Hardy discovered Ramanujan? Not at all: a glance at the facts of 1912 and 1913 shows that Ramanujan discovered Hardy.
And what of the dream of Namakkal, when the goddess Namagiri presumably gave her blessing for his trip to England? What fierce drive to live out his other, truer “dream” did Ramanujan need to contrive, subconsciously, that it turn out as it did?
Ramanujan was a man for whom, as Littlewood put it, “the clear-cut idea of what is meant by proof … he perhaps did not possess at all”; once he had become satisfied of a theorem’s truth, he had scant interest in proving it to others. The word proof, here, applies in its mathematical sense. And yet, construed more loosely, Ramanujan truly had nothing to prove.
He was his own man. He made himself.
“I did not invent him,” Hardy once said of Ramanujan. “Like other great men he invented himself.” He was svayambhu.
Just what did Ramanujan want?
He wanted nothing—and everything.
He sought no wealth, certainly none beyond what he needed to carry out his work, and to give to his family what he felt was expected of him.
He did crave respect, understanding, perhaps even a favorable judgment from history.
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.
That, of course, is no modest wish at all. He wanted “leisure.” And he got it.
In South India today, everyone has heard of Ramanujan. College professors and bicycle rickshaw drivers alike know his story, at least in sketchy outline, just as everyone in the West knows of Einstein. Few can say much about his work, and yet something in the story of his struggle for the chance to pursue his work on his own terms compels the imagination, leaving Ramanujan a symbol for genius, for the obstacles it faces, for the burdens it bears, for the pleasure it takes in its own existence.
Epilogue
By the time he learned of Ramanujan’s death, Hardy had already left Trinity.
In December 1919, about when Ramanujan, at his doctor’s insistence, prepared to leave Kumbakonam for Madras, Hardy was writing J. J. Thomson, master of Trinity College, with the news that he had accepted the Savilian Professorship at Oxford. “The post carries with it a Fellowship at New College, the acceptance of which will vacate my Fellowship here automatically,” he wrote. One reason for the move was the increasing load of administrative responsibility he bore at Cambridge. “If I wish to preserve full opportunities for the researches which are the principal permanent happiness of my life,” he had decided, he would need a position offering “more leisure and less responsibility.” At Oxford, he’d been assured, he would get that.
Unmentioned in the letter but probably weighing more on him than administrative chores were the hard feelings left over from the war, the infighting that surrounded the Russell affair, and the departure of Ramanujan. “If it had not been for the Ramanujan collaboration, the 1914–1918 war would have been darker for Hardy,” wrote Snow. “It was the work of Ramanujan which was Hardy’s solace during the bitter college quarrels.” Now Ramanujan was gone. Trinity, his home for thirty years, had grown ugly to him. He scarcely spoke with some of his colleagues. Earlier, he had urged W. H. Young, an older mathematician who had spent much of his professional life abroad, to apply for the Savilian chair, only to ask him to withdraw his name, which Young did. “Hardy,” recalled Young’s son, Laurence, also a mathematician, “felt he must get away.”
Oxford was the other great English university, less than a hundred miles away. In Camford Observed, Jasper Rose and John Ziman tried to bring it and Cambridge within the compass of a single account: “Oxford is a city of wide and noble thoroughfares, the High, the Broad, St. Giles; in Cambridge all the streets straggle. The great buildings of Oxford face the streets, tall and imposing, and form a series of breathtaking vistas. The great buildings of Cambridge are more isolated, less emphatic, more secretive, giving on to college courts and gardens. Oxford is more coherent; Cambridge more diffuse. Oxford overwhelms—Cambridge beguiles.” Academically, Cambridge tipped slightly more toward the sciences, Oxford toward the classics.
New College was one of Oxford’s two dozen or so distinct colleges. The place was like a walled city, with medieval battlements, pierced by tall, narrow slots through which archers could fire their bows, still enclosing two corners of it and forming a backdrop to the shrubs, trees, and bushes of the College Garden. In moving to New College, Hardy was coming full circle. The college was founded by William of Wykeham in 1379, eight years before he founded Winchester as a feeder to it. It had been the destination of many of Hardy’s abler Winchester classmates twenty-five years before and would probably have been his as well had he not, his head turned by that St. Aubyn book, opted for Trinity instead.
