The Man Who Knew Infinity

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by Robert Kanigel


  “Surely?” “Just as surely?” For English mathematicians untouched by the precision of the Continent, such notions were obvious, scarcely worthy of another thought. But Jordan actually stated these seemingly self-evident truths as theorems and set about trying to prove them rigorously. In fact, he couldn’t do it, or at least not completely; his proofs were laced with flaws, and his successors had later to correct them. But they invoked just the kind of close, sophisticated reasoning that Hardy, coming upon Jordan now, at the age of barely twenty, found beguiling. “I shall never forget,” Hardy later wrote of Jordan’s book, whose second, much-improved edition had just appeared in 1896, “the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.”

  Of course none of this had anything in the least to do with the Tripos, which—now a mathematician again more than ever—Hardy would have to take. And that, realistically speaking, meant studying with a coach. So Hardy—yes, his friend Littlewood later seemed to gloat, “even the rebel Hardy”—surrendered. It was a bitter pill; “real” mathematics was put aside, Tripos mathematics reluctantly embraced. “When I look back upon those two years of intensive study,” he would recall later, “it seems to me almost incredible that anyone not destitute of ability or enthusiasm should have found it possible to take so much trouble and to learn no more.”

  Inaugurating something of a trend among the better students, Hardy took the Tripos at the end of his second year, rather than his third, thus freeing himself from its grip that much sooner. Still he managed to come in fourth—by any measure a superb performance. “Hurrah,” one friend, the future historian G. M. Trevelyan, wrote when Hardy notified him. “It is a great triumph, not only for you but the good cause of taking the triposes in the second year.” And yet for all his contempt for the Tripos system, Hardy told his friend Snow later, it rankled that he wasn’t Senior Wrangler. “He was enough of a natural competitor,” wrote Snow, “to feel that, though the race was ridiculous, he ought to have won it.”

  From then on, though, Hardy’s stature among his generation of English mathematicians steadily rose. In 1898, when he was twenty-one, his first mathematical publication appeared; like Ramanujan’s, it was in the form of a question, followed three issues later by its solution. Hardy graduated in 1899 and the following year took Part II of the Tripos; Part I was the one for which the coaches groomed their students and which determined Wrangler standing, Part II the more provocative and more challenging. On it, Hardy scored first and was promptly named a Fellow of Trinity.

  5. “THE MAGIC AIR”

  At its two-hundred-fiftieth meeting, on May 23, 1901, the Cambridge Shakespeare Society held a reading of the first three acts of Twelfth Night. Hardy was there—not to perform but, as his friends deemed his role, as “critic.” With him was his close friend R. K. Gaye, a classical scholar, who played Malvolio. Others lending retrospective luster to the evening were Lytton Strachey, playing Maria, Leonard Woolf in the dual role of Valentine and the Captain, and J. T. Stephen, the future Virginia Woolf’s brother, who played Sir Toby Belch. James Hopwood Jeans, who came up to Trinity the same year as Hardy and would enjoy almost as distinguished a career in applied mathematics as Hardy would in pure, took photographs by magnesium light. What a pity they don’t survive! The men sported lavish costumes, sparing nothing in the detail they expended on the ladies’ gowns some of them wore. Gaye wore the yellow stockings, cross-gartered of Shakespeare’s text. Stephen wore a stomacher, an elaborately embroidered chest piece. Woolf wore his old bowler hat. It was a madcap evening. The reading went well enough but, as the secretary was delighted to record, “elementary stage rules, such as facing the audience, were neglected by those who should have known better. Let us hope it was modesty!”

  A few months before, on January 22, Queen Victoria had died; the century that bore her name, with its straitlaced proprieties and its moral fervor, was over, and the first stirrings of the new, more relaxed era heralded by Edward’s reign could be felt.

  On September 3, Hardy was in Cranleigh for the funeral of his father, who’d died four days before, at the age of fifty-nine. There he joined his sister and mother in the procession which bore his father’s body, in a wheeled bier covered with wreaths and laced with ivy, from the House, to the school chapel, and thence through the village to the parish church, in the shadow of whose squat, stone tower it was laid to rest.

