Our ablutionary habits were not the only ones that puzzled him. Why, he asked me, did children not stay with their parents after they married? Did they not love their parents? Would they not be lonely? I answered that the English valued independence, and this concept, too, he found strange. Used to sleeping anywhere at all, in a small house shared with many people, he even found it strange to have his own room.
Autumn drew to a close, and the weather started getting cold, colder than anything he had ever known. This is perhaps the aspect of his English experience that I am least able to imagine—I, who from early childhood became habituated to the vagaries of winter: numb fingers, chapped lips, the struggle to compel the blanket to exert a few extra degrees of warmth. Clothes, which he had always looked upon purely as a kind of decoration, a way of embellishing the body while protecting his modesty, he now had to use, for the first time, as layers of defense against the encroachments of winter. Not only did he have to contend with the terrible, pinching shoes, but with gloves, scarves, galoshes, greatcoats, hats. Rain he knew from the monsoons—but warm rain, leaving steam and moisture in its wake. Here, on the contrary, even the brief walk to New Court could be a struggle with wind gusts that threw sheets of sleet and hail into his eyes, and broke the spine of the umbrella I'd given him. Bathing was an ordeal. No wonder the English were, from his point of view, so filthy! For who could endure more than one bath a day when the temperature in the bathroom was below freezing?
When he got to my rooms in the morning, I would watch him unwrap himself and then give him coffee, which he drank gratefully and in quantity. I toasted crumpets for him over the fire. Still, he never seemed to be able to get warm enough. I myself thrived in cold weather; the morning found me bright and vigorous, my cheeks red from a brisk walk. Ramanujan, on the other hand, would be pallid. He wasn't sleeping well, he told me. Perhaps I should have taken this as a warning sign; and yet there was so much to distract the attention in those days of war!
Inattention: the schoolboy's perpetual excuse. I was looking at something else. The other boy hit me first, I wasn't listening, sir. What right have I to resort to it now when I would never accept it from a student?
No, what I am offering is not an excuse. It is a confession.
PART FIVE
A Terrible Dreaming
1
BY SEPTEMBER, Trinity is a different world. Whewell's Court is a barracks. When he goes to meet Hardy each morning, Ramanujan must navigate bunks and tents and a mess. Nevile's Court is an open-air hospital. Wounded soldiers, their faces and limbs bandaged and bloodied, lie in neat rows on metal frame beds under the arcades of the Wren Library. Across the way, lights have been strung from the ceiling of the south cloister, which has been made into an operating theater.
To the extent that he can, Hardy stays in his rooms. Soldiers parade everywhere. In Great Court, Butler preaches to the troops, warning them to resist French temptresses. Colonels and captains in khaki dine at high table, toasting with champagne if the next morning one of their fellows is to be shipped off. This spectacle is so distasteful to Hardy that he starts eating alone in his rooms. Eggs and toast. The food of his childhood. When he does go out, he finds himself strangely drawn to the library arcade, to the soldiers who were running fresh not a month earlier. Now dozens of them arrive every day, feverish from infected wounds, suffering from lockjaw, typhoid, spotted fever. As he passes, they ask him for cigarettes, which he provides, much to the chagrin of the sisters. The sisters don't like to see their patients smoking.
Few others are around, which leaves Hardy feeling a certain sadness that he recalls from his childhood, a sadness associated with the September days before school began, each one shorter than the last, during which it seemed that everyone in the world except him had something to do, somewhere to be. Now, when he walks the river, he never runs into anybody. Littlewood is gone, a second lieutenant in the Royal Garrison Artillery. Keynes is at the Treasury. Russell is off speechifying against the war. Rupert Brooke, thanks to Eddie Marsh's intervention, has got himself a commission in Churchill's Royal Naval Division. Békássy is in Hungary, Wittgenstein in Austria. It doesn't matter that they're fighting on the other side. What matters is that each is defending his fatherland, and, in doing so, taking part in some exalted, immemorial rite of manhood. Or so Norton explains it. Norton makes it his business to explain things. He makes it his business to understand.