Hardy had been in Oxford just a few months when he received the news from Madras:
By direction of the [University] Syndicate, I write to communicate to you, with feelings of deep regret, the sad news of the death of Mr. S. Ramanujan, F.R.S., which took place on the morning of the 26th April.
“It was a great shock and surprise to me to hear of Mr. Ramanujan’s death,” Hardy replied in a letter to Dewsbury. But was there, in what he wrote next, the barest breath of defensiveness?
When he left England the general opinion was that, while still very ill, he had turned the corner towards recovery; he had even gained over a stone in weight (at one period he had wasted away almost to nothing). And the last letter I had from him (about two months ago) was quite cheerful and full of mathematics.
Ramanujan had, after all, been entrusted to Hardy’s care. Was Hardy—in a not uncommon sort of response to a loved one’s death—now trying to assure himself that Ramanujan’s final decline had come only after he had been placed safely aboard the ship to India?
About the impact of Ramanujan’s death on Hardy there can be no doubt:
For my part, it is difficult for me to say what I owe to Ramanujan—his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.
At Oxford, the specter of the Great War still hung heavily over Hardy, as it did all across Europe. Feeling against Germany ran deep. “Let us trust,” one English scientist had written Nature in the closing months of the war, “that for the next twenty years at least all Germans will be relegated to the category of persons with whom honest men will decline to have any dealings.” Mathematicians were not immune to the bitterness; many in England and France felt that Central European mathematicians should be banned from international mathematical congresses.
Hardy had been revolted by the war’s stupid savagery, hated the whole idea of old men sending boys off to die, and felt cruelly cut off from his mathematical friends on the Continent. Now, the war over, he tried to heal the wounds. He wrote the London Times protesting some of the vengeful imbecilities being bruited about. He cooperated in the peacemaking efforts of Gösta Mittag-Leffler, long-time editor of Acta Mathematica, a Swedish mathematical journal founded in 1882 midst similar tensions among mathematicians following the Franco-Prussian War. He wrote with his views of the war to the great German mathematician Edmund Landau; his own views, Landau wrote back with a mathematician’s touch, had been the same—except “with trivial changes of sign.”
While visiting Germany in 1921, Hardy wrote Mittag-Leffler: “For my part, I have in no respect modified my former views, and am in no circumstances prepared to take part in, subscribe to, or assist in any manner directly or indirectly, any Congress from which, for good reasons or for bad, mathematicians of particular countries are excluded.” He had boycotted one such congress in Strasbourg in 1920 from which Germans, Austrians, and Hungarians had been kept out, and he would boycott another in Toronto four years later.
The armistice, the departure of Ramanujan, his own move to Oxford, and Ramanujan’s death had all come wit
hin eighteen months. But by all accounts, Hardy fell in easily at New College, felt at home there in a way he never had in Cambridge. It was, Snow tells us, “the happiest time of his life.” He was accepted. His new Oxford friends made a fuss over him. His conversational flamboyance found new and appreciative ears. Sometimes, it seemed, everyone in the Common Room—the Oxford term for what back at Cambridge was the Combination Room—waited to hear what Hardy was going to talk about.
Meanwhile, his collaboration with Littlewood, conducted largely by mail, continued. He was at the height of his mathematical powers, the zenith of his fame. Mary Cartwright would recall how her bare mention of “Professor Hardy’s class” to a college porter drew a response revealing “a far greater respect for Hardy than the customary deference of those days of any college porter to any don.”
For the academic year 1928–1929, Hardy exchanged places with Princeton’s Oswald Veblen and spent the year in the United States, mostly at Princeton University. While in America, he kept up a busy lecture schedule; he spoke at Lehigh University, for example, on January eleventh, at Ohio State on the eighteenth, at the University of Chicago on the twenty-first. During February and March, he was in residence at California Institute of Technology. At the end of the year, Princeton’s president asked him to stay a bit longer. Hardy wrote back that though he’d had “a delightful time,” his duties at Oxford demanded his return.
