At one point, Hardy admitted that, quoting Hadamard, “ ‘the unconscious is not merely automatic, it has tact and delicacy,’ even that ‘it knows better how to divine than the conscious self, since it succeeds where that has failed.’ But I do not like this kind of language,” Hardy went on; to him it verged on nonsense.
“It is something of a relief,” he wrote in the most revealing admission of all, “to pass to the later chapters, which are full of interesting and less controversial matter.”
This soft, ineffable region of unconscious processes, of vague, hazy connections and suddenly appearing insights, of loose ties and nameless links, was not, Hardy’s remarks suggest, any place where he himself liked to dwell. He was uncomfortable discussing it, uncomfortable thinking about it. That mathematics was a “creative” activity was not the question; it was among the most creative. But as to its source—there he didn’t care to delve. Certainly, then, any resort to Eastern mumbo jumbo to explain Ramanujan’s mathematical gifts would not have drawn from him a warm reception.
• • •
But it was Hardy, the dedicated atheist, who represented the extreme position, and Ramanujan who was more in line with the large body of belief and conviction, within the Western tradition as well as that of the East, that perceived links between creativity and intuition on the one hand and spiritual forces on the other.
The Greeks, for example, invoked the muses—goddesses to whom poets looked for inspiration. Both the English and French languages speak of “divining” the truth. Hadamard himself noted that the sheer inaccessibility of unconscious thought had, to thinkers over the centuries, endowed it with higher powers.
That unconsciousness may be something not exclusively originating in ourselves and even participating in Divinity seems already to have been admitted by Aristotle. In Leibniz’s opinion, it sets the man in communication with the whole universe, in which nothing could occur without its repercussion in each of us; and something analogous is to be found in Schelling; again, Divinity is invoked by Fichte; etc.
Even more recently, a whole philosophical doctrine has been built on that principle in the first place by Myers, then by William James himself … , [in which] the unconscious would set man in connection with a world other than the one which is accessible to our senses and with some kinds of spiritual beings.
Just as India was not alone in attributing creative insights to divine influence, Ramanujan was not alone among mathematicians in holding strong religious beliefs. Newton was an unquestioning believer, felt humility in the face of the universe’s wonders, studied theology on his own. Euler, in E. T. Bell’s words, “never discarded a particle of his Calvinistic faith,” and grew more religious as he grew older. Cauchy was forever trying to convert other mathematicians to Roman Catholicism. Hermite had a strong mystical bent. Even Descartes, that father of Enlightenment rationality, answered the call of the spirit: “His religious beliefs were unaffectedly simple in spite of his rational skepticism,” writes Bell. “He compared his religion, indeed, to the nurse from whom he had received it, and declared that he found it as comforting to lean upon one as on the other.” (Adds Bell, wisely: “A rational mind is sometimes the queerest mixture of rationality and irrationality on earth.”)
Even among mathematicians not religiously minded, one finds evidence of at least respectful allusion to the dark terrain between faith and reason. Gauss, for example, once proved a theorem, as he wrote, “not by dint of painful effort but so to speak by the grace of God.” James Hopwood Jeans, Hardy’s Cambridge classmate and a famous applied mathematician, wrote: “From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.” Even Littlewood, commenting on an incident in which “my pencil wrote down” the solution to a particularly bedeviling problem, could write, “If we may reject divine bounty, it happened exactly as if my subconsciousness knew the thing all the time.” Littlewood’s, of course, was the usual safe, ironic Cambridge skepticism, perhaps no more than a stylistic device—just as the other statements may be seen as no more than metaphor. Yet each contained the barest breath of ambivalence or humility in the face of the mysterious origins of human creativity.
Hardy, though, did not admit to such ambivalence. For him, the whole spiritual realm was just so much bunkum. He knew—this was his faith—that wherever Ramanujan’s genius came from, there was something straightforward to explain it. He would write:
I have often been asked whether Ramanujan had any special secret; whether his methods differed in kind from those of other mathematicians; whether there was anything really abnormal in his mode of thought. I cannot answer these questions with any confidence or conviction; but I do not believe it. My belief is that all mathematicians think, at bottom, in the same kind of way, and that Ramanujan was no exception.