One weekend he arrives back at Trinity from London. He carries, or so it seems to Hardy, the redolence of Bloomsbury, its cloistered, bookish gloom. He asks Hardy what he's planning to do should conscription come, and Hardy replies, “I suppose I'll go to war.”
“You mean you won't be a conscientious objector?”
“I disapprove of conscientious objectors as a class,” Hardy says, by which he means that he disapproves of Norton as a class; of Blooms-bury as a class; of the image he has conjured up, of Strachey and Norton and Virginia Stephen (now Woolf) sitting in their London libraries, gazing out at the rain and muttering, “Oh, the horror!” Strachey, Norton tells him, won't talk about the war. He spends his evenings reading books that take him as far from the war as he can get. Right now, for instance, he's reading Memoirs of the Lady Hester Stanhope. And why does the idea of Strachey sitting up in bed, no doubt in a nightcap, with Memoirs of the Lady Hester Stanhope open on his lap, fill Hardy with such distaste? He's no better, really. His cloister is New Court. And instead of Lady Hester Stanhope, he's rereading The Portrait of a Lady.
As for Norton—well, if there's evidence of the degree to which he's muffled himself, it's that he fails entirely to pick up on Hardy's insult, and says simply that he will certainly declare himself a conscientious objector should the necessity arise—not, Hardy senses, out of conscience but simply to protect himself. And how is Hardy supposed to respond to that? It seems to him that every day he and his old friend have less to say to each other, even though they still sleep together now and then.
What preoccupies him most is this question of what he should call himself. Is he a pacifist? Certainly his disapproval of this shameful war is as absolute as Russell's. And yet he can't claim that he disapproves of all war. He would fight a just war. So the question is: has this war, despite its beginnings, now become a just war? The wounded soldiers, when he sits with them, cannot stop speaking of the atrocities in Louvain, the sacking and burning of houses, shops, farms, and, worst of all, the library, the famous library, as celebrated for its collection of rare and precious books as the one in the shadows of which they now lie. It's curious: few of these men are educated. Most, Hardy imagines, don't read at all. Yet the sacking of the library seems to have shaken them to the marrow. “To burn a library to the ground,” Hardy tells Moore, with whom he now strolls the arcades of Nevile's Court as once they strolled the meadows of Grantchester … But he can't finish the sentence. Who could finish such a sentence? Among the books burned there must have been German books, books by Goethe and Novalis and Fichte. And who burned them? The countrymen of Goethe and Novalis and Fichte.
The trick is to try to maintain some sense of balance, and in this regard, writing letters helps.
To Russell, who is giving a lecture tour in Wales, he writes: “How is it possible that England hungers to crush and humiliate Germany? What is wanted is peace on fair terms.”
To Littlewood, with whom he tries to keep collaborating after a fashion, he writes: “It is proving harder than I suspected to teach him. His mind is like Isabel Archer's, it keeps jumping out the window. I can never keep him on any one topic for long.”
To Gertrude, whom he can see far less often now than before, he writes: “Please tell Mother not to worry. In all likelihood, if called up, I should be rejected on medical grounds—entre nous, I hope not, but don't tell her that.”
Ramanujan, too, is writing letters. He writes to both his parents. “There is no war in this country,” he tells his mother. “War is going on only in the neighboring country. That is to say, war
is waged in a country that is as far as Rangoon is away from Madras. Lakhs of persons have come here from our country to join the forces. Seven hundred Rajas have come here from our country to wage war. The present war affects crores of people. The small country Belgium is almost destroyed. Each town has buildings fifty to a hundred times more valuable than those in Madras city.”
His letter to his father is much shorter. “I have all the pickles,” he writes. “You need not send anything more. Except what you are sending now, do not send any other thing. I am getting on well. Do not allow the gutter to run as usual. Pave the place with bricks. I am getting on well.”
