“I know. I misspoke. A poor effort at a joke. Please, take the letter.”
He holds it out like an offering. Reluctantly Littlewood accepts it. Hardy looks humbled, and Littlewood's umbrage melts. Poor fellow! “Very good, sir,” he says, to show there are no hard feelings, and mimics a military salute. “Goodnight.”
“Goodnight,” Hardy replies, his voice chilly and wistful. He shuts the door.
Littlewood is still young enough that, when he's alone and going downstairs, he bounds, taking the steps two at a time. Right now he's thinking about Mercer—not Mercer as he is today, but as he was when they were both coaching for the tripos. Back then, Mercer only spoke when spoken to. When he was writing, his head bobbed over the paper with metronomic regularity. Littlewood will be the first to admit that Mercer's strange mode of concentration, his apparent obliviousness to everything around him, unnerved him in a way that the stunts perpetrated by his more competitive fellows—gestures meant to distract—never did. And what in Mercer could possibly have appealed to Hardy? Not that he wants to hear the gory details of the case, which in this instance probably aren't even details of sex, but rather of infatuation, which is somehow worse. Littlewood knows, because he's been on the receiving end of infatuation: the hours the poor devils spend trying to “read” a smile, or interpret a pat on the shoulder, or discern the secret import of the loan of a pencil. Schoolgirl nonsense. And the notes: “Although we have never spoken, and I am no doubt invisible to you, may I risk offense by remarking on the pleasure I have taken, so many mornings, watching you bathe …” Still, he'd be curious to hear how things started with Mercer, and why they soured.
The rain keeps up its pluvial dance. He runs all the way to Nevile's Court without opening his umbrella. He likes the feel of the beads of water sliding down his forehead, and only wishes he wasn't so hungry.
One thing to be glad for is solitude. If he chooses to, he can go straight to bed. No phantom lover will visit him in his dreams. (And of whom will Hardy dream? He shudders to think.) Or perhaps he won't go to bed at all. Perhaps he'll sit up all night, studying the Indian's letter. And if he does, there'll be no one to scold him. No shadowed figure in a nightdress, holding a candle, will beg him to come to bed. No child will call him to comfort her after a nightmare.
He steps indoors. The silence of his rooms is familiar, consoling. No two silences are alike, he thinks; each has its own contours and shadings, because inside each silence there is the absence of a sound, and in this case it is the sound of Mozart played badly on a piano, or Beethoven, played beautifully, issuing from the horn of a gramophone. He takes off his jacket, and as he does he smells Anne's scent on it—very faint now. Then he kicks off his shoes, lights his pipe, and sits down to reread the letter.
9
CLOSE TO MIDNIGHT the rain thins a little. Hardy, in his pyjamas, watches it through the window that gives on to the archway. Although of late he's got into the habit of going to bed on the early side, tonight he can't imagine sleeping. Despite his mounting excitement over Ramanujan's new letter, he's fallen into a bad humor, thanks to Littlewood's barb about Mercer. It was his own fault, of course. If he hadn't mentioned Littlewood's having been senior wrangler, Littlewood would never have brought up Mercer. The fact is, Hardy doesn't want to be reminded of Mercer, whom—he cannot pretend otherwise—he has pretty much abandoned. For instance, when Mercer returned to Cambridge last year, he sent Hardy a card inviting him to call on him and his new bride. Hardy never replied. There was no good reason for it, either, other than that Mercer was no longer at Trinity. Then again, Christ's College is hardly the other side of the world.
His new bride. What would Gaye have to say about that?
Almost automatically, Hardy glances across the room. From the mantelpiece, the bust gazes down at him (Gaye gazes), its aspect as reproachful as that of Sheppard's mother. It's a small bust, made when Gaye was fifteen, the expression, as always, glinting and coy. Sometimes Hardy wonders what would happen if he took the bust and smashed it to pieces, or stuffed it away in a cupboard, or presented it as a gift to Butler, who, given the circumstances, would probably stuff it in a cupboard of his own.