Ramanujan’s mathematics, he was saying, was the product of the reasoned working of a reasoning mind, and nothing more needed to be said.
Someone would later observe that “Hardy’s deep reverence for mathematics and for all things of the mind was precisely of the same kind as impels other people to the worship of God; the only enigma about Hardy was that this never seemed to occur to him.” And at least for public consumption, it never did. Had Ramanujan scoured the British Isles, he could have found no one less sympathetic to his spiritual side, no one who, in this one realm, could appreciate him less.
In defending his belief in Ramanujan’s lack of genuine religious feeling, Hardy would argue that “if a strict Brahmin like Ramanujan told me, as he certainly did, that he had no definite beliefs, then it is 100 to 1 that he meant what he said.” No matter that Ramanujan’s statement was, in the context of the relaxed tolerance of Hinduism, by no means incompatible with strong religious feeling. Hardy concludes that “if Ramanujan’s friends assumed that he accepted the conventional doctrines of [Hinduism] … and he did not disillusion them, he was practicing a quite harmless, and probably necessary, economy of truth.”
A harmless economy of truth was indeed what Ramanujan was perpetrating but, almost certainly, it was Hardy who was its object. Ramanujan probably wasn’t long in England before Hardy let him know, perhaps without even realizing it, that invocations of Namagiri were not apt to be well received. Faced with a man once described as “an atheist evangelical,” and hardly wishing to provoke his benefactor and friend on what was such touchy ground, Ramanujan simply never revealed to him the richness and extent of his inner spiritual life.
And that was the problem: with Hardy, Ramanujan could not let his hair down—had to dissemble, could not be himself. There remained between the two men a great, unbridgeable gap. Even after working with him for several years, the conclusion is inescapable, Hardy never really knew Ramanujan—and thus could be no real buffer against the profound loneliness Ramanujan felt in England.
10. SINGULARITIES AT X = 1
Three-quarters of a century later, in 1989, the black dean of an all-black women’s college in Georgia recalled her stint as an administrator at a mostly white college up north. “The black students I knew at Haverford may have done well,” she said, “but I never got the feeling they were happy”—because they couldn’t be themselves, couldn’t be black. And just such a split applied to Ramanujan in Cambridge. He had, under Hardy’s guiding hand, done well; but he was not happy.
He may not have even realized it himself; Ramanujan was not someone closely attuned to his own feelings. It would have been perfectly possible for him to exult in mathematics, to derive enormous satisfaction from his intellectual dialogue with Hardy, to be to all outward appearances content—indeed, to call himself content—and yet, for other needs he could scarcely name and only dimly sense, feel incomplete.
Seasoned travelers invariably note how adjusting to another culture demands flexibility, a willingness to assume the coloration of the new country. The experiences of expatriates, immigrants, and visiting students all attest to the same thing. But flexibility w
as one trait Ramanujan did not possess in great measure. It took enormous energy to cast off the old and take on the new, not to mention the will to do so. And Ramanujan put all his energy into mathematics. He did not flex as the raw English winds blew around him.
So he broke. First in body, then in mind.
• • •
In 1916, Ramanujan’s tutor Barnes had written the University of Madras that, given Ramanujan’s achievements, it seemed likely he would be elected a Fellow of Trinity College the following October. But October 1917 came and went without Ramanujan’s election. At the time, the college was wracked with dissension over the Bertrand Russell affair, and Ramanujan’s champion, Hardy, was squarely in the out-of-favor camp. Then, too, it seems certain, in light of future events, simple racism was a factor; Ramanujan, after all, was a black man.
The disappointment left Ramanujan’s mood darker, the whole structure of his personality that much shakier.
