Authors: David Leavitt
The Indian Clerk (32 page)
T
HE NEXT MORNING Ramanujan fails to show up at Hardy's rooms. "Curious," Hardy says to no one. But he goes about his business
anyway. He reads the papers; works, as best he can, on the partitions formula; finding that he cannot concentrate, picks up
the
Cambridge Magazine,
and then throws it aside. How vexing! The moment of ferment is fading—he can feel it. Important work may be lost, and it will
all be Ramanujan's fault. But there's no point in dwelling on that, so he retrieves the
Cambridge
Magazine
from where he's dropped it. Since a few months ago, Mrs. Buxton, wife of Charles Buxton, who was to have spoken at the ill-fated
meeting of the U.D.C, has been editing a section entitled "Notes from the Foreign Press," which consists of excerpts of articles
from dozens of foreign papers, including enemy papers, which she has managed to obtain permission to import from Scandinavia,
translated into English.
Neue Freie Presse
(chief Vienna daily),
National Tidende
(Copenhagen, conservative),
Vorwarts
(German, Social Democratic) . . . How varied are the responses to the war, how right every side believes itself to be! His
eyes wander to the adverts.
Under the Red
Robe
is playing at the Victoria Cinema, accompanied by
His Soul
Reclaimed
("a very Dramatic Episode of the Staircase Life") and footage of "20,000 German prisoners captured in Champagne." Chivers'
Olde English Marmalade, Officers' Uniforms at Joshua Taylor & Co., "Health Uber Alles" at Le Strange Arms and Gold Links Hotel,
Hunstanton.
Hun
stanton? . . . Outside his window, the sun has come out. Why not a walk? So he puts on his coat, heads downstairs, happens to stroll by Bishop's
Hostel.
On Ramanujan's landing, he encounters a bedmaker. "No sign of him, sir," she says. "And all that food going to waste."
"Why don't you eat it?"
She blushes. "Oh, sir, it's rather strange food what he eats. I'd be afraid."
"Well, let me know when he comes back, would you? Or tell Mrs. Bixby."
"Of course, sir."
That night, at Hall, Russell asks what's happened. "I suspect he's gone to London," Hardy says. "Nothing to be concerned about."
But afterward, when he gets back to New Court, he finds young Ananda Rao waiting at the foot of his stairs in his gown and
mortarboard.
"He is not in London," Ananda Rao says. "I telegraphed Mrs. Peterson. He is not at her boardinghouse."
"I wouldn't worry. I'm sure he'll be fine."
Ananda Rao doesn't move. Is he hoping that Hardy will invite him upstairs?
Should
Hardy invite him upstairs?
"Well, goodnight," he says finally.
"Goodnight, sir," Ananda Rao says. And he turns away. Is there a look of regret on his face as he walks toward the archway?
Hardy closes the door. A missed opportunity perhaps. If so, one better not taken up. After all, he is a student. And, as Ramanujan
himself said, "immature."
F
OUR DAYS PASS, and not a sign of him. Finally Hardy tells Mrs. Bixby to give Ramanujan's bedmaker permission to throw away
the food from the dinner party, which is starting to stink. He sends a note to Chatterjee, asking if he's heard any news.
"I have not," Chatterjee replies. "But I am told by some who know Ramanujan better than I that such disappearances are not
out of character for him. He has done the same thing before."
Then another note arrives, from Mrs. Neville.
Dear Mr. Hardy,
I am deeply distressed to learn from my husband of Mr. Ramanujan's "dinner party" last week and his subsequent disappearance.
What distresses me far more, however, than the question of what provoked his disappearance (a matter on which I can only speculate),
is the impression I have that nothing is being done. Has it not occurred to you that he may be lying ill or injured on a roadside
somewhere? Did he have money with him when he left? Should the police not be notified?
Please inform me as soon as possible what steps have been taken. If I do not hear from you by the end of the day I shall take
steps to notify the police myself.
Alice Neville
Interfering bitch. What business is it of hers, anyway? But he writes the required reply.
Mrs. Neville,
While I understand, of course, your concern over Mr. Ramanujan's well-being, I would beg you not to jump to conclusions. He
is a grown man and capable of taking care of himself. Nor, I gather, is it unusual for him to "disappear" from time to time.
