathematician must leave to happier colleagues the great task of alleviating the sufferings of humanity.

The Riemann zeta function was a simple enough looking infinite series expressed in terms of a complex variable. Here, “complex” means not difficult or complicated, but refers to a variable of two distinct components, “real” and “imaginary,” which together could be thought to range over a two-dimensional plane. In 1860, Georg Friedrich Bernhard Riemann made six conjectures concerning the zeta function. By Ramanujan’s time, five had been proven. One, enshrined today as the Riemann hypothesis, had not

He received no guidance, no stimulation, no money beyond the few rupees he made from tutoring. But for all the economic deadweight he represented, his family apparently discouraged him little- not enough, in any case, to stop him.

Viewed one way, then, for at least five years between 1904 and 1909, Ramanujan floundered- mostly out of school, without a degree, without contact with other mathematicians. And yet, was the cup half-empty or half-full?

Ramanujan had lost all his scholarships. He had failed in school. Even as a tutor of the subject he loved most, he'd been found wanting. He had nothing. And yet, viewed a little differently, he had everything. For now there was nothing to distract him from his notebooks- notebooks, crammed with theorems, that each day, each week, bulged wider.

Then, too, it seems certain, in light of future events, simple racism was a factor; Ramanujan, after all, was a black man.

The cards are stacked, against any original mind, and perhaps properly so.