impressed me as comparable in originality with that of a Mathematics fellow in a Cambridge College; it appears to lack, however, as might be expected in the circumstances, the completeness and precision necessary before the universal validity of the results could be accepted. I have not specialised in the branches of pure mathematics at which he has worked, and could not therefore form a reliable estimate of his abilities, which might be of an order to bring him a European reputation. But it was perfectly clear to me that the University would be justified in enabling S. Ramanujan for a few years at least to spend the whole of his time on mathematics without any anxiety as to his livelihood.
Walker, his letter as much as said, was as mystified by Ramanujan’s work as everyone else was. Heaven knows, he was no pure mathematician. As a young man, he’d shown interest in gyroscopes and electromagnetics. Early prominence had come from his studies of aerodynamic forces on the boomerang, which as an undergraduate he liked to throw on the Cambridge Backs. Now, as India’s chief weatherman, his most recent paper was entitled “The Cold Weather Storms of Northern India.” In other words, he was a mathematician of applied bent whose work lay as far distant from Ramanujan’s as it was possible to be. His statement, I have not specialised … was gross understatement, his admission that he could not form a reliable estimate of his abilities the plain, simple truth.
And yet none of this discouraged him from eagerly recommending Ramanujan for a special scholarship. Because now, in any appraisal of Ramanujan, there was a new factor to consider: Hardy. Spring, who had introduced Walker to Ramanujan’s work, and everyone else at the Port Trust knew that Ramanujan had Hardy’s imprimatur. If Walker harbored any doubt as to Ramanujan’s merits, Hardy’s verdict erased it. The wheels of Ramanujan’s career, for ten years barely creaking along, now, greased by Hardy’s approval, began to whirr and whine like a finely tuned race car engine.
If Ramanujan had doubts about what Hardy’s endorsement might mean to him, they had been dispelled by the last two days and Walker’s ringing endorsement. On February twenty-seventh, he wrote Hardy a second letter, again packed with theorems. “I am very much gratified on perusing your letter of 8th February 1913,” he wrote. “I have found a friend in you who views my labours sympathetically.”
In fact, it was not just Walker, Spring, and others in the Madras mathematical community who had been fortified by Hardy’s letter. It was Ramanujan himself. For all his confidence in his mathematical prowess, Ramanujan needed outside approval, affirmation. Now he had it. Hardy’s letter took him seriously. And the pronouncement delivered by this unseen F.R.S., this man reputed to be the finest pure mathematician in England? It was no vague, empty one filled with glowing accolades that Ramanujan might, in an anxious moment, dismiss, but rather nine pages of specific, richly detailed comment: a statement Ramanujan had written on his sixth page of theorems about a series expressible in terms of pi and the Eulerian constant could be deduced from a theorem in Bromwich’s Infinite Series (the book M. J. M. Hill, in his letter of two months before, had advised that he consult). A theorem on the same page involving hyperbolic cosines Hardy himself had proved in Quarterly Journal of Mathematics. Hardy knew.
That Ramanujan had every bit the “invincible originality” with which Hardy would later credit him didn’t mean he didn’t care what others thought of him. He did care. In assessing Ramanujan’s work, Hardy had informally broken it down into three broad categories—those results already known or easily derived from known theorems; those curious, and perhaps even difficult, but not terribly important; and those promising to be important indeed, if they could be proved. In Hardy’s mind, plainly, it was those in this third category that weighed most heavily.
But not in Ramanujan’s.
“What I want at this stage,” he wrote Hardy, “is for eminent professors like you to recognize that there is some worth in me.” And such “worth,” he felt, accrued not alone, or even primarily, through the theorems Hardy saw as novel and important, but those he’d ranked in the first category, as already known. It was these, he wrote, “which encourage me now to proceed onward. For my results are verified to be true even though I may take my stand upon slender basis.” Before the world whose judgment mattered so much to him, he could stand tall and declare, I have been pronounced by competent authority to be just as I said I was—which was more, for example, than his repeated flunking out of school had seemed to say.