On this or one of his other trips to America, he developed a taste for baseball. Babe Ruth, it was said of him, “became a name as familiar in his mouth as that of the cricketer Hobbs.” One time, he was sent a book, inscribed by “Iron Man” Coombs, stuffed with problems in baseball tactics. “It is a wonderful book,” he wrote a postcard saying. “I try to solve one problem a day (e.g. 1 out, runners at 1st and 2nd, batsman [the cricket term] hits a moderate paced grounder rather wide to 2nd baseman’s left hand—he being right handed. Should he try for a double play 1st to second or 2nd to first? I think the former.)”
His love of cricket and tennis, of course, continued unabated. In tennis, he steadily improved his game. In one snapshot taken while Hardy was at Oxford, it is a bright, sunny day in late spring or early fall and Hardy, looking absolutely smashing in his white tennis gear, stands midst a group of about a dozen other players. They are Beautiful People, ca. 1925 or so, and Hardy, clutching his racket, wearing long-legged tennis togs and a heavy shawl sweater under a jacket, is one of them.
Though happy at Oxford, by 1931 Hardy was back in Cambridge, as Sadleirian Professor, following the death of E. W. Hobson; Cambridge was, after all, still the center, far more than Oxford, of English mathematics, and he was now being offered its senior mathematical chair. Another reason, according to Snow, was that the two universities had different rules about retirement; whereas Oxford would turn him out of his rooms at sixty-five, at Trinity he could occupy them until he died.
For a time, Hardy would periodically return to Oxford for a few weeks at a time to captain the New College Senior Common Room cricket team. And, of course, he was always there at Lord’s for the annual match between Cambridge and Oxford. “There he was at his most sparkling, year after year,” wrote Snow. “Surrounded by friends, men and women, he was quite released from shyness; he was the centre of all our attention, which he by no means disliked; and one could often hear the party’s laughter from a quarter of the way round the ground.”
Hardy’s formerly unpopular antiwar views were now, when not forgotten, actually applauded. The young Cambridge mathematicians, Snow records, “were delighted to have him back: he was a real mathematician, they said, not like those Diracs and Bohrs the physicists were always talking about: he was the purest of the pure.” It was, as Laurence Young portrayed it later, a golden age of Cambridge mathematics. “Spiritually and intellectually, Cambridge was suddenly at least the equal of Paris, Copenhagen, Princeton, Harvard, and of Warsaw, Leningrad, Moscow.” A sprinkle of foreign visitors to Cambridge had now, as Jews and others sought escape from Hitler’s Germany, become a torrent.
Beginning around 1933, Hardy, in cooperation with the Society for the Protection of Science and Learning, used his influence to get Jews and others driven from their jobs to England and other safe havens. Mathematicians of the stature of Riesz, Bohr, and Landau were among those who got out. “Hardy, in many ways, was other-worldly,” A. V. Hill wrote, “but in his deep solicitude for the dangers and difficulties of his colleagues he showed not only a broad humanity but a fine and resolute loyalty to the universal integrity and brotherhood of learning.”
Hardy resigned from at least one German organization of which he had been a member—not because it was German, but because of what it did. “My attitude towards German connections of this kind,” he wrote Mordell in the early Nazi period, “is that I do nothing unless I am positively forced to; but if anti-Semitism becomes an ostensible part of the programme of any periodical or institution, then I cannot remain in it.”
In 1934, Hardy wrote to Nature responding to a University of Berlin professor who purported to show the influence of blood and race upon creative style in mathematics. There were, it seems, “J-type” and “S-type” mathematicians, the former of good Aryan stock, the latter Frenchmen and Jews. Hardy icily surveyed Professor Bieberbach’s assertions, made a show of seeking ground on which to excuse them, finally found himself “driven to the more uncharitable conclusion that he really believes them true.”
