AGAIN, HE ENCOUNTERS Ramanujan with his Indian friends. This time they are sitting by the river. The shadows of an elm afford him the chance to study them more carefully.
The stooped one with the turban is reading something aloud to the others. The youngest one—the one whose mortarboard blew away—has intense, darting, faunlike eyes. When he notices Hardy, he turns away.
The next morning, Ramanujan says, "Ananda Rao is quite in awe of you."
"Why?"
"Because he is studying mathematics, and you are the great mathematician. The great Hardy. But he is shy to introduce himself."
"He need not be."
"I tell him that, but he won't listen. He is a youngster."
"Tell him he can come to see me anytime."
Hardy opens his notebook, indicating that the time has come to go to work. "Ananda Rao is preparing an essay for the Smith's Prize," Ramanujan says.
"Oh, good for him."
"Might I submit an essay for the Smith's Prize?"
"But the Smith's Prize is for undergraduates. You're well beyond that."
"I do not have a B.A."
"Yes, the requirement was waived in your case."
"I should like to have a B.A."
"Well, I suspect we could arrange that."
"How?"
"You could do it 'by research,' as they say. Maybe your paper on highly composite numbers. You'll need to ask Barnes."
The next morning Ramanujan says, "I have asked Barnes, and he agrees. I can do the B.A. by research with the paper on highly composite numbers."
"Fine."
"Then I can submit my research for the Smith's Prize?"
"But you're eons beyond the Smith's Prize! Why should you even bother with the Smith's Prize?"
"You won the Smith's Prize."
"Prizes are meaningless. Just things to gather dust on the mantel." Then he catches himself. For how can he convey the meaninglessness of prizes to one who has suffered so from not having won enough?
"Hardy," Ramanujan says, "may I ask you a kindness?"
"What?"
"I wonder if you would allow me . . . if I did not come to see you for the next three days."
"Oh? And why's that?"
"Chatterjee has invited me to go to London with him."
"To London?"
"With him and Mahalanobis and Ananda Rao. He has found a boardinghouse with a very pleasant landlady who serves, he says, excellent vegetarian food."
"And what will you do in London?"
"We will see Charley's Aunt."
"Charley's Aunt!" Hardy suppresses a laugh. "No, of course. I mean, yes. You should start getting to know more of England than the corridors of Trinity."
"Thank you. I promise that I shall continue my work in London. I shall have the mornings free."
"There's no need for that. Take a break from work. It'll clear your head."
"No, I shall work every morning, from eight to noon."
Four days later he's back at Hardy's fireside.
"So how was London?"
"Very pleasant, thank you."
"And you enjoyed Charley's Aunt?"
"I laughed very much."
"What else did you do?"
"I went to the zoo."
"The zoo in Regent's Park?"
"Yes. And I saw Mr. Littlewood and his friend. They took me to tea." He waggles his head. "She is very amiable, Mr. Littlewood's friend."
"So I've heard."
"And then after tea they took me to see Winnie."
"Who is Winnie?"
"Winnie is a black bear cub from Canada. She was brought by a soldier. Her name is short for Winnipeg, not Winifred. But then the soldier's brigade was sent to France, and now Winnie lives at the zoo."
"And what is Winnie like?"
"She is very tame. A gentleman from the zoo fed her. I stayed and watched her for an hour, with Mr. Littlewood and his friend."
"So you shall go to London again?"
"I think so, yes. The boardinghouse was very comfortable. It is in Maida Vale."
"Very convenient for the zoo."
"And the landlady—Mrs. Peterson—she has taught herself Indian cooking. She even made sambar one night. Well, a sort of sambar."
"That would no doubt please your mother."
"She would be pleased. May I ask your guidance on a small matter?"
"Of course."
"On the train back, Mahalanobis showed us a problem from the Strand magazine. They are published every month—mathematical puzzles—and this one he could not solve."
"What was it?"
Ramanujan fishes a magazine cutting from his pocket and hands it to Hardy. "Puzzles at a Village Inn"; the setting, familiar to Hardy, is the Red Lion Inn in the Village of Little Wurzelfold. Only now the men speak of the war.
"I was talking the other day," said William Rogers to the other villagers gathered round the inn fire, "to a gentleman about that place called Louvain, what the Germans have burnt down. He said he knowed it well—used to visit a Belgian friend there. He said the house of his friend was in a long street, numbered on his side one, two, three, and so on, and that all the numbers on one side of him added up exactly the same as all the numbers on the other side of him. Funny thing that! He said he knew there was more than fifty houses on that side of the street, but not so many as five hundred. I made mention of the matter to our parson, and he took a pencil and worked out the number of the house where the Belgian lived. I don't know how he done it."
"Well," Hardy says, "and what is the solution? It shouldn't be difficult—for you."
"The solution is that the house is number 204 out of 288. But that is not what is interesting."
"What is interesting?"
"It is a continued fraction. The first term is the solution to the problem as stated. But each successive term is the solution for the same type of relation between two numbers as the number of houses increases toward infinity."
"Very good."
"I think I should like to publish a paper on continued fractions. Perhaps this continued fraction. You see, with my theorem I could now solve the puzzle no matter how many houses there were. Even on an infinite street."
An infinite street, Hardy thinks, of Belgian houses. And Ramanujan pacing the rubble, holding his continued fraction before him like a sextant. And all the houses burning.
"I suspect that it would make an excellent paper," he says.
"Might it be a paper," Ramanujan asks, "with which I could win the Smith's Prize?"