It was around this time that he entered Matlock, which could hardly have lifted his spirits. English sanatoriums were typically presided over by stern, patriarchal figures, strict disciplinarians who ruled with an iron hand. And Matlock was in the mold. A friend would later recall that Ramanujan was “cowed down by Dr. Ram, who seems to have told him, ‘As long as you are a patient and not well you are not free and the doctor has control over your movements.’ ”
Matlock was typical of English sanatoriums in at least one other respect: it was out-of-the-way geographically. “There is much evidence to suggest,” writes Bryder in her study of British tuberculosis care, “that inmates of sanatoria felt estranged from the outside world. Not only did their geographical isolation make visits difficult and therefore infrequent, but social attitudes accentuated that isolation.” At Matlock, located about 150 miles northwest of London, in the Peak District of Derbyshire, Ramanujan enjoyed no steady stream of visitors. Getting there was not easy. The following year, a friend who did make the trip, A. S. Ramalingam, would write of the “cold weary journey” on the night train he’d had to endure. Hardy was almost certainly thinking of the Matlock period when he wrote, a few months after Ramalingam’s visit, of Ramanujan’s “long illness and the spells of comparative solitude” influencing his mental state.
At Matlock, Ramanujan was cold and miserable much of the time. The Trinity fellowship rejection rankled. And he was too sick to be productive mathematically, which also distressed him. The doctors didn’t suit him. He couldn’t get food to eat and the food he could get he didn’t like; sometimes he craved the hot dosai, a kind of pancake, that Anantharaman’s mother would cook up for him back in Kumbakonam. Finally, he was getting little in the way of nurturing and emotional support from home. And he wasn’t getting it from Hardy, either.
He grew profoundly depressed. At one point, he had nightmares in which he was visited by images of his own abdomen as a kind of mathematical appendage with “singularities,” points in space marked by indefinable mathematical surges like those he and Hardy had explored in their partitions work. Intense pain might show up at x = 1, half as much pain at x = − 1, and so on. The nightmares recurred.
Ramanujan was at a low ebb, balanced precariously on the edge of mental instability.
• • •
Undeterred by the Trinity rebuff and hoping to boost Ramanujan’s morale, Hardy set about trying to get his friend the recognition he felt he deserved. On December 6, 1917, Ramanujan was elected to the London Mathematical Society. Then, two weeks later, on December 18, Hardy and eleven other mathematicians—Hobson and Baker were among them, as were Bromwich, Littlewood, Forsyth, and Alfred North Whitehead, Bertrand Russell’s collaborator on Principia Mathematica—together put him up for an honor more esteemed by far than any fellowship of a Cambridge college: they signed the Certificate of a Candidate for Election that nominated him to become a Fellow of the Royal Society.
The Royal Society was Britain’s preeminent scientific body, going back to 1660 when Christopher Wren and Robert Boyles helped found it. There were, at about the time Hardy put up Ramanujan, 39 foreign members, including the Russian Ivan Pavlov, the American Albert Michelson (of Michelson-Morley experiment fame), and 6 other Nobel Prize winners. The Royal Society counted in all 464 members in physics, chemistry, biology, mathematics, and every branch of science. Being an F.R.S. meant that forevermore those three little letters would be appended to your name, appear on your own scientific papers, and on letters addressed to you. It was the ultimate mark of scientific distinction. Younger scientists lusted after it, older scientists lamented their lack of it.
C. P. Snow tells the story of H. G. Wells, author of War of the Worlds, The Time Machine, many other scientific romances, and serious works of history and social comment as well. But while famous and the recipient of numerous honors, “there was,” as Snow would write of him, “precisely one honor he longed for. It went back to his youth, when he day-dreamed about being a scientist. He wanted to be an F.R.S. And this desire, instead of becoming weaker as he got older, became more obsessive.” He never received it, because though he had studied science in school and had, in Snow’s words, “been the prophet of twentieth century science more effectively than any man alive,” he had not himself actually made original research contributions.