The genius often has odd habits. Until there is reasonable cause to do so, I cannot see what benefit would be gained from
contacting the police, short of humiliating Mr. Ramanujan and leading him to believe that he is not, in our country, free
to go where he pleases and do what he pleases.
G. H. Hardy
No reply is forthcoming, at least not from Alice. Gertrude writes, though.
Dear Harold,
Alice is in a state of extreme anxiety over Ramanujan which your note did little to allay. Can you do nothing to ease her
worry? Short of that, will you promise me no longer to add to it? She is very sensitive and genuinely cares about Ramanujan.
Your loving sister,
Gertrude
Well, what's this about? And from Gertrude, of all people! Has Alice somehow won her over? Gertrude, he knows, has little
patience for hysteria. So how is it that suddenly she has become Alice Neville's advocate?
The ways of women will never cease to perplex him.
T
UESDAY, A WEEK since the dinner party, there is a knock on his door. He opens it and sees Chatterjee.
"I have received a telegram from Ramanujan," Chatterjee says.
"Thank God. Where is he?"
"Oxford."
"What's he doing there?"
"He doesn't say. He only asks me to send him five pounds."
"Good lord!"
"The address is a boardinghouse. I suspect he has to pay the bill and his train ticket back to Cambridge."
"Have you sent it?"
Chatterjee looks at the floor. "I could do so in a week," he says, "but at the moment, old chap, I don't have five pounds
to spare . . . the wedding arrangements . . . I could manage two . . ."
"Not to worry," Hardy says. "I'll send it. What's the address?"
Chatterjee hands him a slip of paper. They walk together to the telegraph office. "Do let me know when you hear from him,
will you?" Hardy says afterward, as they're heading out into the street.
"Of course. Good of you to help him out."
"And I'm sorry about the dinner . . . I hope Miss Rudra wasn't offended."
"She's a simple girl. Such things don't affect her."
They shake hands and part. Hardy returns to his rooms. All that afternoon and evening he fights the impulse to stroll by Bishop's
Hostel, or—stronger still—to check the train schedule, to wait at the station for the trains from Oxford.
Instead he asks Mrs. Bixby to ask Ramanujan's bedmaker to let her know once he's come back.
"He returned late last night, sir," Mrs. Bixby tells him the next morning.
"Good. Thank you," Hardy says. Then he runs about, setting things up in the room to give the impression that in the interval,
he hasn't even missed Ramanujan. Newspapers spread on the table, figures on the blackboard, paper on the desk.
As expected, around nine, there is a knock on the door. Hardy opens it.
"Good morning," Ramanujan says.
"Good morning," Hardy says.
Ramanujan steps inside. He is holding what appears to be a page torn from the
Daily Mail,
soiled and crumpled. "I believe I have made some refinements to the partitions formula," he says.
"Excellent. I'm eager to see them."
Ramanujan unballs the page from the
Daily Mail,
the margins of which, Hardy sees now, he has covered with tiny figures and symbols, written in his familiar, tidy hand. "It
is far from complete. Still, with low values I obtain a result that is fairly close to p(n). About five percent off."
"Yes, I obtained much the same result, working on my own, while you were gone."
"Did you? Well, then . . ."
Ramanujan folds up the ball of paper; sits. Hardy sits across from him.
"The trouble is, we need a table of high values in order to have accurate solutions with which to compare the results of the
formula."
"Indeed." Hardy is quiet for a few seconds. Then he says, "Ramanujan, I don't want to pry, nor are you in any sense obliged
to answer, but. . . Well, we were all rather worried when you left. Tell me, why did you go to Oxford?"
Ramanujan looks into his lap. He rubs his hands together.
"It was the ladies," he says after a moment.
"The ladies?"
"Miss Rudra and Miss Chattopadhyaya. They would not accept the food I offered."
"But they did accept it."
"I offered them third bowls of
rasam
and they would not accept. I was hurt and insulted, and I went out in despair. I didn't want to come back. Not while they
were there. But I had a little money in my pocket, so I went to the station and caught the first train to Oxford."