Hardy’s sympathies lay invariably with the underdog, and his political views were decidedly left-wing. Until about 1927, he was active in the National Union of Scientific Workers, even made recruiting speeches on its behalf. In one, as J. B. S. Haldane paraphrased it later, he said to his audience of scientists “that although our jobs were very different from a coalminer’s, we were much closer to coalminers than capitalists. At least we and the miners were both skilled workers, not exploiters of other people’s work, and if there was going to be a line-up he was with the miners.” Visitors to Hardy’s rooms often noted that on his mantelpiece stood photographs of Einstein, the cricketer Jack Hobbs—and Lenin.
But within the mathematical community, he, Littlewood, and those in their camp stood squarely in the Establishment. English mathematicians, Hardy wrote in 1934, no longer labored under “the superstition that it is impossible to be ‘rigorous’ without being dull, and that there is some mysterious terror to exact thought.” The revolution he had helped usher in a quarter century before had won the day. Indeed, some would grumble later that it had actually impeded progress in such fields as algebra, topology, functional analysis, and other topics within pure mathematics. By the 1930s, in any case, Hardy was seen as part of the older generation.
During these years, the honors, large and small, rolled in. On March 6, 1929, the one-hundredth anniversary of the death of the great Norwegian mathematician Abel, Hardy, in the presence of the king of Norway, received an honorary degree from the University of Oslo.
On December 27, 1932, he got the Chauvenet Prize, awarded every three years for a mathematical paper published in English, for his “An Introduction to the Theory of Numbers.”
On February 29, 1934, he received a letter, on the hammer-and-sickle embossed stationery of the Soviet Union, from J. Maisky, the Soviet ambassador to Britain, congratulating him on his election as an honorary member of the Academy of Sciences in Leningrad.
The universities of Athens, Harvard, Manchester, Sofia, Birmingham, and Edinburgh awarded him degrees. He received the Royal Medal of the Royal Society in 1920, its Sylvester Medal in 1940. He was made an honorary member of many of the leading foreign scientific academies. Without a doubt, he was the most distinguished mathematician in Britain.
To this period, his prime, much Hardy lore is owed. One year, Hardy’s New Year’s resolutions were to:
1. Prove the Riemann hypothesis.
2. Make 211 no out in the fourth innings of the last test match at the Oval [which was something like hitting a grand slam home run while behind by t
hree runs in the ninth inning of the World Series’ final game].
3. Find an argument for the nonexistence of God which shall convince the general public.
4. Be the first man at the top of Mt. Everest.
5. Be proclaimed the first president of the U.S.S.R. of Great Britain and Germany.
6. Murder Mussolini.
Another story neatly combined his love of cricket, his pleasure in the sun, his warfare with God, and his madcap bent. One of his collaborators, Marcel Riesz, was staying at the place Hardy shared with his sister in London. Hardy ordered him to step outside, open umbrella clearly in view, and yell up to God, “I am Hardy, and I am going to the British Museum.” This, of course, would draw a lovely day from God, who had nothing better to do than thwart Hardy. Hardy would then scurry off for an afternoon’s cricket, fine weather presumably assured.
In long talks with Hardy beginning in 1931 and extending over the next fifteen or so years, C. P. Snow came away steeped in Hardy’s “old brandy” sensibilities. By old brandy Hardy meant any “taste that was eccentric, esoteric, but just within the confines of reason.” For example, he once wrote Snow that “the half-mile from St. George’s Square to the Oval [in London] is my old brandy nomination for the most distinguished walk in the world.” Old brandy was a sort of studied eccentricity—youthful foolishness transformed into a “mature” form, made a little self-conscious, ossified …
And that, indeed, is what had happened to Hardy. Somehow, he had become an old man. Even by the fall of 1931, when he was fifty-four, you could see signs of it. Back in Cambridge for the year, Norbert Wiener noticed that “by now, Hardy had become an aged and shriveled replica of the young man whom I had met in Russell’s rooms” twenty years before. Hardy knew it, too. On his return to Cambridge, he was distressed by all the new, young faces he saw among the mathematicians. “There is,” he wrote, “something very intimidating to an older man in such youthful quickness and power.”
The Man Who Knew Infinity Page 46
