The Indian Clerk Page 3
Should they bring the Indian to England? As he mulls over the idea, Hardy's heart starts to beat faster. He cannot deny that it excites him, the prospect of rescuing a young genius from poverty and obscurity and watching him flourish … Or perhaps what excites him is the vision he has conjured up, in spite of himself, of Ramanujan: a young Gurkha, brandishing a sword. A young cricketer.
Outside his window, the moon rises. Soon, he knows, the gyp will arrive with his evening whiskey. He will drink it by himself tonight, with a book. Curious, the room feels emptier than usual—so whose presence is he missing? Gaye's? Littlewood's? An odd sensation, this loneliness that, so far as he can tell, has no object, at the other end of which no mirage of a face shimmers, no voice summons. And then he realizes what it is that he misses. It is the letter.
4
HE TRIES TO remember when it started. Certainly before he knew anything. Before he learned it was one of the great problems, if not the greatest of them all. He was eleven, maybe twelve. It started with fog.
The Cranleigh vicar had taken him for a walk—at his mother's request, because he seemed not to be paying attention at church. It was foggy out; now he can imagine the gears shifting in the vicar's brain as he landed upon the idea of using the fog to explain faith. The fog, and something a boy would like. A kite.
“If you fly a kite in the fog, you cannot see the kite flying. Still, you feel the tug of the string.”
“But in the fog,” Harold said, “there is no wind. So how could you fly a kite?”
The vicar moved slightly ahead. In the humid stillness, his torso blurred and wavered like a ghost's. It was true, there was not a touch of wind.
“I use an analogy,” he said. “You are, I trust, familiar with the concept.”
Harold did not answer. He hoped the vicar would mistake his silence for pious contemplation, when in fact the young man had just eradicated any last shred of faith that the boy held. For the facts of nature could not be denied. In fog there was no wind. No kite could fly.
They returned to his house. His sister, Gertrude, was sitting in the drawing room, practicing reading. She had only had the glass eye a month.
Mrs. Hardy made tea for the vicar, who was perhaps twenty-five, with black hair and thin fingers. “As I have been trying to explain to your son,” the vicar said, “belief must be cultivated as tenaciously as any science. We must not allow ourselves to be reasoned out of it. Nature is part of God's miracle, and when we explore her domain, it must be with the intention of better comprehending His glory.”
“Harold is very good at mathematics,” his mother said. “At three he could already write figures into the millions.”
“To calculate the magnitude of God's glory, or the intensity of hell's agonies, one must write out figures far larger than that.”
“How large?” Harold asked.
“Larger than you could work out in a million lifetimes.”
“That's not very large, mathematically speaking,” Harold said. “Nothing's very large, when you consider infinity.”
The vicar helped himself to some cake. Despite his emaciated figure, he ate with relish, making Mrs. Hardy wonder if he had a tapeworm.
“Your child is gifted,” he said, once he had swallowed. “He is also impudent.” Then he turned to Harold and said, “God is infinity.”
That Sunday, as on every Sunday, Mr. and Mrs. Hardy took Harold and Gertrude to church. They were believers, but more importantly, Mr. Hardy was the bursar at Cranleigh School; it mattered that the parents of his pupils see him in the pews. To distract himself from the drone of the vicar's sermon, Harold broke the numbers of the hymns down into their prime factors. 68 gave 17 × 2 × 2, 345 gave 23 × 5 × 3. On the slate behind his eyelids, he wrote out the primes, tried to see if there was reason to their ordering: 2, 3, 5, 7, 11, 13, 17, 19 … It seemed there was none. Yet there had to be order, because numbers, by their very nature, conferred order. Numbers meant order. Even if the order was hidden, invisible.
The question was easy enough to pose. But that did not mean that the answer would be easy to find. As he was quickly learning, often the simplest theorems to state were the most difficult to prove. Take Fermat's Last Theorem, which held that for the equation xn + yn = zn, there could be no whole number solutions greater than 2. You could feed numbers into the equation for the rest of your life, and show that for the first million n's not one n contradicted the rule—perhaps if you had a million lifetimes, you could show that for the first billion n's, not one contradicted the rule—and still, you would have shown nothing. For who was to say that far, far down the number line, far past the magnitude of God's glory and the intensity of hell's agonies, there wasn't that one n that did contradict the rule? Who was to say there weren't an infinite number of n's that contradicted the rule? Proof was what was needed—immutable, incontrovertible. Yet once you started looking, how complicated the mathematics got!