2
THAT AUTUMN, Ramanujan begins to publish. The Quarterly Journal of Mathematics brings out his “Modular equations and approximations to π.” To celebrate, Hardy takes him to a pub, where he refuses to drink anything. He tells Hardy that he's at work on a big paper on highly composite numbers. His equation is ingenious, and distinctly Ramanujanian (an adjective that Hardy has no doubt will soon be in circulation). It looks like this:
n = 2a2×3a3×5a5×7a7×…pap
where n is the highly composite number and a2, a3, a5 … ap are the powers to which the successive primes need to be raised so that the number can be written out as a multiple of primes. Thus, if we are dealing with the highly composite number 60, we can write it out as
60 = 22 × 31 × 51
Here a2 = 2, a3 = 1, and a5 = 1. If we are dealing with the largest highly composite number that Ramanujan has found, 6746328388800 (he writes it out on a torn piece of newspaper; he has not lost his Indian habit of hoarding scraps of paper), we would write
6746328388800 = 26 × 34 × 52 × 72 × 11 × 13 × 17 × 19 × 23.
What Ramanujan has managed to prove is that, for any highly composite number, a2 is always going to be bigger than or equal to a3, a3 is always going to be bigger than or equal to a5, and so on. And for every highly composite number—an infinity of highly composite numbers—the last factor is always going to be 1, with two exceptions: 4 and 36. In many ways it's the exceptions that intrigue Hardy the most, in that they reveal, once again, how notoriously resistant numbers are to the ordering impulse that, by their very nature, they invoke. Whenever you seem to be getting close to seeing the whole in all its lovely symmetry—the palace emerging from the autumn mist, with all its stately storeys, as Russell once put it— mathematics throws you a ball you can't hit. This is why, despite all the evidence to the contrary, Hardy won't accept the truth of the Riemann hypothesis without a proof. The numbers 4 and 36 come early on. But with the zeta function, the exceptions could come at lengths so remote from the human capacity to count that Hardy can barely conceive them. As Ramanujan has learned the hard way—as every mathematician has learned the hard way—the world of numbers brooks neither compromise nor shortcut. You cannot cheat there. You will always be caught out.
In any case, no one he has ever met seems to know the numbers as intimately as Ramanujan does. “It's as if each of the integers is one of his personal friends,” Littlewood said early on, a witticism that misses, in Hardy's view, the eroticism of working with numbers, the heat that rises off them, their vibrancy and unpredictability and, sometimes, danger. As an infant his mother gave him a set of numbered blocks, and then lamented that all he would do with them was hit them against one another, the 7 with the 1, the 3 with the 9. What she failed to recognize was his need, even then, to penetrate to the rumble of life within. Attractions and repulsions, euphonies and banshee screeches. Soon he had broken all of them except for the 7. All his life 7 has been his favorite number. Despite his atheism, he respects its mystic allure, just as he respects the less salubrious association carried by two other numbers that he refuses to speak, much less write down. It's not that he believes in the specific superstitions; it's that he's convinced that the numbers themselves give off vapors of malevolence. Other numbers that most people would consider perfectly benign he also despises: 38. And 404. And 852. Still others he loves. He loves nearly all the primes. He loves, for reasons that elude him, 32,671. And, now that Ramanujan has introduced him to them, he loves the highly composite numbers, and of the highly composite numbers, he loves 4 and 36 the most, because they defy Ramanujan's rule—4, and 36, and 9, the bridge between them; 9, which is 32. He crosses the bridge and steps into fields in which he knows Ramanujan has already tarried. So far as he can see, nothing edible grows here. They are sterile, or picked clean.
3
THE TIMES HAS made it official: half the men at Cambridge are gone to war. “Among the 50 percent of those left in residence,” Hardy reads, “many are foreigners and Orientals, and many of the others are beneath the age limit or have been rejected by the doctors on account of physical defects.”
So where does that leave him?
The Times also tells him the university has halted organized athletics for the present: “there are no men, there is no mind for the river and the playing-fields.” Well, he's tempted to write, there's at least one man who has a mind for cricket—indeed, for one man at least, the prospect of a spring without cricket is almost unbearable to contemplate. But this letter, even though he copies it out, he never sends.