  Back at Trinity, where he now occupied rooms in Great Court, twenty-four-year-old Hardy took up his old life again. Shy and sensitive though he was, Hardy had, since taking the Tripos in 1898, become something of a social animal. He was now part of a circle to which the sons of schoolteachers normally did not belong and whose values his family might scarcely have been able to imagine. He attended Shakespeare Society meetings. He belonged to Decemviri and Magpie & Stump, two Cambridge debating societies, which took up such questions as “An enlightened selfishness is the highest virtue,” and “The complete degradation of the Latin races is final and irrevocable.” But he also belonged to another group, which neither advertised its meetings, nor openly recruited members, nor even proclaimed its existence.

  Woolf and Strachey were both present or future members of a secret intellectual society known as the Apostles. So were two others in the Twelfth Night cast. And so was Hardy.

  It had been started in 1820 as the Conversazione Society, one of many Cambridge student groups devoted to debate and good fellowship. Founded as it was by twelve men, it soon became known as the Apostles, and in time as simply the Society. By the time Hardy joined, its ranks had included some of the most brilliant men Cambridge had ever produced. There was Tennyson, the poet; Whitehead, the philosopher; James Clerk Maxwell, the physicist; Bertrand Russell; and many others whose names are less recognizable today. Of the ten whom Leonard Woolf would later count as the nucleus of “Old Bloomsbury,” the iconoclastic intellectual community that would reach full flower in the 1920s and 1930s, no fewer than seven were Apostles.

  A scientist, as one Apostle noted round this time, was elected only if “he was a very nice scientist.” Hardy, apparently, was nice enough; his crystalline intellect, his sly charm, his aesthetic sensibilities, his good looks, his love of good conversation—all these would have endeared him to such men. Actually, for reasons unknown, he first declined membership. But finally, in a gala, well-attended meeting of the Society on the evening of February 19, 1898, he was inducted.

  His “father,” the man putting him up for membership, was G. E. Moore. Leonard Woolf would later write of Moore that he pursued truth “with the tenacity of a bulldog and the integrity of a saint.” An Apostle since 1894, he was a charismatic philosopher who brooked no imprecision in thought, feeling, or expression; always he was asking, What do you exactly mean to say? His philosophy, set out in Principia Ethica in 1903, coupled with what Woolf would call “his peculiar passion for truth, for clarity and common sense,” made him the dominant influence on his whole generation of Cambridge intellectuals, and ultimately on Bloomsbury as a whole.

  Each Saturday night the Apostles met. (The normal fare was “whales,” the name given to sardines or anchovies on toast.) One of them read a paper on some intellectual topic, such as, “Is Any Event Necessary?” Or, “Can Moral Philosophy Provide Any Antidote for Unhappiness?” Or, “Does Youth Approve of Age?” The question would then be debated and put to the floor for a vote. (On that last one, Hardy voted no.) The group wanted for nothing in arrogance and preciousness, as its peculiar jargon suggested: An “embryo” was a candidate for membership, a “birth” his induction ceremony. “Phenomena” was the rest of the world—anything or anyone not an Apostle; “reality” was the Society, its members and activities.

  “There were to be no taboos, no limitations, nothing considered shocking, no barriers to absolute freedom of speculation,” wrote Bertrand Russell, who was inducted six years before H
ardy. “We discussed all manner of things, no doubt with a certain immaturity, but with a detachment and interest scarcely possible in later life.” Meetings lasted till about one in the morning, followed by informal discussion up and down the cloisters of Nevile’s Court, at Trinity, which along with King’s supplied most of the group’s members during this period. “The soul of the thing, as I felt it,” wrote Goldsworthy Lowes Dickinson, who had joined in 1885, “is incommunicable. When young men are growing in mind and soul, when speculation is a passion, when discussion is made profound by love, there happens something [that would be unbelievable] to any but those who … breathe the magic air.”

