The Last Theorem - Arthur Charles Clarke [60]
Ranjit didn’t know when he first began to have long one-sided talks with his friends. With his absent friends, that is, since none of them was physically present in his cell.
Of course, none of them could hear what he said to them. It would have been interesting if, for example, Myra de Soyza could have, or Pru No-Name. Less interesting for Gamini Bandara because, after reporting on his own emptily monotonous existence, about all Ranjit had to say to his absent lifelong friend was that he really should have budgeted more time to be with Ranjit and less for the American woman, who, after all, would never see him again.
Some of Ranjit’s best absent friends were people he had never known in the flesh. For instance, there was the no-longer-living Paul Wolfskehl. Wolfskehl had been a nineteenth-century German business tycoon whose best-beloved sweetheart had turned down his proposal of marriage. That meant that, in spite of all his wealth and power, life was no longer worth living for Wolfskehl, so he sensibly decided to commit suicide. That didn’t work out, though. While Wolfskehl was waiting for the exact right moment to do himself in, he idly picked up a book to read.
The book chanced to concern Fermat’s Last Theorem, written by a man named Ernst Kummer. As it happened, Wolfskehl had attended a couple of Kummer’s lectures on number theory; curiosity made him read the new essay….
And, like many other amateur mathematicians, before and after, Wolfskehl was immediately hooked. He forgot about killing himself, being too busy trying to plumb the mysteries of a-squared plus b-squared equals c-squared, and the paradox that if the quantities were cubed, they never did equal each other.
Then there was the also long deceased Sophie Germain, whose teenage years had been spent during the frightening time of the French Revolution. Why this should have persuaded young Sophie to resolve on a career in mathematics is not immediately obvious. But it did.
Of course, that was not an easy ambition for a female to accomplish. As Elizabeth I of England had once put it, Sophie was cursed by being split rather than fringed, and so everything she tried to do was vastly harder for her than for her fringed colleagues.
Then, when his imaginary conversation partners ran out of steam, something Myra de Soyza had said began to cudgel Ranjit’s mind.
What had it been? Something about seeing what tools other mathematicians had possessed at the time Fermat had jotted his cursed boast in the margin of his book?
Well, what tools were they?
He remembered that Sophie Germain was said to have been the first mathematician of any gender to make any headway at all with the Fermat proof. So just what headway had she made?
Ranjit, of course, had no way of looking that up. Back at the university, equipped with a password, all he would have had to do was hit a few keys on the handiest computer and the damn woman’s entire life production would have been laid out for him to study.
But he didn’t have the computer. All he had was his memory, and he was not sure that it was adequate to the task at hand.
He did remember what a “Sophie Germain prime” was—that is, any prime, p, such that 2p + 1 was also a prime. Three was the littlest Sophie Germain prime: 3 × 2 + 1 = 7, and seven was a prime, all right. (Most of the other Sophie Germain primes were much larger, and thus hardly any fun at all.) Ranjit was quite pleased with himself for remembering this, though no matter how much he thought about it, he could not see any way in which a Sophie Germain prime could lead him to a solution of the Fermat problem.
There was one other thing. After profound labor Germain had produced a theorem of her own:
If x, y, and z are integers,