The answer, of course, is that it would make no difference. Gaye's hand is all over the room. Grant him this much: he had taste. He picked the Turkey carpet, and soaked the chintz curtains in a bathtub full of tea to give them their look of having hung for years in a country house. He chose the checked fabric for the cushions on Hardy's rattan chair—the very cushions Hardy is sitting on now. All this, even though Hardy was leaving him. Poor Gaye, always so drawn to martyrdom! The old painting of Saint Sebastian he kept over his bed should have been a clue. It's gone now, taken away by his brother, along with everything else that was of any value.
And why did Gaye's brother not take the bust? It's true, when he came around, Hardy made a point of standing it in a back corner of his bedroom, not the most likely place to look. But he didn't hide it. Afterward, for years, he kept expecting a letter from the family, demanding restitution of the bust. None ever came. Perhaps they were as eager to forget about Gaye as everyone else was.
Around one, he gets into bed. Still, he can't sleep. Figures swirl in his head, fragments memorized for the tripos, and oddities from Rama-nujan, and the zeta function, its peaks and valleys and the spire soaring up to infinity when it takes the value of 1 … This often happens to him. Sometimes such insomnia bodes well, means that a breakthrough will come in the morning. More often he wakes ill-humored and unable to work. So why doesn't he share Littlewood's terror of false hope?
And then—just, it seems, as he is falling asleep (though later he will realize that he had been asleep for almost two hours)—there is a knock on the door. At another time in his life, this wouldn't have surprised him. A visitor at three in the morning would have been routine. Now, though, the knock disorients him, throws him into a panic. “Just a minute,” he calls, putting on his dressing gown. “Who is it?”
“Me. Littlewood.”
He opens the door. Littlewood strides in, dripping and umbrellaless.
“The stuff about primes is wrong,” he says.
“What?”
“Oh, sorry. Have I woken you?”
“It doesn't matter. Come in.”
Without even removing his coat, Littlewood heads for the blackboard, still covered with Hardy's earlier scribblings. “I couldn't sleep so I started looking over the letter and—may I?”
“Of course.”
“Right, so this is what I think he's done.” He wipes the blackboard clean. “Here's his formula for calculating the number of primes less than n. Well, it's the usual Riemannian formula, except that he's left
out the terms coming from the zeros of the zeta function. And his results—I've tested them—are just what you'd get if the zeta function had no non-trivial zeros.”
“Damn.”
“I have a vague theory as to how the mistake came about. He's staking everything on the legitimacy of some operations he's doing on divergent series, banking on a hunch that if the first results are correct, the theorem must be true. And the first results are correct. Even up to a thousand the formula gives exactly the right answer. Unfortunately, he had no one around to warn him that the primes like to misbehave once they get larger.”
“Still, leaving out the zeros … it's not an encouraging sign.”
“Oh, but there I disagree, Hardy. I think it's a very encouraging sign.” Littlewood steps closer. “You must realize, ordinary mathematicians don't make mistakes like this. Even very good mathematicians don't make mistakes like this. And when you consider the other stuff, the stuff on continued fractions and elliptic functions … I can believe he's at least a Jacobi.”
Hardy raises his eyebrows. Now this is high praise. Since starting at Trinity, he's kept up a mental ranking of the great mathematicians, putting each in the class of a cricketer whom he admires. He judges himself the equal of Shrimp Levison-Gower, Littlewood on a par wit
h Fry, Gauss in the category of Grace, the greatest player in the history of the game. Jacobi, the last time Hardy ranked him, was somewhere above Fry but below Grace—in the vicinity of the young and dazzling Jack Hobbs—which means that Ramanujan, if Littlewood is correct, might have the potential to be another Grace. He could well prove the Riemann hypothesis.
“What about the rest?”
“I haven't had a chance to go over these other asymptotic formulas, but at first glance, they look to be totally original. And significant.”
“But no proofs.”