  A classical scholar by way of King’s, a short, vigorous man of formidable charm who had briefly swerved into medicine and later would become a peace activist, Dickinson was also a homosexual. Not all the Apostles were homosexual, perhaps not even most; and yet a homosexual current ran through the Society and, in the years after Hardy joined, intensified. In 1901, E. M. Forster, who was to write A Passage to India, joined; he was homosexual. In 1902, Lytton Strachey joined, and in 1903 John Maynard Keynes, the economist (who once advised Hardy that had he followed stocks as avidly as he did cricket, he would have become rich). Both were homosexual, too, and their election, as one chronicler of the Society later put it, transmuted “its naughty verbal mannerisms and Walt Whitmanesque feelings of comradeship into overt full-blooded—almost aggressive—homosexuality.” Homosexuality was elevated almost to the status of an art form or aesthetic doctrine. “The Higher Sodomy,” Apostles termed it—the assertion that the love between man and man could be higher and finer than that of man for woman, thus raising homosexual relationships to an almost spiritual plane.

  At the time Hardy joined, the Apostles had not yet reached the point where, as Duncan Grant would put it, “even the womanisers pretend to be sods, lest they shouldn’t be thought respectable.” But while he formally “took wings” from the Society just before Strachey and Keynes joined, Hardy maintained friendships with “brethren,” many of them homosexual, for years thereafter.

  That Hardy himself was at least of homosexual disposition is scarcely in doubt. No woman, aside from his mother and sister, played the slightest substantive role in his life. And he had numerous male friends of whom he was passionately fond.

  In 1903, for example, he shared a double suite of rooms at Trinity with R. K. Gaye, who was also a fellow of the college. Gaye, who had joined in the Twelfth Night revelry two years before, entered Trinity the same year as Hardy and showed evidence of being as brilliant a classical scholar as Hardy was a mathematician. Already, at twenty-five, he had received a host of medals and prizes, soon to include the Hare Prize for his Platonic Conception of Immortality and Its Connexion with the Theory of Ideas. Much later, he would commit suicide. But for now, Leonard Woolf would write, he and Hardy “were absolutely inseparable; they were never seen apart and rarely talked to other people.” Woolf records them in their rooms sitting in domestic tranquility beside the fire, quiet and dejected after returning from the veterinarian with their emaciated, worm-ridden cat.

  A younger mathematician who knew Hardy much later, when during the 1920s he was at Oxford, says that there was indeed a “rumor of a young man” then. Later, when Hardy visited America in the 1930s, he would impress the mathematician Alan Turing, himself homosexual, as, in the words of his biographer, Andrew Hodges, “just another English intellectual homosexual atheist.” And during this period, too, he would meet an Oxford man many years his junior to whom he would later dedicate a book and whom one account simply refers to as “his beloved John Lomas.”

  But all that came later, and if Hardy was a practicing homosexual during his early days as a Trinity undergraduate and fellow, he was remarkably discreet about it. Several of those who knew him well, while willing to see in him homosexual leanings, note that he never displayed any of the stereotyped mannerisms of dress and behavior imputed to homosexuals. Littlewood, who worked with him for almost forty years, called him “a non-practicing homosexual.” Then, too, no explicit record of homosexual activity comes down to us, none of the kind of blunt, gossipy X-was-lovers-with-Y tales that, in recent years, surround other venerable Cambridge figures. Indeed, the only sure knowledge we have of Hardy as sexual being is that one Saturday night in 1899, when the Apostles debated whether masturbation (they called it “self-abuse”) was bad as an end, as opposed to a means, Hardy voted with the ayes.

  Hardy was a product of the English public schools, a monastic environment that served as a crucible for homosexual relations among the boys. Everyone knew it, everyone accepted it, no one took it seriously, and for most, such adolescent flings didn’t carry into adult life. In their pioneering look at homosexuality, Sexual Inversion, published in 1897, the year after Hardy left Winchester, Havelock Ellis and John Addington Symonds took note of “these schoolboy affections and passions,” noting that most passed with time.

  If Hardy did have homosexual experiences during this time, he would scarcely have been likely to bruit the news about. A suggestion that homosexuality might be instinctual, and was no proper matter for the exercise of moral control, came through Edward Carpenter in Homogenic Love, published in 1896, and The Intermediate Sex, published in 1908. But these were no more than bubbles of tolerance in a sea of homophobia. Indeed, the year 1895, while Hardy was in his teens, brought the anguish of the Oscar Wilde trials, in which the great dramatist was sentenced to two years’ hard labor for homosexual acts; his wife changed her name and those of her two sons as well, and Wilde’s plays stopped being produced. That was the norm; Carpenter and Havelock Ellis, who also wrote of homosexuality as natural, were the barest breath in the cultural wind. “The last five years of the century were much less open to discussions of love, sex, and marriage,” one chronicler of the era, Samuel Hynes, has written in The Edwardian Turn of Mind. “It was as though the Victorian age, in its last years, had determined to be relentlessly Victorian while it could.”

