The Last Theorem

14 RENDITION TO THE HIGHEST BIDDER

Although Ranjit hadn’t known any part of it, quite a few things had been going on outside the walls of his place of detention. Cathedrals had been blown up, railroad trains derailed, office buildings poisoned with radioactive dust in their ventilation systems. And assassinations? Oh, yes, there had been plenty of assassinations, by throat-cutting or defenestration from an upper floor; by handgun, shotgun, and assault rifle; quite often by poisoning, administered in sometimes quite ingenious ways. Not to mention, in one case, assassination by dropping a piano on the victim’s head, and in another, by standing on the victim’s chest to hold him to the bottom of his bathtub as its taps filled it with lukewarm water. And, of course, there were the wars. Perhaps the most violent of the new ones revived an old plague spot as a Sunni incursion into Kurdish territory threatened to set off another round of the turmoil that characterized post-occupation Iraq.

However, not everything that had transpired had been bad. Under the close supervision of four of the five Scandinavian nations—Iceland, with its own domestic unrest, stayed outside the group—several of the most bitterly fought wars were in, however brief, remission. Even Myanmar, the country that was more commonly called Burma (except by its own intransigent governing clique), had without warning released all of its political prisoners and invited foreign diplomats to monitor its next set of elections. Finally—a development that would have greatly pleased Ranjit, if he could have known of it—after endless stalling, the World Bank had come through with a decent billion-dollar start-up grant for an actual Artsutanov space elevator. True, a World Bank grant was a long way from the actual wheels turning, with the cars going up and down the cables, the hardware that you could hop onto and be drawn to low earth orbit at three hundred kilometers an hour. But it was a real first step.

Those, of course, were not the only data with a significant bearing on his own life that Ranjit did not know. For example, he didn’t know why he had been taken to this place and why he had been tortured in it. And then, when the torturing had stopped, he didn’t know why that had happened, either. Ranjit had never heard of extraordinary rendition or the momentous decision that had been handed down, decades earlier, by the British Law Lords.

Of course, Ranjit’s torturers could have helped him out with some information if they had chosen to. They didn’t choose to.

After the first day without inflicted pain, he didn’t see Bruno, the belly-slap and electrical-cable guy, again at all. He did see Squinty quite often, but only after Squinty had extracted a promise from him that he would stop asking why he had been tortured and whether he would ever be released, and indeed pretty much any question that Ranjit really wanted answered. Squinty did supply a tiny bit of information. (“Bruno? Oh, he’s been promoted upstairs. He just doesn’t know what to do with a prisoner unless he’s hurting him, and it doesn’t look like we’re going to be hurting you anymore.”)

That was, Ranjit reminded himself, a fact of life not to be scorned. It was a big improvement over the previous diet of thrashings and water-boardings. But it was, especially after Squinty quit coming around because Ranjit couldn’t keep his promise to stop asking forbidden questions, pretty damn boring. Ranjit wasn’t left entirely without human company. There was a limping old man who brought him his food and carried away his slop buckets, but that one was no use for conversation. He no doubt spoke some language or other, but it didn’t seem to be one that Ranjit possessed.

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, and if x⁵ + y⁵ = z⁵, then x, y, or z must be divisible by five.

Like every other stepping-stone toward a proof that Ranjit had managed to quarry out of the refractory stone of his mind, this one was a disappointment. The equation made no sense. Fermat’s whole theorem was supposed to prove that no such equality as x⁵ + y⁵ = z⁵ could ever exist in the first place. So it wasn’t of any use at all….

Or was it? That is, forget Sophie Germain’s useless theorem itself, but how did she get to it?

And wasn’t that what Myra had suggested to him at Dr. Vorhulst’s party, back in the days when Ranjit could sometimes go to a party?

There was one other person (well, sort of person) with whom Ranjit had never, or never yet, had any personal dealings, but who (or which) could have supplied him with very useful data. It is probably about time that we spent a little more time with him (or them, or it, or maybe even her).