“I don't think he really understands what a proof is, or that it's important to give one, because he's been working on his own all these years, and who knows what books, if any, he has access to. Perhaps no one's taught him. Could you teach him?”
“I've never tried to teach anyone why you have to give proofs. My students have always just … understood.”
There is a moment of quiet, now, of which Hermione takes advantage by rubbing herself against Littlewood's leg. When he tries to pick her up, she runs for cover beneath the ottoman.
“A tease, that female. Come here, kitten!”
“She can't hear you. Remember?”
“Oh, of course.” Littlewood regards the floor.
“And what are we to do now?” Hardy asks.
“Is there any question? Bring him to England.”
“He's said nothing about wanting to come.”
“Of course he wants to come. Why else would he have written? And what's he got in Madras? A clerkship.”
“But if we get him here, will we know what to do with him?”
“I think the more apt question is, will he know what to do with us?” Littlewood pushes his glasses up on his nose. “Have you heard from the India Office, by the way?”
“Not yet.”
“Well, if you want my advice, which you may not, there's only one course to take, and that's to get a man to Madras. And soon. I think Neville's supposed to give some lectures there in December.”
“Neville?”
“Don't scoff. He's a decent chap.”
“Neville is a perfectly capable mathematician who will never in his life do anything of consequence.”
“The ideal emissary, then.” Littlewood laughs. “Let's bring him in on it, shall we? And then, when he gets to Madras, he can see this Ramanujan, feel him out, see what he wants and if he's what we want.”
“But is Neville capable of such discernment?”
“If he's not, his wife is. Have you met Alice Neville? An impressive young woman.” Littlewood is already moving toward the door. “Yes, it's the best plan. What's the saying? If you can't bring Mohammed to the mountain, bring the mountain to Mohammed.”
“Wrong religion,” Hardy says.
“Oh, well, Vishnu then! Good God, Hardy, you can be quite a stickler.” But Littlewood is laughing as he says this, laughing as he descends the stairs, laughing as, with a whistle and whoop, he steps out onto the rain-soaked paving stones of New Court.
10
New Lecture Hall, Harvard University
ON THE LAST DAY of August, 1936, the great mathematician G. H. Hardy put down his chalk and returned to the dais. “The real tragedy about Ramanujan,” he said, “was not his early death. It is of course a disaster that any great man should die young, but a mathematician is often comparatively old at thirty, and his death may be less of a catastrophe than it seems. Abel died at twenty-six and, although he would no doubt have added a great deal more to mathematics, he could hardly have become a greater man. The tragedy of Ramanujan was not that he died young, but that, during his five unfortunate years, his genius was misdirected, sidetracked, and to a certain extent distorted.”
He paused. Did his audience understand what he meant? Might they think that he was referring to the five years Ramanujan spent in England?
No, he wanted to say, not his years in England. I mean the crucial years just before he came to England, when he needed education as a newborn child needs oxygen.
Or perhaps—and here, in his own mind, he stepped back—I really do mean his years in England, which in their way were also years of damage.
He would have liked to say:
So little seems certain anymore. Words that I wrote in the immediate aftermath of his death, when I read them today, strike me as rank with sentimentality. They emanate the desperation of a man trying to escape guilt and blame. I tried to make a virtue of his ignorance, to persuade myself and others that he profited from the years he spent in isolation, when in fact they were an insurmountable handicap.
Nothing ever came easily to him, and there is no way to pretend that this was to his good. He was very poor and lived in a provincial town, more than a day's journey from Madras. And though he went to school (he was of a high caste), school was not kind to him. Starting when he was fifteen, sixteen, he was treated as a pariah. The Indian educational system, in those years, was terribly rigid, far more rigid than our own, on which it was modeled. The system rewarded the nebulous ideal of “well-roundedness”; it was designed to churn out the bureaucrats and technicians who would oversee the Indian empire (under our supervision, of course). What it was not designed to do was to recognize genius—its obsessiveness and its blindness, its refusal to be anything other than what it is.