In his second long letter to Hardy, Ramanujan seemed buoyant, pumped up, cocky. Hardy wanted proof? Well, he wrote
If I had given you my methods of proof I am sure you will follow the London Professor [Hill]. But as a fact, I did not give him any proof but made some assertions as the following under my new theory. I told him that the sum of an infinite no. of terms of the series:- 1 + 2 + 3 + 4 + … = −1/12 under my theory. If I tell you this you will at once point out to me the lunatic asylum as my goal. I dilate on this simply to convince you that you will not be able to follow my methods of proof if I indicate the lines on which I proceed in a single letter. You may ask how you can accept results based upon wrong premises. What I tell you is this: Verify the results I give and if they agree with your results, got by treading on the groove in which the present day mathematicians move, you should at least grant that there may be some truths in my fundamental basis.
Got by treading on the groove! Ramanujan was flying high. Four years of hawking his mathematical wares had left him neither shy about going after what he needed nor above stooping to self-pity: “I am already a half-starving man,” he wrote Hardy now. “To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the University or from Government.”
In this vein Ramanujan continued for two pages, then proceeded to pile up more theorems, expanding on the ideas about prime numbers on which Hardy had challenged him, and going on to new work—in all, nine more theorem-stuffed pages. “I have also given meanings to the fractional and negative no. of terms in a series as well as in a product,” he wrote, “and I have got theorems to calculate such values exactly and approximately. Many wonderful results have been got from such theorems… .”
Later, many would see in Ramanujan an appealing and genuine humility. But here were hints of another Ramanujan, one already dreaming of a place for himself in mathematical history: “You may judge me hard that I am silent on the methods of proof,” he wrote. But his silence was due only to lack of space in which to set them down, not unwillingness to do so. No, he wrote, “I do not mean that the methods should be buried with me.”
Humble? E. H. Neville would later describe Ramanujan as “perfect in manners, simple in manner, resigned in trouble and unspoilt by renown, grateful to a fault and devoted beyond measure to his friends.” Nowhere, though, did he call him humble, or suggest that Ramanujan shrank from a sanguine assessment of his own gifts. Nor does his later remark to Janaki that, in her words, “his name would live for one hundred years,” suggest undue humility. There had been a stubborn, self-confident streak in Ramanujan all along; for him to work, unrecognized and alone for years, fortified only by his delight in the work itself, it had to have been there. And here, in his second letter to Hardy, it unabashedly surfaced.
Hardy, we may be sure, was not put off by any of this. “Good work,” he once wrote, “is not done by ‘humble’ men.”
• • •
On March 13, spurred by Walker’s letter, B. Hanumantha Rao, professor of mathematics at the engineering college, invited Narayana Iyer to a meeting of the Board of Studies in Mathematics to discuss “what we can do for S. Ramanujan… . You have seen some of his results & can help us to understand them better than the author himself.” On the nineteenth, the board met and recommended to the syndicate, the university’s governing body, that Ramanujan receive a research scholarship of seventy-five rupees a month—more than twice his Port Trust salary—for the next two years.
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p; But when the syndicate met on April 7, Ramanujan’s case encountered a setback. Such scholarships were reserved for those with master’s degrees, and Ramanujan lacked even a bachelor’s; why, he’d flunked out of every college he’d ever attended. By one Indian account, it was the English—led by Richard Littlehailes, an Oxford-educated professor of mathematics at Presidency College and later portrayed as one of Ramanujan’s champions—who invoked this technicality and, “with all their vehement speeches,” lined up against him. In any case, the syndicate’s vice-chancellor, P. R. Sundaram Iyer, chief justice of the Madras High Court, then rose. Did not the preamble of the act establishing the university, he asked, specify that one of its functions was to promote research? And, whatever the lapses of Ramanujan’s education, was he not a proven quantity as a mathematical researcher?
That argument won the day. “The regulations of the University do not at present provide for such a special scholarship,” the registrar later wrote. “But the Syndicate assumes that Section XV of the Act of Incorporation and Section 3 of the Indian Universities Act, 1904, allow of the grant of such a scholarship, subject to the express consent of the Governor of Fort St. George in Council.”
