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there was an infinity
     of primes. Yet when he asked his maths master at Winchester if there was a formula for calculating the number of primes up
     to a given number n, the master didn't know. Even at Trinity, seat of British mathematics, no one seemed to know. He nosed
     around, and eventually found out from Love, one of the Trinity fellows, that in fact the German mathematician Karl Gauss had
     come up with such a formula in 1792, when he was fifteen, but had been unable to provide a proof. Later, Love said, another
     German, Rie-mann, had proven the formula's validity, but Love was hazy on the details. What he did know was that the formula was inexact. Inevitably
     it overestimated the number of primes. For instance, if you counted the primes from 1 to 2,000,000, you would discover that
     there were 148,933. But if you fed the number 2,000,000 into the formula, it would tell you that the number was 149,055. In
     this case, the formula overestimated the total by 122.
    Hardy wanted to learn more. Might there be a means, at the very least, of improving upon Gauss's formula? Of lessening the
     margin of error? Alas, as he was discovering, Cambridge wasn't much interested in such questions, which fell under the rather
     disgraced heading of pure mathematics. Instead it put its emphasis on applied mathematics—the trajectory of planets hurtling
     through space, astronomical predictions, optics, waves and tides. Newton loomed as a kind of God. A century and a half earlier,
     he had waged an acrimonious battle with Gottfried Leibniz over which had first discovered the calculus, and though in America
     and on the continent it had long since been agreed that Leibniz had made the discovery first, but that Newton had made it
     independently, at Cambridge the battle raged as bitterly as if it were fresh. To deny Newton's claim of precedence was to
     speak sacrilege. Indeed, so steadfast was the university's loyalty to its famous son that even at the turn of the new century
     it still compelled its mathematics students, when working with the calculus, to employ his antiquated dot notation, his vocabulary
     of fluxions and fluons, rather than the simpler system—derived from Leibniz—that was favored in the rest of Europe. And why?
     Because Leibniz was German, and Newton was English, and England was England. Jingoism, it seemed, mattered more than truth,
     even in the one arena in which truth was supposed to be absolute.
    It was all very disheartening. Among his friends, Hardy wondered loudly if he should have gone to Oxford. He wondered if he
     should give up mathematics altogether and switch to history. At Winchester he had written a paper on Harold, son of Godwin,
     whose death in 1064 in the Battle of Hastings was portrayed in the Bayeux tapestries. The subject of the paper was the complicated
     matter of Harold's promise to William the Conqueror not to seek the throne, yet what really fascinated Hardy was that in the
     battle Harold took an arrow in the eye. This was, after all, just a few years after Gertrude's accident, and he had a morbid
     obsession with eyes being put out. Of course, there was also the coincidence of the name. In any case Fearon, his headmaster,
     admired the paper enough to pass it on to the Trinity examiners, one of whom later told Hardy that he could just as easily
     have got a scholarship in history as in mathematics. He kept this in the back of his mind throughout his undergraduate years.
    His first two years at Cambridge, he led a bifurcated life. On the one hand, there was the mathematical tripos. On the other,
     there were the Apostles. The former was an examination, the latter a society. Only a few members of the society took the examination;
     still, the life they led within the rooms in which they held their meetings undermined its very foundations.
    The Apostles first. Election was highly secretive, and, once "born," the "embryo," as he was called, was made to swear that
     he would never speak