The Last Theorem - Frederik Pohl

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his theorem held true for third-, fourth-, and fifth-power exponents. Well, think about it. Does doing that make any sense at all? I mean, if the man already did possess a general proof that the rule was true for all exponents greater than two, why would he bother trying to prove a few isolated examples?”

      Ranjit gritted his teeth. It was a question that, on dark nights and disappointing days, he had asked himself often enough. Without ever finding a good answer, either. He gave Davoodbhoy the not wholly good answer he had usually tried to content himself with: “Who knows? How can someone like you or me try to guess why a mind like Fermat’s went in any direction it liked?”

      The mathematician looked at him with an expression that somewhat resembled tolerance but also resembled, to some degree, respect. He sighed and spread his hands. “Let me offer you a different theory of what happened, Subramanian. Let’s suppose that in—what was it, 1637?—in 1637 Monsieur Fermat had just completed what he thought was a proof. Then later that night, while he was reading himself to sleep in his library, let’s suppose he just couldn’t help himself, and in a fit of exuberance he scribbled that note in his book.” He paused there for a moment, giving Ranjit what could only be described as a quizzical look. When he went on, however, his tone would have been appropriate for a respected colleague as much as for an undergraduate expecting to be disciplined. “Then let’s suppose that sometime later he went over his proof to double-check it, and found it possessed a fatal error. It wouldn’t have been the first time, would it? Because that had already happened with other ‘proofs’ of his that he later admitted were wrong, hadn’t it?” Mercifully he didn’t require an answer from Ranjit but kept right on going. “So he tried to repair his proof every way he could. Unfortunately, he failed. So, trying to salvage something from his mistake, he then tried the more limited task of proving the argument for an easier case like p equals three, and there he succeeded; and for p equals four, and succeeded again. He never did get a proof of the p equals five case, but he was still pretty sure that one existed. He was right, too, because somebody else proved it after Fermat died. And all that time his scribble in Diophantus was sitting on a shelf in his library. If he ever remembered he’d written it, he thought, well, he probably ought to go back and erase that bad guess. But, after all, what’s the chance that anyone would ever see it? And then he died, and somebody was riffling through his books and did see it… and didn’t know that the great man had changed his mind.”

      Ranjit didn’t change expression. “That,” he said, “is a perfectly sensible theory. I just don’t happen to believe that it’s what happened.”

      Davoodbhoy laughed. “All right, Subramanian. Let’s leave it at that. Just don’t do it again.” He thumbed through the papers before him, then nodded and closed the file. “Now you can go back to your classes.”

      “All right, sir.” He tarried for a moment after picking up his backpack, then asked the question: “But am I going to be expelled?”

      The mathematician looked surprised. “Expelled? Oh, no, nothing like that. It was only a first offense, you know. We don’t expel for that unless it’s something a lot worse than stealing a password, and anyway the dean received some extremely glowing letters of support for you.” He opened Ranjit’s folder again and thumbed through the papers. “Yes. Here we are. One is from your father. He is quite positive you are basically of good character. In itself, to be sure, a father’s opinion of his only son might not carry great weight, but then there is this other one. It is very nearly as commending as your father’s, but it comes from someone who is, I think, not very close to you but who is a person of considerable importance in the university. In fact, he’s the university’s attorney, Dhatusena Bandara.”

      And now Ranjit had a new puzzle to mull over. Who would have suspected that Gamini’s father would have exerted himself to save his son’s friend?

       7

       GETTING THERE

      The school year limped toward its end. It picked up speed remarkably in the all too brief periods when Ranjit was in his astronomy class, but the remainder of each week’s hours were in no hurry to move on at all.

      For a little while Ranjit thought he had hopes of one bright—fairly bright—spot. Remembering the lecture on what they’d called the hydro-solar plan for Israel’s Dead Sea, he went back to the lecture series. But then what the lecturer was talking about was the increasing salinity of a lot of oceanfront wells, all over the world, and then about how some of the world’s great rivers no longer ran to the sea, any sea, because they were drained for farming and flushing city toilets and watering city folks’ front lawns first. Ranjit didn’t need more discouragement. After that he stayed away.

      He even briefly considered trying to take, or at least pretend to take, his schooling seriously. Studying, for example, could be considered a game, and a fairly easy one to win. It did not at all resemble that insatiable thirst for learning that had marked his early consecration to the Fermat theorem. Now all he had to do was guess what questions each of his instructors would ask on each test and look up the answers. He didn’t always get it right, but then to attain a merely passing grade he didn’t have to.

      None of this, of course, applied to Astronomy 101.

      There Dr. Vorhulst managed to make every session a pleasure. Like what happened when they were talking about terraforming—that is, reworking planetary surfaces so that human beings could live on them. And, if you were going to do that, how did you get there to do the terraforming?

      Ranjit’s answer would have been “rocket ships.” His hand was already halfway toward the raised position so that he could offer that answer when the teacher froze it mid-motion. “You’re going to say ‘rocket ships,’ aren’t you?” Dr. Vorhulst asked, addressing the whole class and particularly the dozen or so who, like Ranjit, had been putting their hands up. “All right. Let’s think about that for a bit. Let’s suppose that we want to start terraforming Mars, but all we have to work with is an absolute minimum of heavy-duty earthmoving machinery. One very big backhoe, for instance. One bulldozer. A couple of medium-size dump trucks. Fuel enough to run them all for, let’s say, six months or so. Long enough to get the job started, anyway.” He paused, eyes on a hand from the second row that had just sprouted. “Yes, Janaka?”

      The boy named Janaka eagerly shot to his feet. “But, Dr. Vorhulst, there’s a whole plan to make fuel from Martian resources that are already there!”

      The professor beamed at him. “You’re absolutely right, Janaka. For instance, if there really is a large amount of methane under Mars’s permafrost, as many people think there is, then we could burn that for fuel, assuming we could find some oxygen to burn it with. Of course, to do that we’d really have to have a bunch more heavy machinery, which would need a bunch more fuel to run it until the extraction plants were working.” Vorhulst gave the boy a friendly smile. “So, Janaka,” he said, “I think that if you wanted to start any terraforming in the near future, probably you’d want to fly your fuel in after all. So let’s see.”

      He turned to the whiteboard and began writing. “Say six or eight tons of fuel to start. The earthmoving machines themselves—what would you say, at least another twenty or thirty tons? Now to get those at least twenty-eight tons of cargo from low earth orbit, known as LEO, to Mars, we need to put them into some kind of spaceship. I don’t know what that would mass, but let’s say the ship itself would run fifty or sixty tons, plus the fuel to get it from LEO to Mars.” He stepped back to look at his figures on the board and frowned. “I’m afraid we have a problem,” he said to the class, addressing it over his shoulder. “All that stuff won’t start out in low earth orbit, will it? Before the ship can start heading for Mars, we have to get it into LEO. And I’m afraid that’s going to be expensive.”

      He paused, looking with a sorrowful expression at his class. He was waiting for some student to rise to the occasion, and after

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