He remained preoccupied with the primes. Up to 100—he counted—there were 25. How many were there up to 1000? Again he counted—168—but it took a long time. At Cranleigh he had replicated, on his own, Euclid's astonishingly simple proof that there was an infinity of primes. Yet when he asked his maths master at Winchester if there was a formula for calculating the number of primes up to a given number n, the master didn't know. Even at Trinity, seat of British mathematics, no one seemed to know. He nosed around, and eventually found out from Love, one of the Trinity fellows, that in fact the German mathematician Karl Gauss had come up with such a formula in 1792, when he was fifteen, but had been unable to provide a proof. Later, Love said, another German, Rie-mann, bad proven the formula's validity, but Love was hazy on the details. What he did know was that the formula was inexact. Inevitably it overestimated the number of primes. For instance, if you counted the primes from 1 to 2,000,000, you would discover that there were 148,933. But if you fed the number 2,000,000 into the formula, it would tell you that the number was 149,055. In this case, the formula overestimated the total by 122.
Hardy wanted to learn more. Might there be a means, at the very least, of improving upon Gauss's formula? Of lessening the margin of error? Alas, as he was discovering, Cambridge wasn't much interested in such questions, which fell under the rather disgraced heading of pure mathematics. Instead it put its emphasis on applied mathematics—the trajectory of planets hurtling through space, astronomical predictions, optics, waves and tides. Newton loomed as a kind of God. A century and a half earlier, he had waged an acrimonious battle with Gottfried Leibniz over which had first discovered the calculus, and though in America and on the continent it had long since been agreed that Leibniz had made the discovery first, but that Newton had made it independently, at Cambridge the battle raged as bitterly as if it were fresh. To deny Newton's claim of precedence was to speak sacrilege. Indeed, so steadfast was the university's loyalty to its famous son that even at the turn of the new century it still compelled its mathematics students, when working with the calculus, to employ his antiquated dot notation, his vocabulary of fluxions and fluons, rather than the simpler system—derived from Leibniz—that was favored in the rest of Europe. And why? Because Leibniz was German, and Newton was English, and England was England. Jingoism, it seemed, mattered more than truth, even in the one arena in which truth was supposed to be absolute.
It was all very disheartening. Among his friends, Hardy wondered loudly if he should have gone to Oxford. He wondered if he should give up mathematics altogether and switch to history. At Winchester he had written a paper on Harold, son of Godwin, whose death in 1066 in the Battle of Hastings was portrayed in the Bayeux tapestries. The subject of the paper was the complicated matter of Harold's promise to William the Conqueror not to seek the throne, yet what really fascinated Hardy was that in the battle Harold took an arrow in the eye. This was, after all, just a few years after Gertrude's accident, and he had a morbid obsession with eyes being put out. Of course, there was also the coincidence of the name. In any case Fearon
, his headmaster, admired the paper enough to pass it on to the Trinity examiners, one of whom later told Hardy that he could just as easily have got a scholarship in history as in mathematics. He kept this in the back of his mind throughout his undergraduate years.
His first two years at Cambridge, he led a bifurcated life. On the one hand, there was the mathematical tripos. On the other, there were the Apostles. The former was an examination, the latter a society. Only a few members of the society took the examination; still, the life they led within the rooms in which they held their meetings undermined its very foundations.
The Apostles first. Election was highly secretive, and, once “born,” the “embryo,” as he was called, was made to swear that he would never speak of the society to outsiders. Meetings took place every Saturday evening. As an active member—as one of the brethren—you were obliged to attend every meeting during term so long as you were in residence. Eventually, each member “took wings” and became an “angel,” at which point he would attend only those meetings he chose to.
