The Last Theorem Page 5

  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:

  Buddhih.4-14.Sarvatra.1984.Bhrajate

  And the world of mathematical documents was open to him!

  4

  FORTY DAYS OF DATA DOWNPOUR

  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.

  The plan was not working. With less than a week before the new school year began, Ranjit faced the fact that he was trying to work too many angles at once. It was something like the very GSSM syndrome Gamini had warned him against.

  So he determined to simplify his attack. Being Ranjit Subramanian, his idea of simplifying was to make a head-on attack on that hated and endlessly long Wiles proof, the one that only a handful of the world’s leading mathematicians dared claim they understood.

  He gritted his teeth and began.

  The first steps were easy. But then he worked further into Wiles’s ugly chain of reasoning and it began to get—well, not hard, exactly, not for the likes of Ranjit Subramanian, but at least it began to require concentrated attention for every line. Because that was when Wiles began considering the equations for curves in the x-y plane, and for elliptical curves, and for the many solutions to the equation for modularity. Which was when Wiles, for the first time ever, was able to demonstrate that what was called the Taniyama-Shimura-Weil conjecture—namely, that any infinite class of elliptical curves was modular—was valid. And then, while Gerhard Frey and Kenneth Ribet had demonstrated that a certain elliptical curve could not be modular, Wiles himself was able to demonstrate that that same curve necessarily had to be modular….

  And, aha! There it was! A veritable contradiction!

  A contradiction was the mathematical pot of gold that—sometimes!—lay at the end of some interminable mathematical trail. A contradiction was the thing that math
ematicians gladly devoted their lives to finding, because if logical deductions from your starting equation wind up with two conclusions that contradict each other, then your starting equation itself must be wrong!

  And so it was proved—sort of proved—that Fermat had spoken truth. The square was the limit. The sum of no two cubes would ever be another cube, and so on for every other exponent this side of infinity. But Ranjit was no nearer to finding his own less daunting proof of what Fermat had so casually mentioned so long ago.

  And—oh, yes—he was not aware that his picture was being taken.

  The beings that were doing the picture taking were another of those client races of the Grand Galactics. These were called the Machine-Stored, and of course Ranjit never saw them. They didn’t intend to be seen. They generally weren’t ever seen, either, although under certain rare combinations of starlight, moonlight, and gegenschein, a few of them had occasionally been detected by an occasional human being. When reported, these sightings were generally referred to as sightings of flying saucers, thus adding to the vast catalog of fakes, mistakes, and downright lies that made it nearly certain no respectable scientist would ever pay any attention to them.

  What the Machine-Stored were doing on Earth at that time was anticipating a need of the Grand Galactics, whose needs and wishes the Machine-Stored always catered to. The Grand Galactics hadn’t ordered this activity, but the Machine-Stored were permitted to use their own discretion in certain limited circumstances. The special quality of the Machine-Stored lay in the fact that they had trashed their planet even more diligently than the One Point Fives, to the point where organic life on its surface was now completely impossible. The One Point Fives had dealt with the problem by adding infinite prostheses to their vulnerable organic bodies. The Machine-Stored took a different tack. They abandoned their physical planet, and indeed abandoned everything physical at all. They reconstituted themselves as something like computer programs and allowed their now quite frail and sickly bodies the privilege of death, while the individuals lived on in cyberspace. (Since which their despoiled planet had begun to show the beginning signs of regeneration. Not all of its liquid water was now toxic, for instance—though it still would have been pretty much a hellhole for anything organic.)

  And the Machine-Stored themselves?

  Why, they made themselves useful. Sometimes, when the Grand Galactics chose to move a certain quantity of objects or beings from one star system to another, the Machine-Stored were instructed to do the moving. And when they had detected those first microwave and then nuclear pulses from Earth, they’d known the Grand Galactics would take an interest. They didn’t wait for orders. They at once began to survey the planet and everything on it, and to pass those findings at once to the corner of the galaxy where the Grand Galactics swam in their dark energy streams.

  Of course, the Machine-Stored had no good idea of just what the human race was up to in its various activities. For that, they would have needed to understand human languages. That didn’t happen. The Grand Galactics preferred that their client races be ignorant of any languages but their own, because if the races could freely talk to one another, who knew what they might be saying?

  Ranjit would have been astonished to know that his own picture had been flashed across interstellar space in that manner. It had, though. So had the pictures of everyone, and almost everything, on Earth, because the Machine-Stored—if not omnipotent—were diligent.

  And hoped that the Grand Galactics would appreciate, or at least tolerate, that diligence.

  When Ranjit’s bedside radio woke him for the first day of his new term, he leaped out of bed in order to turn it off. His first class, Astronomy 101: The Geography of the Solar System, was also pretty close to his last hope that the university would provide him with anything interesting over the next three years. That was mildly cheering in itself. And then, as he was leaving the building, the porter handed him a letter—from London, and therefore from Gamini—and Ranjit actually did feel a little bit cheerful.

