The Last Theorem

6 MEANWHILE, BACK ON EARTH

Things were looking up for Ranjit Subramanian—well, they were, that is, if you didn’t count the fact that Gamini was still nine thousand kilometers away and Ranjit’s own father might almost as well have been. And things were hotting up again in Iraq, where muscular Christian thugs with assault rifles were guarding one end of a bridge that they didn’t want crossed by Islamists; the bridge was guarded at the other side by equally husky and well-armed Islamists who didn’t want Christians polluting their side of the river.

There were many more such things going on, but those certainly weren’t the things that were giving some provisional happiness to Ranjit.

Such things did exist, though. He was not only enjoying Astronomy 101, he was doing very well in it. The worst of his quizzes received scores in the upper eighties, the goodwill of his teacher (as measured in the compliments he gave Ranjit’s questions and discussion) scoring perhaps even higher. Of course, Dr. Vorhulst found some way to compliment nearly everyone else in the class, too. It wasn’t just that he was an indulgent or lazy teacher, Ranjit decided. More likely it was that no one would sign up for his class who wasn’t fascinated by the idea of sometime, somehow seeing human beings going off to visit some of those bizarre other worlds. When Ranjit got his third straight hundred on a quiz, it occurred to him for the first time that perhaps he might actually have the makings of the kind of student who would make his father proud.

So as an experiment he tried taking his other classes a bit more seriously. He checked his philosophy teacher’s list of extra-credit reading and picked a book that had at least an interesting title. But when he took Thomas Hobbes’s great work Leviathan home, it quickly stopped being interesting. Was Hobbes saying that the human mind was like a machine? Ranjit wasn’t sure. Nor could he make sense of, say, the distinction between meritum congrui and meritum condigni. And while he was quite confident he knew what Hobbes was saying when he praised a “Christian state” as the highest form of government, that was not a notion that appealed to the doggedly agnostic son of the head priest of a Hindu temple. Nothing in Hobbes, for that matter, seemed very relevant to the life of anybody Ranjit knew. Glumly he took the book back to the library and headed to his room, hoping for nothing but a peaceful hour’s nap.

He found two letters waiting for him. One was in a creamy-textured envelope embossed with the university’s golden seal. Most likely, Ranjit thought, a notice from the student banking people to inform him that his father had sent along another quarter’s dorm rent. But the other was from London and thus from Gamini. Ranjit ripped it open at once.

If he had hoped that hearing from Gamini would brighten this unsatisfactory day, he was disappointed once more. It didn’t. The letter was short and it did not at any point say that Gamini was missing him. What it principally talked about was attending a performance of one of Shakespeare’s less amusing comedies at something called the Barbican. For some reason, Gamini said, the director had dressed the entire cast in featureless white, so that half the time neither he nor Madge had been able to tell who was speaking.

It was, Ranjit realized as he reached for the letter on university stationery, the third, maybe the fourth, time Gamini had mentioned this Madge person. He was contemplating the possible implications of this fact while extracting a letter on the same creamy paper as the envelope, and then Gamini’s possible failing went right out of his mind. The stationery was engraved with the name of the dean of students, and the letter said:

And it was signed by the dean of students.

According to her nameplate the woman at the dean’s reception desk was a Tamil, which was encouraging, but she was also as old as Ranjit’s father. Her look was cold. “You are expected,” she informed him. “You may go right into the dean’s private office.”

Never before had Ranjit had occasion to visit the dean of students. He knew what the man looked like, though—the faculty file on the university’s home page supplied photos—and the elderly man reading a newspaper at the huge mahogany desk definitely was not him. But he put down his paper and rose, not exactly with a smile but certainly without the hanging-judge look Ranjit had expected. “Come in, Mr. Subramanian,” he called. “Sit down. I’m Dr. Denzel Davoodbhoy, chairman of the mathematics department, and as mathematical matters seem to play a significant role here, the dean asked me to conduct this interview for him.”

That hadn’t been a question, and Ranjit had no idea what response would have been appropriate. He simply went on gazing at the mathematician with an expression that, he hoped, conveyed attentive concern but no admission of guilt.

Dr. Davoodbhoy didn’t seem to mind. “First,” he said, “there are a couple of formal questions I must put to you. Did you use Dr. Dabare’s password to earn money you were not otherwise entitled to?”

“Certainly not, sir!”

“Or to alter your math grades?”

This time Ranjit was offended. “No! I mean, no, sir, I wouldn’t have done that!”

Dr. Davoodbhoy nodded as though he had expected both answers. “I think I can tell you that no evidence has been presented to suggest either charge. Finally, how, exactly, did you obtain his password?”

As far as Ranjit could see, there did not appear to be any reason to try to conceal anything. Hoping that this was so, he began with his discovery that the teacher would be out of the country for a prolonged visit and ended with that return to the library computer when he found the solution waiting on the screen.

When he finished, Davoodbhoy gazed at him in silence for a moment. Then he said, “You know, Subramanian, you might have a future in cryptography. It would be a better chance than continuing to spend your life trying to prove Fermat’s Last Theorem.”

He looked at Ranjit as though expecting a response. Ranjit didn’t choose to give him one, so Davoodbhoy added, “You’re not alone, you know. When I was your age, like every other math major in the world, I got interested in the final theorem myself. It is compelling, isn’t it? But then, when I was a little older, I gave up on it because—you know this, don’t you? Because the odds are pretty great that Fermat never did have the proof he was claiming.”

Unwilling to be baited, Ranjit kept his attention set at politely attentive and his mouth closed. “I mean,” Davoodbhoy added, “look at it this way. You do know, I suppose, that Fermat spent a lot of his time, right up to the day he died, trying to prove that 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?