  Hardy reached young adulthood in the early 1900s, with its freer Edwardian sensibilities. But his attitudes had been formed earlier, in the Victorian era, a time preoccupied with public morality. It was a time when the face you put on things, as Gertrude Himmelfarb has stressed in Manners and Morals Among the Victorians, was taken with the utmost seriousness. Whatever people did on the sly, they were careful to keep it quiet, and led whole lives that way; it wasn’t “hypocrisy,” but simple propriety. Vastly less play was given “natural” drives. If anything, the idea was to bottle them up, or channel them, but in any case to control them; whatever your private fantasies, you didn’t have to act on them, for goodness sake, and shouldn’t.

  Hardy’s Cambridge in the early 1900s was a curious blend of the old Victorianism and the new, freer Edwardianism. If within the Apostles and in Cambridge generally the homosexual undercurrent surged toward the surface, it never broke through. Even among these, the most avant of the avant-garde, Victorian echoes sounded. As Himmelfarb has pointed out, referring to the Bloomsbury movement that largely grew out of the Apostles:

  It is ironic that people who prided themselves on their honesty and candor, especially in regard to their much-vaunted “personal affections”—in contrast, as they thought, to Victorian hypocrisy and duplicity—should have succeeded for so long in concealing the truth about those personal affections. Even so perceptive and psychoanalytic-minded a critic as Lionel Trilling was able to write a full-length study of Forster in 1943 without realizing that he was a homosexual. Nor did Roy Harrod, in his biography of Keynes published in 1951 (the definitive biography, as it seemed at the time and as it remained for more than thirty years), see fit to mention Keynes’ homosexuality—a deliberate suppression, since Harrod was a friend of Keynes and was perfectly well aware of his sexual proclivities and activities. Nor did Leonard Woolf, in a five-volume autobiography that was entirely candid about his wife’s mental breakdowns, give any indication of the frenetic sexual affairs of everyone around him.


  Given the times out of which they came, then, that Hardy’s long-time friend, Littlewood, called him “a non-practicing homosexual” may mean little. Littlewood was himself known to have fathered a child by a married woman but would not publicly acknowledge her until near his death in 1977. (When he did idly mention it one day in the Combination Room at Trinity, he was stunned that no one seemed to care.) Homosexuality, of course, defied a yet more rigid taboo. So if Hardy did lead a homosexual life about which Littlewood knew, Littlewood might well have denied it.

  Then again, Littlewood may have known nothing, Hardy keeping the various parts of his life scrupulously walled off from one another. Hardy knew all the Apostles, went to meetings. And his name shows up in diaries, memoirs, and biographies of Strachey, Forster, Woolf, Russell, and the others. But it doesn’t show up much; one senses him at the edge of their world, not its center. Being a mathematician, and a pure mathematician at that, may have isolated him; within the Shakespeare Society, for example, he was gently ribbed for putting “his knowledge of higher mathematics” to use in calculating the tab for a recent dinner at five shillings, one penny—an “alarming sum.” In the avant-garde world of which he was part, Hardy was tolerated, respected, appreciated for his inimitable personal charm; but the core of his life, one gathers, lay elsewhere.

  In mathematics? Certainly.

  In a homosexual underworld? Only perhaps.

  That Hardy’s life was spent almost exclusively in the company of other men, that he scarcely ever saw a woman, was, in those days, not uncommon. After all, among Havelock Ellis’s thousand or so British “geniuses,” 26 percent never married. In the academic and intellectual circles of which Hardy was a part, such a monastic sort of life actually represented one pole of common practice.

  Thus, at Cranleigh School, all the teachers, except for the House staff, were men, most of them bachelors; dormitory masters had to be bachelors. Winchester was the same way. So was Cambridge. “In my day we were a society of bachelors,” wrote Leslie Stephen in Some Early Impressions of his time at Cambridge during the early 1860s. “I do not remember during my career to have spoken to a single woman at Cambridge except my bedmaker and the wives of one or two heads of houses.”

 

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