"But the ladies had already eaten two bowls. I don't know how it is in India, but you must remember, in England, at least,
ladies like us to think, well, that they have smaller stomachs. They feel it would be impolite, unfeminine, to eat too much."
"I worked for more than a week preparing that meal. They insulted me. I could not sit by while—"
"Still, you could have let me know. The fact is, it was quite an inconvenience, your being away."
"I wasn't idle. As I said, I made some improvements on the formula. And now if we could just obtain some high values for the
function, we would be in a position to test it out."
"Oh, don't worry about that. We'll ask Major MacMahon."
"Who is Major MacMahon?" Ramanujan asks.
"You shall soon see," says Hardy. "He's very curious to meet you."
W
HO
IS
MAJOR MACMAHON? He is the sort of man who might best be summed up by his titles. Among other things, he is, or has been, Deputy
Warden of the Standards
of the Board of Trade, Member of the
Comite International des Poids
et Mesures,
General Secretary of the British Association, Fellow of the Royal Society, Former president of both the London Mathematical
Society and the Royal Astronomy Society, Member of the Permanent Eclipse Committee, and Member of the Council of the Royal
Society of Art.
Major MacMahon is the son of Brigadier-General P. W. MacMahon. For some years he was with the Royal Artillery in Madras, where
he participated in a famous punitive attack against the Jawaki Afridis in Kashmir. Upon his return to England he was named
professor of mathematics at the Artillery College in Woolwich, where Littlewood now toils. Then he retired from the military,
and now he lives with Mrs. Major MacMahon on Carlisle Place in Westminster. He has enormous whiskers, and would be the first
to tell you that he enjoys nothing better than a glass of good port and a game of billiards.
In March of 1916, Hardy takes Ramanujan to see him. When they arrive at his house, the maid leads them not into the sitting
room but the billiards room, the floor of which is laid with Indian carpets pillaged, in all probability, during that famous
raid in Kashmir. All the furniture—the sofa, the Queen Anne chair with its ball-and-claw feet, even the billiards table itself—drips
gold and red bullion fringe. From over the hearth, a deer's head gazes down with that expression of mingled contempt and boredom
at which taxidermists seem to specialize. Ramanujan looks at it, then turns away, clearly disconcerted.
"Haven't you ever seen a hunting trophy?" Hardy asks.
He shakes his head no.
"In England they kill for sport. I say 'they' because I myself would never take part in such a barbaric form of self-amusement."
"And do they eat the deer?"
"Only occasionally."
Now Major MacMahon comes into the room, accompanied by Mrs. Major MacMahon, who immediately announces that she doesn't understand
a thing about mathematics and must go to the kitchen to oversee some bottling. Then she leaves. The major motions for Hardy
and Ramanujan to sit on the sofa. He opens a box of cigars, takes one out and lights it; offers the box to Hardy and Ramanujan,
both of whom decline. "Well, I'll smoke alone then," he says, with a twinge of mild affront. "So, Mr. Ramanujan"—blowing smoke
in his direction—" I understand you're a crack calculator. As Hardy may have told you, I'm rather decent at mental arithmetic
myself. How about a little contest?"
"Contest?"
"Yes, contest." The major stands again, and pulls a blackboard on wheels from the corner. "Here's what I want you to do, Hardy.
I want you to write down a number, any number you like, and then we'll see which of us can break it down first."
He throws Ramanujan a piece of chalk, which Ramanujan fails to catch.
"You stand here, next to me. When you've got the answer, put it on the blackboard."
But Ramanujan is on the floor, trying to find the piece of chalk, which has rolled under the sofa. Only once he's retrieved
it does he walk to the blackboard.
"All right," the major says, rubbing his big hands together. "First number?"
"Let's say . . . 2,978,946."
A few seconds pass. Then both men are scratching with the chalk.
The major finishes first—the answer is 2 × 3
2
× 167 × 991—though Ramanujan isn't far behind.
"Too close to call?" asks Hardy.
"I believe the major bested me," Ramanujan says.
"Then let's go on." And Hardy calls out another number. And another. More often than not, the major wins.