Hardy was elected to the society in 1898. He was number 233. His sponsor, or “father,” was the philosopher G. E. Moore (no. 229). At this point the active members of the Society, in addition to Moore, were R. C. and G. M. Trevelyan (nos. 226 and 230), Ralph Wedgwood (no. 227), Eddie Marsh (no. 228), Desmond McCarthy (no. 231), and Austin Smyth (no. 232). The angels most likely to be in attendance were O. B. (no. 142), Goldie Dickinson (no. 209), Jack McTaggart (no. 212), Alfred North Whitehead (no. 208), and Ber-trand Russell (no. 224), who had taken wings only the year before. Nearly all were from King's or Trinity, and of them, only two— Whitehead and Russell—had taken the mathematical tripos.
And what was the mathematical tripos? Reduced to its skeleton, it was the exam that all mathematics students at Cambridge were obliged to take, and had been obliged to take since the late eighteenth century. The word itself referred to the three-legged stool on which, in olden times, the contestants would sit as they and their examiners “wrangled” over points of logic. Now a century and a half had gone by, and still the tripos tested the applied mathematics that had been current in 1782. The highest scorers on the exam were still classed as “wranglers,” then ranked by score, the very highest being deemed the “senior wrangler.” After the wranglers came the “senior optimes” and the “junior optimes.” Much ceremony attended the ritual reading of the names and scores, the honors list, which took place annually at the Senate House on the second Tuesday in June. To have any future in mathematics at Cambridge, you had to score among the top ten wranglers. To be named senior wrangler guaranteed you a fellowship or, if you chose not to pursue an academic career, a lucrative post in government or law. Whitehead in his year had been fourth wrangler, Russell seventh.
The tripos had something of the quality of a sporting event. Wagers preceded it, revels followed it. The third week in June, no man in Cambridge was as famous as the senior wrangler, whose photograph street vendors and newsagents sold, and whom undergraduate aspirants and girls followed through the streets, asking for his autograph. Starting in the 1880s, women were allowed to take the examination, though their scores didn't count, and when, in 1890, a woman beat the senior wrangler, no less worthy an organ than the New York Times reported on her astonishing victory.
Some, generally those who had no personal experience of it, thought the tripos rather fun. O. B., for instance. A historian by inclination and profession, he adored pomp of any kind, and therefore could not understand why Hardy should object so vociferously to what was for him just a nice bit of Cambridge pageantry. In particular—and this was typical of O. B.—he loved the wooden spoon. Each year on degree day, when the poor fellow who had got the lowest score of all—the last of the junior optimes—knelt before the vice-chancellor, his friends would lower down to him from the Senate House roof an immense spoon, five feet long, elaborately hued and emblazoned with the insignia of his college as well as bits of comic verse in Greek along the lines of:
In Honours Mathematical
None in Glory this shall equal.
Senior Wrangler, shed a tear
That you this Spoon shall never bear!
The fellow would then carry the spoon off with him into the distance with as much pathos and equanimity as he could muster. For the rest of his life, he would be known as that year's wooden spoon.
Once, in the mingling hour that followed an Apostles meeting, O. B. said to Hardy, “What's he supposed to do with it, stir his tea?”
“Who?” Hardy asked.
“The wooden spoon.”
Hardy did not want to talk about the wooden spoon. Already he despised the tripos, the preparations for which he considered an undue burden, pulling him away from those matters to which he would have preferred to devote his energy, such as the prime numbers. For him, the tripos was an exercise in archaism. When taking it, you had not just to employ Newton's out-of-date vocabulary, but to recite the lemmas of his Principia Mathematica just upon being given their numbers, as if they were psalms. Because few dons lectured on this mathematics, a cottage industry of private tripos coaches had sprung up, their fees proportionate to the number of senior wranglers they “produced.” These coaches were in many ways more famous than their counterparts, the dons. Webb was the most famous of all, and it was to Webb that Hardy was sent.
