Arthur Clarke - The Last Theorem

Which were, as he had more or less expected, nonexistent.

There had not been enough data for the program to do its job. By then he already had more data to feed it, though, having spent one hour of the night wearing the rough clothes of a garbageman and collecting all the refuse Dr. Dabare’s household had set out for the real collectors of everything unwanted. Most of what Ranjit acquired was not only worthless but offensive to the nose, but there had been several dozen sheets of paper—statements of account from various shops and service providers; offers for tours, car rentals, and e-bank lending facilities; and, best of all, a dozen or so personal letters. Tragically most of them were in German, the language of the country where the professor had taken some graduate courses, a language as opaque to Ranjit as Inuit or Choctaw, but from the letters in English or Sinhalese he extracted Dabare’s driver’s license number, his exact height in centimeters, and the PIN for his cash machine card. (And wouldn’t it be only fair if Ranjit took a thousand rupees or so for the trouble the math professor was causing him? No, he concluded, it wouldn’t. Such a thing was feloniously illegal. But it was amusing to think about.)

The computer of course had long since run out of permutations to try and so had stopped. Ranjit typed in all the new candidates, hit the go button, and left once more. Yes, he might be divorcing himself from the real world. But the real world seemed to have very little to offer a friendless and—at least temporarily—fatherless Tamil boy.

But then, when he got to his room to get a long-delayed sleep, there waiting for him was something that brightened the whole day. It was a letter with a London postmark, and it was from Gamini.

Dear Old Ranjit:

Got here safe and sound, also totally exhausted. It was a nine-hour flight, counting changing planes twice, but when I got to London, it was only four and a half hours later, which meant it was nearly another eight hours before I could get to bed, and I was a physical wreck. Oh, and missed you like hell.

It had taken long enough for Gamini to get around to saying the good part, but there it was. Ranjit took the time to read that sentence over three or four times before going on with the rest of the letter. Which was newsy but not very personal. Gamini’s classes were interesting but maybe more demanding than he would have liked. The food at the London School was, naturally, horrible, but there were plenty of Indian take-out places everywhere, and some of them knew what to do with a curry. The school’s housing wasn’t much better than the food, but Gamini wasn’t going to have to stay in it forever. As soon as he got the go-ahead from his father’s London lawyers, he was going to sign a lease on what the landlord called “a superb maisonette” just a five-minute walk from most of his classrooms. Such things you could do, Ranjit thought as he looked without enjoyment around his own bleak room, when you were lucky enough to possess a rich father. And, oh, yes, Ranjit, the letter went on, you’d be thrilled to be here because the school is no more than ten minutes away from the cluster of theaters and restaurants around Leicester Square. Gamini had already found time to see a revival of She Stoops to Conquer and a couple of musicals.

So Gamini Bandara, though nine thousand kilometers away, was having fun.

Ranjit sighed, spared a moment to be glad that his absent friend was doing so well—or, at least, spared a moment to tell himself that he was glad—crawled into his lonesome bed, and went to sleep.

It took Ranjit long enough to get the code-cracking job done—eleven days, actually, with much of each day devoted to dredging up additional possible entries or inventing new ways for the computer to mix and match them. But then there was the morning when he came in, expecting little, and got the supreme delight of seeing his computer screen announcing “Dr. Dabare password identified.” What it turned out to be was the motto of the University of Colombo, Buddhih Sarvatra Bhrajate— “wisdom shines forth everywhere”—with his wife’s birthday cut in half and interpolated between the words:

And the world of mathematical documents was open to him!

So in the remaining six weeks before the new school year began, Ranjit for the first time in his life found himself very nearly drowning in the cascades of the precise sort of information he most desired.

To begin with there were the journals of number theory. There were two major ones in the English language and one or two apiece in French, German, and even Chinese (but he decided early on not to bother with anything he would need to get translated). And the books—so many books! And all now available to him through the interlibrary loan! Ones that looked interesting, though perhaps not directly relevant to his quest, were those such as Scharlau and Opolka’s From Fermat to Minkowski and Weil’s Basic Number Theory, which according to the reviews was not all that basic, indeed quite advanced even for Ranjit. Less promising, because apparently written for an audience not as informed as Ranjit himself, were Simon Singh’s Fermat’s Enigma and Yves Hellegouarch’s Invitation to the Mathematics of Fermat-Wiles and the book by Cornell, Silverman, and Stevens called Modular Forms and Fermat’s Last Theorem. Well, the list was long, and that was only the books! What about the papers, the hundreds, maybe even the thousands, of papers that had been written on this most famous of mathematical conundrums and published—well, everywhere: in England’s Nature and the American Science, in mathematical journals refereed and respected and circulated around the world, and in mathematical journals issued in obscure universities in places such as Nepal and Chile and the Duchy of Luxembourg, and perhaps hardly respected at all.

Somewhat saddeningly he kept finding little curiosities that he would have liked to share with his father. There was, it seemed, a strong tradition of elements of number theory in Hindu literature as far back as the seventh century A.D. and even earlier—Brahmagupta, Varahamihira, Pingala, and, in the Lilavati of all places, Bhaskara. As well as that seminal Arab figure abu-i-Fath Omar bin Ibrahim Khayyám, best known to those who had ever heard of him at all, a number which had not previously included Ranjit Subramanian, as Omar Khayyám, the author of the long collection of poetic quatrains called The Rubaiyat.

None of this was particularly helpful in Ranjit’s dogged pursuit of Fermat. Even Brahmagupta’s famous theorem meant nothing to him since he did not particularly care that in a certain kind of quadrilateral a certain kind of perpendicular would always bisect its opposite side. However, when Ranjit came across the fourth or fifth mention of Pascal’s triangle and the taking of roots in connection with Khayyám, he sat down and composed an e-mail to his father telling of his discoveries. And then he sat for some time with his finger poised over the send button before he sighed and pushed cancel instead. If Ganesh Subramanian wanted to have a social relation with his son, it was his duty, not his son’s, to make the first move.

Four weeks later Ranjit had read, or read part of, every one of the seventeen books and nearly one hundred and eighty papers in his bibliography. It hadn’t been rewarding. He had hoped for some stray insight that would clarify everything else. That didn’t come. He found himself led up a dozen different blind alleys—over and over, because many of the mathematician authors were following the same paper trails as himself. Five or six times each he was reexamining Wieferich’s relatively prime exponents and Sophie Germain’s work on certain odd primes and Kummer’s theory of ideals and, of course, Euler, and, of course, every other mathematician who had innocently ambled into Fermat’s lethally inviting tar pit and, bellowing in fear and pain like any other trapped dire wolf, mastodon, or saber-toothed cat, had never escaped.