Everywhere he goes, he sees Indians. They never take off their gowns and mortarboards, perhaps to insure that no one question their presence here. Under the best of circumstances they would be nervous. Now the war seems only to have amplified their self-consciousness. One afternoon, for instance, as he's walking through the Corn Exchange, he watches a gust of wind yank the mortarboard off the head of an Indian youth in King's College robes. With amusement and pity, he observes the comic turn of the youth chasing the mortarboard and bending to retrieve it, only to see it dashed off once again— playfully, cruelly—by the wind. Finally the mortarboard lands at Hardy's feet. He rescues it, dusts it off, and hands it to the Indian, who is out of breath from running. The Indian thanks him, then hurries in the opposite direction.
A few minutes later, Hardy sees him again, gathered at the corner of Trinity Street and Bridge Street with three of his countrymen. One is Chatterjee, the handsome cricketer with whom (it seems an eon ago) he conflated Ramanujan. The second is tall and stooped and wears spectacles and a turban. The third is Ramanujan himself. He waggles his head at Hardy. And what is Hardy supposed to do in response? Wave? Walk over and say hello? He chooses, on this occasion, just to wave.
The next morning, he asks Ramanujan who he was with. “Chat-terjee,” Ramanujan says. “He is from Calcutta. And Mahalanobis— he is also from Calcutta, studying natural sciences at King's—and Ananda Rao.”
“Oh yes,” Hardy says. “Isn't he the one who was coming to England on an Austrian ship? As I recall, you were worried he might not make it.”
“He had quite an adventure. By the time he and Sankara Rao reached Port Said, the war had begun. Near Crete an English ship started firing on them and ordered them to stop. Luckily their ship carried no guns. If the ship had carried guns, and the sailors had shot back, they would have been sunk.”
“What happened after that?”
“Everyone was taken prisoner and brought to Alexandria, where the ship was seized. The Indians and the Englishmen were put on another ship and sent to England. So he and Sankara Rao arrived safely.”
“And the tamarind?”
“It was undamaged.”
“What do you make with it again?”
“Rasam. It is a thin soup of lentils. Very spicy and very sour. The English in India call it ‘pepper water.’ If you like, I shall make some for you, Hardy. It tastes like rasam now. It did not when I used your lemons.”
“I should like to try it.”
“Perhaps I shall have a dinner. I shall invite some friends. Chatterjee and Mahalanobis, perhaps.”
“I would enjoy that,” Hardy says. But Ramanujan either changes his mind or forgets that he made the offer in the first place, for the invitation—to Hardy's mild regret—doesn't come.
4
New Le
cture Hall, Harvard University
ON THE LAST DAY of August, 1936, as the light outside waned, Hardy continued his imaginary lecture, all the while writing equations on the board and disquisiting, with his voice, on hypergeometric series:
I wonder (he did not say) if I can convey to you tonight—young Americans that you are, raised by your fathers to feel yourself victorious, and rightly so, flush with the knowledge that you both won and profited from the war—I wonder if I can convey to you how dark and lost and strange those years were for England. For me it was at once a busy time, my finger stirring a thousand pots, and trying to stop, as it were, a thousand dykes; and yet it was also a dull and dreary time, during which the rain never seemed to cease, and there was always ample opportunity to fret and anticipate, no matter how full the days might be. For we longed to feel that our lives, and the world we lived in, were real, despite the governmentally sanctioned unrealities that the newspapers routinely fed us. Sometime in the autumn of 1915, for instance, we were told that Servia would from now on be known as “Serbia,” in order that its honorable people should not think that we looked upon them as “servile.” Advertisements for “war kits at short notice” shared the same newspaper page with ones for motor cars. Most recreational sports having been more or less forcibly put on hold, the popular press took to likening the war to a cricket match. A certain Captain Holborn of the artillery division made it his habit to kick a football into enemy territory before launching an attack. This was regarded as behavior worthy of laudation. Even the puzzles in the Strand began to have war-related titles: “Exercising the Spies,” “Avoiding the Mines.” Which did not stop me from doing them.
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