School after school failed Ramanujan because at school after school he ignored all his subjects except mathematics. Even at mathematics he was at times mediocre, because the mathematics that he was being taught bored and irritated him. From his youth—from when he was seven, eight years of age—he was following the signposts of his own imagination.
One example will suffice. When he was eleven, studying at Town High School in Kumbakonam, his maths teacher explained that if you divide any number by itself, you will get 1. If you have sixteen bananas and divided them among sixteen people, each will get one banana. If you have 10,000 bananas and divide them among 10,000 people, each will get one banana. Then Ramanujan stood up and asked what would happen if you divided no bananas among no people.
You see, even then, when he was still doing well, the troublemaker in him was starting to emerge.
I think I sensed all this from his early letters. He was a man whom the dispensers of prizes had failed to esteem properly and he resented them for it. Naturally this rejection led him to doubt his own worth; and yet from the start he also displayed a certain hubris, a faith in his genius, and took a solitary pride in knowing that he was better than his time and place. If the world in which he lived failed to value him, it was that world's fault, not his own. Why should he then cooperate? Yet this is a very lonely sort of victory.
Of course, in this regard I was his opposite. I was the boy who won all the prizes—this, though I despised prize day with an intensity that today only the sight of a church procession is likely to rouse in me. To hear my name called, and then to have to get up before the entire school to accept my prize, provoked in me such a furor of shame and self-loathing as to make my legs wobble; I would stagger onto the stage in a kind of fever, take the book or token with clammy hands, grit my teeth so as not to vomit. By the time I got to Winchester, this peculiar variant of stage fright had got so bad that I started deliberately giving the wrong answers on examinations, just in order to be spared the ordeal of the prize. But not—I must be truthful about this— often enough that I might jeopardize my future. For I craved the imprimatur of Oxford or Cambridge, the approbation that Ramanujan was denied.
Why such hatred of prizes? I think it was because I knew, even as I excelled on its greeneries, that the playing field was rigged. It was rigged to reward the rich, the well fed, the well cared for. And, as my parents made sure constantly to remind me, I was not one of these. I was lucky to be there at all. Talent would not assist the son of the miner in Wales: he'd spend his life in the mines, even if he had the proof for the Riemann hypothesis in his head. Always my parents told me to pray for my own good fortune, and theirs.
Perhaps it i
s a sign of weakness that I played by the rules. No doubt some future biographer (if I merit one) will censure me for this failure of nerve. For there is another way to look at Ramanujan: as the resolute mind whom genius permits no other course but to follow its instincts, even at its own peril.
Once I arrived at Cambridge my mistrust of prizes, rather than abating, found a new target in the tripos. The men I despised the most were the ones who, unlike me and Littlewood, viewed victory on the tripos as a goal in its own right, and made wranglerhood the object of their education. It was to stop in its tracks the system that encouraged such fevered ambitions and immoderate hungers that I set out to reform the tripos, if not abolish it outright. And the ironic result of my success was this: never was the fever for tripos victory so intense as it was in 1909, the year the last senior wrangler was to be crowned.
Which brings me to Eric Neville—the man some credit with persuading Ramanujan to come to England. Later on, we became friends, and remain friends to this day, his wife notwithstanding. In 1909, however, Neville existed for me merely in one dimension, as the man considered the favorite, that year, to be senior wrangler. As it turned out, he came in second, and I remember gloating a little bit, thinking that he would never recover from the disappointment. He wanted so desperately to go down in history as the last of the senior wranglers.
But it is not of this tripos that I am thinking tonight; no, it is of an earlier tripos, the tripos of 1905, the one tripos during which I myself (I am ashamed to admit it) played the very role I now vilify: that of coach.
The boy I coached was named Mercer. James Mercer.
How to explain my closeness to Mercer? I suppose, at first, I was drawn to him because, like me, he was an outsider. He had come to Cambridge from University College, Liverpool, and was consequently older than most of the other men. Shy of his accent. The first time he came to see me, he covered his mouth with his hand.
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