These are not days that he remembers with any fondness. Three times a week, during the term and also during the long vacation, at precisely 8:15 in the morning, he would be sat down with five other young men in a room that was damp in summer and freezing in winter. The room was in Webb's house, and Webb spent the entirety of every day in it, hour after hour, coaching successive groups of six until dusk fell, while Mrs. Webb, dour and silent, hovered in the kitchen, filling and refilling the tea urn. The routine never varied. Half the meeting was devoted to rote memorization, the other half to practice against the clock. Hardy thought it a colossal waste of time, yet what made his suffering all the worse was the conviction that he was alone in experiencing it. Ambition seemed to have blinded the other men to the folly of what they were doing. He didn't know then that in Germany the professors made a game of mocking the questions on the exam: “On an elastic bridge stands an elephant of negligible mass; on his trunk sits a mosquito of mass m. Calculate the vibrations of the bridge when the elephant moves the mosquito by roaring his trunk.” Yet this was exactly the sort of question in which the tripos specialized, and for the sake of which generations of Cambridge men had given up the chance to have a real education, just at the moment when their minds were ripest for discovery.
Later, he tried to explain all this to O. B. Through the Apostles they had become, in a peculiar way, friends. Although O. B. never made his famously salacious jokes to Hardy, or tried to touch him, he did have a habit of dropping by Hardy's rooms unexpectedly in the afternoons. Often he would speak of Oscar Wilde, who had been his friend and whom he greatly admired. “Just before he died I saw him in Paris,” O. B. said. “I was driving in a cab and passed him before I realized who he was. But he recognized me. Oh, the pain in his eyes …”
At this stage in his life, Hardy knew little of Wilde beyond what rumors had managed to slip through the fortifications that his Winchester masters had erected to protect their charges from news of the trials. Now he asked O. B. to tell him the whole story, and O. B. obliged: the glory days, Bosie's perfidy, the notorious testimony of the hotel maids … Even today, only a few years after Wilde's death, the scandal was still fresh enough that one dared not risk being seen carrying a copy of one of his books. Still, O. B. loaned Hardy The Decay of hying. When Hardy touched the covers, heat seemed to rise off them, as off an iron. He devoured the book, and afterward copied out, in his elegant hand, a passage that had made a particularly strong impression on him:
Art never expresses anything but itself. It has an independent life, just as Thought has, and develops purely on its own lines. It is not necessarily realistic in an age of realism, nor spiritual
in an age of faith. So far from being the creation of its time, it is usually in direct opposition to it, and the only history that it preserves for us is the history of its own progress.
So of art, he decided, of mathematics. Its pursuit should be tainted neither by religion nor by utility. Indeed, its uselessness was its majesty. Suppose, for instance, that you proved Fermat's Last Theorem. What would you have contributed to the good of the world? Absolutely nothing. Advances in chemistry aided the cotton mills in developing new dyeing processes. Physics could be applied to ballistics and gunnery. But mathematics? It could never serve any practical or warlike purpose. In Wilde's words, it “developed purely on its own lines.” Far from a limitation, its uselessness was evidence of its limitlessness.
The bother was, whenever he tried to articulate this to O. B., he got tied up in knots—such as on the evening when he complained that the mathematics tested on the tripos was pointless.
“I don't understand you,” O. B. said to him. “One day you're carrying on about how gloriously useless mathematics is, the next you're grumbling that the mathematics that the tripos tests is useless. Which of you am I to believe?”
“I don't mean it the same way,” Hardy said. “The stuff on the tripos isn't useless the way pure mathematics is useless. It's not a question of applicability. If anything, the tripos stuff is eminently applicable … just antiquated.”
“Latin and Greek are antiquated. So should we give those up?”
Hardy tried to put his position in a language O. B. would understand. “All right, look,” he said. “Imagine you're taking an exam in the history of English literature. Only for the purposes of the exam, you have to write your answers in Middle English. It doesn't matter that you'll never be called to write an exam, or anything else for that matter, in Middle English ever again, you still have to write your answers in Middle English. And not only that, the questions you have to answer—they're not about major writers, they're not about Chaucer and Milton and Pope, they're about, I don't know, some obscure poets no one's ever heard of. And you have to memorize every word that the poets wrote. And these poets wrote hundreds of thousands of terribly boring poems. And on top of that, you have to memorize twelve sixteenth-century treatises on the nature of melancholy and be prepared to recite any chapter upon being told its number. If you can imagine that, then perhaps you can imagine what it's like to take the tripos.”