It was a measure of how far, six weeks after receipt of Hardy’s letter, Madras opinion had swung behind Ramanujan: now, the authorities were stretching the rules to accommodate him.
By April 12, Ramanujan had learned the good news. The scholarship set him free to do mathematics, to attend lectures at the university, to use its library. So that now, as Neville would write, he “entered the Presidency College in Madras to practice as a virtue that singleminded devotion to mathematics which had been a vice in Kumbakonam nine years earlier.”
3. “DOES RAMANUJAN KNOW POLISH?”
It was a great open space that, as you came out of the alleys leading to it, offered a broad blue sweep of sky, a little as the piazza of an Italian hill town does. But it was not a piazza, or a square, or a park. It was a “tank,” a sort of religious swimming pool—an expanse of water, normally almost square, with a sandy bottom, granite steps leading down to the water on several sides, and a man-made island of richly detailed religious sculpture at its center.
This one was large, perhaps a hundred yards across, and notably handsome. Its legendary predecessor gave the whole district its name—Triplicane, a corruption of Tiru Alii Keni, meaning “sacred lily tank.” Adjacent to it stood the ancient Parthasarathy Temple, a Vaishnavite shrine whose principal deity was Krishna as the “sarathi,” or charioteer, in the great battle of the Bhagavad Gita, and which still bore the inscription of a Pallava king’s gift of land in A.D. 792. Here Muslim, Dutch, and French soldiers had encamped over the centuries. Here the faithful would bathe on ritual occasions—sometimes a few at a time, occasionally hundreds or thousands of them, closely packed together, a sea of bare-chested brown men.
Off one street bordering the tank to the south ran a little lane, Hanumantharayan Koil Street. And a few doors down, almost where the street turned abruptly left, was a little house, set back a courtyard’s depth from the street. Here, about a mile and a half from Presidency College, Ramanujan and his family now lived. With research scholarship in hand and on leave from the Port Trust, they no longer had to stay in congested Georgetown, and probably around May had moved back to Triplicane.
Ramanujan had nothing to do now but pursue mathematics and, every three months, submit a progress report. For this he received seventy-five rupees a month. Back in Kumbakonam, the five or ten rupees the family got monthly from boarders made for a sizable chunk of their income. Even at the Port Trust, he’d still only made twenty-five or thirty rupees, possibly as much as fifty at one point. And what with at least Janaki, Komalatammal, and Komalatammal’s own mother to provide for, that didn’t go far; sometimes he’d had to moonlight, tutoring college students on the side. Now, though, he was almost flush, almost at the hundred rupees a month, for example, that the Indian Mathematical Society set as its threshold for paying full dues. Ramanujan had friends in high places now, was published in mathematical journals, was corresponding with one of the West’s top mathematicians.
During the early mornings, and then again at night, he’d work with Narayana Iyer, no longer boss now, but colleague. Sometimes he’d borrow math books from K. B. Madhava, a statistician who lived down the street. Often, he could be found in the alcoves of the Connemara Library, a wing of which also housed the university collection. The Connemara, named for a former governor of Madras, was like a secular church, a soaring chamber of arching stained-glass windows, filled with wood engravings and columns and arches rich with molded plaster ornamentation, an Indo-Saracenic temple of learning. Here Ramanujan would lose himself on some of those deliciously free days after his scholarship had set him free.
It was a little like the period before his marriage. More completely than ever he was able to throw himself into mathematics, leaving day-to-day cares to others. Sometimes, Janaki would recall, “he would ask his mother or grandmother to wake him up after midnight so that he could go on with his work in the silent and cooler hours of the after-night.” Sometimes he “had to be reminded about his food. On some occasions his grandmother or mother would serve, in his hand, food made of cooked rice mixed with sambhar, rasam, and curd successively. This they did so that his current of thought might not be broken.” At other times, she or his mother would prepare brinjal in just the way he liked. Normally this teardrop-shaped vegetable, about the size of a peach, was eaten cooked. But he had learned to love it the special way his mother made it for him—quartered, then quartered again, but with a tab of flesh keeping all eight segments together, the junction steeped in tamarind and masala for an hour or so, then eaten raw.