  Hunched over his breakfast, he read the letter. It didn’t take very much time. The letter was even shorter than its predecessor and almost entirely devoted to describing Gamini’s “superb maisonette”:

  You enter from the street and go up a flight of stairs. Then you’re in the living room (the Brits call it the “reception”). Next to that room is a doll-size kitchen, and that’s all there is on that floor. There’s a separate flight of stairs going down from the reception to the back, where there’s a spare room that looks out on a few square meters of mud that might be supposed to be a garden. I guess I’ll call that the guest room, but I don’t plan to be putting up any overnight guests in it. (Unless, my man, you want to drop by for a weekend sometime!) Going back to the reception floor, there’s another flight of stairs that takes you up to the bedroom and bath. Not very convenient for anybody sleeping in the guest room if he needs to have a pee in the middle of the night. And let’s go back to the kitchen. It’s got everything you’d want in a modern kitchen, but in dollhouse sizes: tiny fridge, tiny stove, tiny sink, and the tiniest washer-dryer you’ve ever seen. I said it was about big enough to handle a pair of socks, but Madge said it could only if you did just one sock at a time.

  Anyway, such as it is, it’s mine! Even if all the furnishing is Early Cheap. Only now I’ve got to run, because a bunch of us are going to see the new Stoppard revival and we want to have dinner first.

  Ranjit managed a smile at the thought of Gamini doing laundry—the Gamini for whom laundry had always been what you took home and gave to the servants, who the next morning would return it to you, cleaned, ironed, and folded.

  That did not keep him from wondering just who this Madge was.

  So he showed up for his first class prepared for disappointment….

  But then, wonderfully, miraculously, that was not at all what happened!

  5

  FROM MERCURY TO THE OORT

  The place where Astronomy 101 was given wasn’t a regular classroom. It was one of the rooms that were designed like miniature theaters, with curved rows of seats enough for a hundred students. Almost every seat was occupied, too, right down to the level that held a desk, a chair, and a lecturer who didn’t look to be much older than Ranjit himself. His name was Joris Vorhulst. He was obviously a Burgher, and it was almost as obvious that he had chosen to leave the island for his graduate schooling.

  The schools he had gone to impressed Ranjit, too. They were hallowed names for astronomers. Dr. Vorhulst had got his master’s at the University of Hawaii at Hilo, where he had interned on the vast old Keck telescopes, and he’d gone on to his doctorate at Caltech, with a side order of working at the Jet Propulsion Laboratory in Pasadena. At JPL he had been part of the team that ran Faraway, the spacecraft that had flown by Pluto into the Kuiper Belt—or into the rest of the Kuiper Belt, as Vorhulst would say, because he was loyal to the old profession-wide decision that had stripped Pluto of its claim to true planethood, so that now it was just one more of the countless millions of Kuiper snowballs. (Actually, Vorhulst told the class, Faraway had gone pretty much all the way through the Kuiper Belt by now and was already taking aim at the nearer fringes of the Oort cloud.)

  Vorhulst went on to explain what all those unfamiliar (at least to Ranjit) things were, and the boy was fascinated.

  And then, when the class was nearly over, Vorhulst gave them some good news. Everyone in the class, he announced, would have the privilege of looking through Sri Lanka’s best telescope at the observatory on the slopes of Piduruthalagala. “A really neat two-meter reflector,” he said. And then he added, “It was a present from the government of Japan, replacing a smaller one they’d given us earlier.” That got a smattering of applause from the students, but that was nothing compared to what they did when he said, “Oh, and by the way, my computer password is ‘Faraway.’ You’re all welcome to use it to access any astronomical material on the Web.” Then there were actual cheers, among the loudes
t the ones that came from the Sinhalese boy in the seat next to Ranjit. And when the professor looked at the timer on the wall and said the remaining ten minutes could be used for questions, Ranjit was one of the first to have a hand up. “Yes,” Vorhulst said, looking at the identifying board on his desk, “Ranjit?”

  Ranjit stood up. “I’m just wondering if you’ve ever heard of Percy Molesworth.”

  “Molesworth, eh?” Vorhulst shaded his eyes to get a better look at Ranjit. “Are you from Trincomalee?” Ranjit nodded. “Yes, he’s buried there, isn’t he? And yes, I have heard of him. Did you ever look up his crater on the moon? Go ahead. ‘Faraway’ will give you access to the JPL page.”

  That was precisely what Ranjit did, the minute the class was over. He quickly located Jet Propulsion Laboratory on the World Wide Web on the rank of computers in the hall and downloaded a splendid image of the lunar crater named Molesworth.

  It was indeed impressive, nearly two hundred kilometers across. Though an almost flat plain, its interior was dotted with a dozen genuine meteor-made craters, including one with a magnificent central peak. Ranjit thought of his visits to Molesworth’s grave in Trincomalee with his father. How nice it would have been to let his father know that he had seen the lunar crater for himself. But to do that seemed impossible.

  The rest of Ranjit’s courses, naturally, were nowhere near as interesting as Astronomy 101. He’d signed up for anthropology because he’d expected it would be easy for him to get through without actually thinking much about it. As it developed, it was easy, although the other salient fact about it, as Ranjit learned, was that it was very nearly terminally tedious. And he’d signed up for psychology because he’d wanted to hear more about this GSSM syndrome. But in the first session the teacher informed him that he didn’t believe in GSSM, no matter what some other professor in some other class might say. (“Because if multitasking made you stupid, how would any of you ever manage to graduate?”) Finally, he was taking philosophy because it looked like the kind of thing you could bluff your way through without the necessity of a lot of studying.