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

by Robert Kanigel

His was a mind, perhaps, whose critical faculty was weak compared to its creative and synthetical.

unconscious activity often plays a decisive part in discovery; that periods of ineffective effort are often followed, after intervals of rest or distraction, by moments of sudden illumination; that these flashes of inspiration are explicable only as the result of activities of which the agent has been unaware—the evidence for all this seems overwhelming.

The number of its partitions—or to invoke a precision that now becomes necessary, the number of its “unrestricted” partitions—is 42.

“Ramanujan represents so extreme a fluctuation from the norm that his being born an Indian must be considered to a large extent as accidental.”

And yet, its underground tendrils ranged into fields far distant from pure mathematics—and into applications which, Hardy might have cringed to learn, were by no means “useless.”

Whether and how the engineers and chemists might indeed apply Ramanujan’s work to the common purposes of life strikes a sensitive chord in India, beset as it is by practical problems of great urgency and less naturally inclined to trust in research whose rewards may accrue only decades or centuries later. “Several theorems of Ramanujan are now being widely used in subjects like particle physics, statistical mechanics, computer science, cryptology and space travel in the United States—subjects unheard of during Ramanujan’s time,” The Hindu assured its readers in its December 19, 1987 issue. But efforts to justify Ramanujan’s work on utilitarian grounds go back almost to his lifetime.

An important problem in statistical mechanics has also proved vulnerable to Ramanujan’s mathematics—a theoretical model that explains, for example, how liquid helium disperses through a crystal lattice of carbon. As it happens, the sites helium molecules may occupy in a sheet of graphite, say, can never lie adjacent to one another. Since each potential site is surrounded by six neighbors in a hexagonal array, once it is filled, the six around it define an unbreachable hexagonal wall. Reviewing in 1987 the work for which he received the prestigious Boltzmann Medal seven years earlier, R. J. Baxter of the Australian National University in Canberra set out the thinking behind his “hard hexagon model.” Mathematically, he showed, it was built on a particular set of infinite series. And “these series,” he observed, “are precisely those that occur in the famous Rogers-Ramanujan identities” (though he hadn’t realized it back in 1979 when he’d found them on his own). Based on them, he found a way to determine the probability that any particular site harbored a helium molecule; predictions borne of the model agreed closely with experiment. “The Rogers-Ramanujan identities,” Baxter concluded, “are perhaps not so remote from ‘ordinary human activity’ as Hardy would have liked!”

Because it lies on a cool, ethereal plane beyond the everyday passions of human life, and because it can be fully grasped only through a language in which most people are unschooled, Ramanujan’s work grants direct pleasure to only a few—a few hundred mathematicians and physicists around the world, perhaps a few thousand. The rest of us must either sit on the sidelines and, on the authority of the cognoscenti, cheer, or else rely on vague, metaphoric, and necessarily imprecise glimpses of his work.

Watson concluded his presidential address to the London Mathematical Society in 1937 by saying that one Ramanujan formula gave him “a thrill which is indistinguishable from the thrill which I feel when I enter the Sagrestia Nuova of the Capelle Medicee and see before me the austere beauty of the four statues representing, ‘Day,’ ‘Night,’ ‘Evening,’ and ‘Dawn’ which Michelangelo has set over the tombs” of the Medicis.

Paul Erdos has recorded that when Hardy was asked about his greatest contribution to mathematics, he unhesitatingly replied, “The discovery of Ramanujan.” At another time, indeed, Hardy went on record as calling him “my discovery.”

Ramanujan did what he wished to do, went his own way. It was only later, after he had indulged in an orgy of mathematical creation, that he might wake up and realize how far he had strayed from the common run of human intercourse. Only then might he begin to care, sometimes painfully much, how others thought of him.

Hardy discovered Ramanujan? Not at all: a glance at the facts of 1912 and 1913 shows that Ramanujan discovered Hardy.

“I did not invent him,” Hardy once said of Ramanujan. “Like other great men he invented himself.” He was svayambhu.

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.