Ramanujan now had his own workroom upstairs. He and Janaki usually slept at separate times, but it seemed that “whenever I opened my eyes,” as she would recall, “he would be working,” the scratch of stylus on slate sounding through the house. Once, on the spur of the moment, he rigged up a little science experiment for her; from a jug of water and some kind of tubing, he made a siphon and showed her how gravity drew the water to lower points. But otherwise, contact between them was slight. Janaki was barely fourteen. He worked in the heady realms of pure mathematics, whereas she, beyond simple Tamil, had no education at all. Occasionally, when he took a break, he would ask her to later jog his memory with language like, “the one you were working on downstairs,” or “the one you were working on before eating.” But intellectually, they could share nothing. Nor did he try to force-feed her. She didn’t ask him to, and he didn’t volunteer.
• • •
Ramanujan and Hardy, meanwhile, danced around one another uncertainly. In their correspondence, Hardy was defending the mathematical revolution he had wrought in England, trying to wrest rigorous proofs from Ramanujan. Ramanujan held back, offering excuses. At least that was how his stance could be read, and by mid-March the situation verged on a real row. “How maddening his letter is in the circumstances,” Littlewood wrote Hardy. “I rather suspect he’s afraid that you’ll steal his work.” Taking up the issue in his next letter, Hardy took pains to reassure him:
Let me put the matter quite plainly to you. You have in your possession now 3 [Ramanujan had only two] long letters of mine, in which I speak quite plainly about what you have proved or claim to be able to prove. I have shown your letters to Mr. Littlewood, Dr. Barnes, Mr. Berry, and other mathematicians. Surely it is obvious that, if I were to attempt to make any illegitimate use of your results, nothing would be easier for you than to expose me. You will, I am sure, excuse my stating the case with such bluntness. I should not do so if I were not genuinely anxious to see what can be done to give you a better chance of making the best of your obvious mathematical gifts.
Whether Hardy and Littlewood had misread Ramanujan’s letter or not, Ramanujan now denied misgivings and even managed, rather successfully, to seem hurt. “I am a little pained to see what you have written at the suggestion of M
r. Littlewood,” he wrote in mid-April.
I am not in the least apprehensive of my method being utilised by others. On the contrary my method has been in my possession for the last eight years and I have not found anyone to appreciate the method. As I wrote in my last letter I have found a sympathetic friend in you and I am willing to place unreservedly in your possession what little I have.
Ramanujan the special research student, Ramanujan the friend of Cambridge was now a hot topic in Madrasi circles, and people were forever trooping through his house, as if to do him homage. In August, his name came up at a get-together of professors and their students; everyone marveled how Ramanujan had garnered such intellectual standing “without,” as one there that evening put it, “the help of books or teachers.”
In September, Narayana Iyer submitted some theorems on the summation of series to the Journal of the Indian Mathematical Society, at one point adding: “The following theorem is due to Mr. S. Ramanujan, the Mathematics Research Student of the Madras University.”
On October 26, perhaps out to win over one who had before campaigned against Ramanujan’s scholarship, Narayana Iyer took Ramanujan to see Richard Littlehailes, professor of mathematics at Presidency College and soon to become Madras’s director of public instruction. Ramanujan was never good at explaining his own methods, so Narayana Iyer did the talking. Littlehailes assured them that, after the first of December, he looked forward to studying Ramanujan’s results.
In November, the mathematician E. B. Ross of Madras Christian College, whom Ramanujan had met a few years before, stormed into class, his eyes glowing. “Does Ramanujan know Polish?!?” he asked his students. Ramanujan didn’t, of course. Yet his most recent quarterly report had anticipated the work of a Polish mathematician whose paper had just arrived by the day’s mail.
The Man Who Knew Infinity Page 23