Finally Hardy throws out the number 4,324,320.
Instantly Ramanujan writes the answer: 2
5
× 3
3
× 5 × 7 × ll × 13.
"But that's not fair, Hardy," the major says. "That's one of his highly composite numbers. He has the advantage."
"I don't see why that should matter," Hardy says. "Though it's true that he's figured them out through—how many?"
"6,746,328,388,800," Ramanujan says.
"Yes, but you missed one," the major says.
"He missed one?"
"I've been looking forward to telling you." And now the major fishes in his jacket pocket, drawing out a crumpled sheet of
paper.
"29,331,862,500," he reads. He hands Ramanujan the paper, at which Ramanujan stares with a stricken look on his face.
"How did you find it?" Hardy asks.
"It's my specialty," the major says. "It's why you've come here."
Combinatorics is an old science. As the major explains, it has its origins in Ramanujan's country, in an Indian treatise of
the sixth century B.C. entitled the
Sushruta Samhita.
"It's actually a cookery book," the major says. "What it does is take the six different flavors, which are bitter, sweet,
salty, hot. . . Oh damn, what's the fifth? Now let me see. Bitter, sour, sweet, salty, hot . . ."
"Tart?"
"Yes, tart. Thank you." As he speaks, he's setting up a game of billiards.
"Anyway, so the treatise takes the six flavors and combines them, first one at a time, then two at a time, then three at a
time, and you end up with sixty-four possible combinations in total if you add in the possibility of English cookery—no flavor
at all. Ha! And that, in essence, is enumerative combinatory analysis. Only of course our methods today are somewhat more
sophisticated." The major hits a ball into a pocket. He aims again, misses, and hands the cue to Ramanujan.
"Have you ever played billiards before?"
"No."
"It's simple, just hold the stick like so"—he stands behind Ramanujan, lines him up—"and aim for the white ball."
Ramanujan concentrates. With surprising expertise, he cues, shoots, and gets a ball into the pocket. "Bravo," the major says,
applauding. "Now go again." Again, Ramanujan aims. This time, however, he stumbles, nearly ripping the green baize with his
cue stick. The white ball goes bouncing over the edge of the table, then rolls along the floor, only to bump against one of
the armchair's clawed feet.
"Never mind," the major says, retrieving the ball. "It's your first time out."
Ramanujan says that he'd prefer to watch and learn, so Hardy takes the stick from him. As he and the major play, they talk
about partitions. What Hardy and Ramanujan are after is a theorem: that machine into which you would insert the billiard ball
emblazoned with one number only to see it emerge, a few seconds later, emblazoned with another. Of course, because the theorem
will be derived from an asymptotic formula, the number won't, in all probability, be exact; it will have to be rounded off.
This bothers Ramanujan more than it does Hardy. "The great weakness of young mathematicians confronted with a numerical problem,"
Hardy says, "is that they can't see where accuracy is essential and where it's beside the point."
"You might think of combinatorics as a machine, too," the major says. "A different sort of machine, though. Have you heard
of Babbage's analytical engine? He never built it. Well, combinatorics is like that machine that Babbage never built. And
Byron's daughter—she was a mathematician, you know, worked with Babbage—she said of it"—the major clears his throat as he
cues up—" 'We may say most aptly, that the Analytic Engine weaves algebraic patterns just as the jacquard loom weaves flowers
and leaves.' Nicely put, which is no surprise, coming from Byron's daughter." He hits and gets a ball into a pocket. "Well,
that's what I do. I weave patterns. I have an analytic engine of my own—right here." He taps his own skull.
"And am I correct in understanding that of late you've been weaving partition numbers?" Hardy asks.
"You are indeed correct. I'm working my way up the number line, roughly, skipping a few here and there."
"How far have you got?"
"Yesterday I got p(n) for 88."
"How long did that take?"
"A few days."
"And what was the answer?
"You expect me to have it memorized?" The major chuckles. Then he puts his right hand on his chest, thrusts out his left arm,
and declaims, "44,108,109."
"44,108,109," Ramanujan repeats. As he stands there, he seems to fondle the number.
"A man after my own heart," the major says, patting him on the back.