The Indian Clerk by David Leavitt Read Free Book Online

had conjured—out of what? out of the ether?—a famous hypothesis concerning
     the distribution of the prime numbers. Yes, the Riemann hypothesis, which Hardy once made the mistake of trying to explain
     to the brethren. Still unproven. That was how he began his talk. "It is probably the most important unproven hypothesis in
     mathematics," he said from the hearthrug, which sent a ripple of comment through the audience. Then he tried to lead them
     through the series of steps by which Riemann established a link between the seemingly arbitrary distribution of the primes
     and something called the "zeta function." First he explained the prime number theorem, Gauss's method for calculating the
     number of primes up to a certain number n. Then, by way of indicating how far Cambridge had fallen behind the continent, he told the story of how, upon his arrival at
     Trinity, he had asked Love whether the theorem had been proven, and Love had said, yes, it had been proven, by Riemann—when
     in fact it had been proven only years after Riemann's death, independently, by Hadamard and de la Vallee Poussin. "You see,"
     he said, "we were that provincial." At this Lytton Strachey, a recent birth (no. 239), gave a high-pitched, snorting laugh.
    The problem was what Hardy called the error term. The theorem inevitably overestimated the number of primes up to n. And though Riemann and others had come up with formulae to lessen the error term, no one had been able to get rid of it altogether.
    This was where the zeta function came in. Hardy wrote it out on a blackboard:

    The function, when fed with an ordinary integer, was fairly straightforward. But what if you fed it with an imaginary number?
     And what was an imaginary number? He had to backtrack. "We all know that 1 × 1 = 1," he said. "And what does — 1 × — 1 equal?"
    "Also 1," Strachey said.
    "Correct. So by definition, the square root of — 1 doesn't exist. Yet it's a very useful number."
    He wrote it in on the blackboard:. "We call this number i ."
    He knew where this was going to lead: a long argument about the phenomenal and the real. If outside this room, Strachey said,
     outside this Saturday evening, i was imaginary, then in this room, on this Saturday evening, i must be real. And why? Because in the world that was not this room, this Saturday evening, the opposite was true. For the
     brethren, only the life of the meetings was real. Everything else was "phenomenal." Thus the Apostles embraced i without having the faintest idea what it meant.
    After the talk was over, O. B. patted him on the back. "God willing, you'll be the man to prove it," he said, which was deliberate
     provocation: O. B. knew as well as any of them that Hardy had long since renounced God, going so far as to ask the dean of
     Trinity for permission not to attend chapel, and then, at the dean's insistence, writing to inform his parents that he was
     no longer a believer. Gertrude pretended to weep, Mrs. Hardy wept, Isaac Hardy refused to speak to his son. A few months later,
     his father contracted pneumonia, and Hardy's mother begged him to reconsider his choice. To placate her, he agreed to meet
     with the vicar—the same, thin-fingered vicar by whom, years before, he'd been taken on a walk in the fog to discuss the kite.
     While they talked, the vicar ate chocolates from a tray. At a certain point Hardy noticed that the vicar was glancing, not
     very subtly, at his trousers. Well, well, he thought.
    His father died the next evening. From that day on, Hardy never again set foot inside a Cambridge chapel. Even when some formal
     protocol required him to go into a chapel, he refused. Eventually Trinity had to issue a special dispensation on his behalf.
     By then, though, the college was more pliable. After all, Hardy was a don. And Oxford had sent out lures.
    Occasionally, when he was working on the hypothesis, he'd remember his walk with the vicar. Looking for a proof, he'd think— that's like