That, Ranjit knew, he owed to his father because of the book his father had given him on his thirteenth birthday. The book was G. H. Hardy’s A Mathematician’s Apology. It was in that book that Ranjit first encountered the name of Srinivasa Ramanujan, the impoverished Indian clerk, with no formal training in mathematics, who had been the wonder of the mathematical world in the dark years of World War I. It was Hardy who received a letter from Ramanujan with some hundred of the theorems he had discovered, and Hardy who brought him to England and to world fame.
Ramanujan was an inspiration to Ranjit—clearly mathematical genius could come from anyone—and the book had left him with a specific, dominating interest in number theory. Not just number theory: in particular the wonderful insights that were the work of the centuries-old genius Pierre de Fermat, and even more in particular that towering question Fermat had left for his successors, the proof—or the proof that there was no proof—of Fermat’s celebrated Last Theorem.
That was Ranjit’s obsession, and it was the subject he proposed to devote the next hour to thinking about. It was too bad that he didn’t have his calculator in his pocket, but his best friend had talked him out of that. “You remember my cousin Charitha?” Gamini had said. “The one who is a captain in the army? He says that some of the guards in the trains are confiscating calculators. They sell them for what they can get. Your two-hundred-dollar Texas Instruments calculator they would sell for perhaps ten dollars to somebody who only wants to keep track of his cash outlays, so leave it at home.” Which Ranjit sensibly had done.
The calculator’s absence was an annoyance, but not a particularly important one, for the wonderful thing about Fermat’s Last Theorem was its simplicity. After all, what could be simpler than a2 + b2 = c2? That is, the length of one arm of a right triangle, squared, added to the squared length of the other arm equals the square of the hypotenuse. (The simplest case is when the arms are three units and four units in length and the hypotenuse is then five units, but there are many other cases with unitary answers.)
This simple equation anyone could prove for himself with a ruler and a little arithmetic. What Fermat had done to obsess generations of mathematicians was to claim that such a relationship worked only for squares, not for cubes or for any higher power. He could prove it, he said.
But he didn’t publish his proof.
(If you would like a fuller discussion of the “last” theorem, one is included at the end of this book, under the title “The Third Postamble.”)
Ranjit stretched, yawned, and shook himself out of his reverie. He picked up a pebble and threw it as hard as he could, losing sight of it in the dusk long before it struck the water below. He smiled. All right, he confessed to himself, some part of what he knew other people said about him wasn’t totally untrue. For instance, it wasn’t entirely wrong to say that he was obsessed. He had chosen his loyalties early, and he stayed with them, and now he was what one might call a Fermatian. If Fermat claimed he had a proof, then Ranjit Subramanian, like many a mathematician before him, took it as an article of faith that that proof did exist.
By that, however, Ranjit certainly did not mean an aberration like the so-called Wiles proof that he had tried to get his math professor to discuss at the university. If that cumbersome old turkey (it dated from the closing years of the twentieth century) could be called a proof at all—and Ranjit hesitated to use “proof” for something no biological human could read—Ranjit didn’t deny its technical validity. He simply thought it was trash. In fact, as he had told Gamini Bandara just before that confounded porter had opened the door on the two of them, it certainly was not the proof that Pierre de Fermat had boasted of when he’d scribbled in the margin of his volume of Diophantus’s Arithmetica.
Ranjit grinned again, wryly, because the next thing he had said to Gamini was that he was going to find Fermat’s proof for himself. And that was what had started the laughing put-downs and the friendly horseplay that had led directly to what the porter had walked in on. And Ranjit’s mind was so filled with the memories of that time that he never heard his father’s footsteps, and didn’t know his father was there until the old man put a hand on his shoulder and said, “Lost in thought, is that what you are?”
The pressure of Ganesh’s hand kept his son from rising. Ganesh seated himself beside him, methodically studying Ranjit’s face, dress, and body. “You are thin,” he complained.
“So are you,” Ranjit told him, smiling, but a little worried, too, because on his father’s face was a look he had never seen before, a worry and a sorrow that did not befit the usually upbeat old man. He added, “Don’t worry. They feed me well enough at the university.”
His father nodded. “Yes,” he said, acknowledging the accuracy of the statement as well as the fact that he knew quite well just how adequately his son was fed. “Tell me what else they do for you there.”
That might have been taken to be an invitation to say something about a boy’s right to a personal life and some freedom from being spied upon by servants. Ranjit elected to postpone that subject as long as he could. “Mainly,” he said, improvising hastily, “it’s been math that has kept me busy. You know about Fermat’s Last Theorem—” And then, when the look on Ganesh’s face showed real amusement for the first time, Ranjit said, “Well, of course you do. You’re the one who gave me the Hardy book in the first place, aren’t you? Anyway, there’s this so-called proof of Wiles. It’s an abomination. How does Wiles construct his proof? He goes back to Ken Ribet’s announcement that he had proved a link between Fermat and Taniyama-Shimura. That’s a conjecture that says—”
Ganesh patted his shoulder. “Yes, Ranjit,” he said gently. “You needn’t bother to try to explain this Taniyama-Shimura thing to me.”
“All right.” Ranjit thought for a moment. “Well, I’ll make it simple. The crux of Wiles’s argument lies in two theorems. The first is that a particular elliptical curve is semi-stable but it isn’t modular. The second says that all semi-stable elliptical curves that possess rational coefficients really are modular. That means there is a flat contradiction, and—”
Ganesh sighed fondly. “You are really deeply involved in this, aren’t you?” he observed. “But you know your mathematics is far beyond me, so let’s talk about something else. What about the rest of your studies?”
“Ah,” Ranjit said, faintly puzzled; it was not to talk about his classes, he was quite sure, that his father had brought him to Trincomalee. “Yes. My other classes.” As conversational subjects went, that one was not nearly as bad as the one about what the porter would have passed along. It wasn’t really wonderful, though. Ranjit sighed and bit the bullet. “Really,” he said, “why must I learn French? So I can go to the airport and sell souvenirs to tourists from Madagascar or Quebec?”