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By Root 1745 0

was nothing to see but water—in fact nothing at all for more than a thousand kilometers, apart from a few scattered islands, until you reached the coast of Thailand. Tonight there had been a lull in the northeast monsoon, and the sky was perfectly clear. A brilliant star, its light slightly tinged with orangey-red, lay low in the east, the brightest star in the sky. Idly, Ranjit wondered what it was named. His father would know, of course. Ganesh Subramanian was a devout and sincere believer in astrology, as a temple priest should be. But he had also had a lifelong interest in secular science of all kinds. He knew the planets of the solar system, and the names of many of the elements, and how it was that a few rods of metallic uranium could be made to manufacture the electrical power that could light a city, and he had passed some of that love on to his son. What remained with Ranjit, though, was not so much about the astronomy and physics and biology of the world, but most of all that one subject that bound everything else together, mathematics.

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.