It was this signal honor Hardy sought for his friend and for which he set out Ramanujan’s “Qualifications” in his distinctive calligraphic hand:
Distinguished as a pure mathematician, particularly for his investigations in elliptic functions and the theory of numbers. Author of the following papers amongst others: “Modular Equations and Approximations to Pi,” Quarterly Journal, vol. 45; “New Expressions for Riemann’s Functions ξ(s) and Ξ (t),” ibid, vol. 46; “Highly Composite Numbers,” Proc. London Math. Soc, vol. 14 … Joint author with G. H. Hardy, F.R.S., of the following papers: “Une formule asymptotique pour le nombre des partitions de η,” Comptes Rendus, 2 Jan. 1917 …
Thus it continued, listing Ramanujan’s papers, and ending with perhaps the most important of all—“Asymptotic Formulae in Combinatory Analysis,” the big partitions paper still awaiting publication in the Proceedings of the London Mathematical Society.
On January 24, 1918, the names of Ramanujan and 103 other candidates were read out at a meeting of the society. If past experience applied, only a few of them would be elected.
There was no question in Hardy’s mind, or Littlewood’s, or anyone else’s, that Ramanujan merited the honor. Still, few candidates made it the first time out, and by normal practice his nomination was premature. Hardy had been thirty-three years old when elected in 1910. Littlewood himself had made it only the previous February, also at age thirty-three—more than a decade, and dozens of notable mathematical papers, beyond his early glory as a Senior Wrangler. Ramanujan, still twenty-nine at the time of his nomination, had contributed to European mathematics for just a few years and still had a modest publication record, at least in number.
But Hardy’s concern for Ramanujan’s health moved him to press his claim with unusual urgency. J. J. Thomson, discoverer of the electron, winner of the Nobel Prize in 1906, and then president of the Royal Society, had asked him to outline the circumstances surrounding Ramanujan’s candidature. “If he had not been ill I would have deferred putting him up a year or so,” Hardy admitted: “not that there is any question of the strength of his claim, but merely to let things take their ordinary course. As it is, I felt no time must be lost.”
Ramanujan might not make it to the next election, he was saying, and the society would have to live forever with its failure to honor him. “I am nervous about trying to rush him,” Hardy continued,
and I am aware that for the time being I am not an ideal supporter. And I realize that the R.S. has many other things to consider. But there is no doubt that (especially after his disappointment in the Fellowships) any striking recognition now might be a tremendous thing for him. It would make him feel that he was a success, and that it was worth while going on trying
. It is this much more than the fear of the R.S. losing him entirely which seems to me important.
I write on the hypothesis that his claims are such as, in the long run in any case, could not be denied. This is to me quite obvious. There is an absolute gulf between him and all other mathematical candidates.
Hardy’s letter suggested another reason for Ramanujan’s mental anguish: it would make him feel that he was a success. For all Hardy’s encouragement, Ramanujan had come to understand how great a price he’d paid for his isolation in India. From the moment he’d stepped off the boat he’d been confronted, through Hardy, with how much he hadn’t known, learned, or appreciated before—with function theory, with Cauchy’s integral theorem, with so much else that was common knowledge in the West and which, by rights, he should have learned ten years before.
“It is perhaps useless to speculate as to his history had he been introduced to modern ideas and methods at sixteen instead of twenty-six,” Hardy would write after Ramanujan’s death. “It is not extravagant to suppose that he might have become the greatest mathematician of his time.”
Of Ramanujan’s work in India, Hardy would observe that it was inevitable that much had been anticipated, since Ramanujan labored under “an impossible handicap, a poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe.”
And this was what he had to say of the period between when Ramanujan left Government College and when he joined the Madras Port Trust: “The years between eighteen and twenty-five are the critical years in a mathematician’s career, and the damage had been done. Ramanujan’s genius never had again its chance of full development.”
Given his relentless honesty, could Hardy have failed to convey such sentiments to Ramanujan? And could Ramanujan have failed to have been wounded by them?
Ramanujan may have known nothing of Hardy’s efforts to have him named an F.R.S.; but if he did know of them, by now he doubtless assumed they would come to nothing, could lead only to the kind of humiliating blow he had suffered when Trinity turned him down in October.
The Man Who Knew Infinity Page 37
