Arthur Clarke - The Last Theorem

Ranjit shook his head. “I wish I liked my job as much as you like yours,” he said, feeling a tiny stab of what he could recognize only as jealousy.

Dr. Vorhulst gave his former student a considering look. “Have a refill,” he offered. And then, while he was mixing one, he said, “And while we’re here, how would you like to tell me how you and the university are getting along?”

Ranjit would have, of course, liked nothing better. It didn’t take long for him to unload his problems onto his former teacher, and not as long as that for Joris Vorhulst to get the picture. “So,” he said thoughtfully, again replenishing their glasses, “let’s get back to basics. You don’t have any trouble filling a class, do you?”

Ranjit shook his head. “For the first seminar, they had a waiting list thirty or forty people long that couldn’t get in.”

“So then, why do people sign up for a class with you? It isn’t because you’re a great teacher—even if you were, they wouldn’t have had any chance to find that out. It isn’t because abstruse mathematics has suddenly got popular. No, Ranjit, the thing that pulls them in is you yourself, and how you plugged away at that problem for all those years. Why don’t you teach them to do as you did?”

“Tried it,” Ranjit said glumly. “They said they’d heard me lecture on that already. They wanted something new.”

“All right,” Joris said, “then why don’t you show how someone else solved a problem like that, step by step….”

Ranjit looked at him with dawning hope. “Huh,” he said. “Yes, maybe. I know a lot about the way Sophie Germain tried to do Fermat herself—didn’t succeed, of course, except partially.”

“Fine,” Joris said with satisfaction, but Ranjit was still thinking.

“Or, wait a minute,” he was saying, suddenly excited, “do you know what I could do? I could take one of the grand old problems that nobody has solved—say, Euler’s reworking of the Goldbach conjecture; you can explain that in words of one syllable that anybody can understand, though nobody’s ever been able to produce a proof. What Goldbach proposed—”

Joris’s hand was raised. “Please don’t explain this Goldbach conjecture to me. But, yes, that sounds good. You could do it as a sort of class project. Everybody working on it together, the students and you as well. Who knows? Maybe you could even solve the thing!”

That produced an actual laugh from Ranjit. “That would be the day! But it doesn’t matter; the students would at least get a feeling of what it takes to solve a big problem, and that ought to hold their interest.” He nodded to himself, pleased. “I’ll try it! But it’s getting late and you have to get up in the morning, so thanks, but let’s call it a night.”

“We’d better do that before my mother catches me still up,” Vorhulst agreed. “But there’s something else I wanted to talk to you about, Ranjit.”

Ranjit, on the point of getting up to leave, paused with his hands on the arms of his chair, ready to lift. “Oh?”

“I’ve been thinking about that committee you were invited to go to work for at old Peace Through Transparency. It occurs to me that maybe we need something like it for the ladder. Famous people keeping an eye on what we’re doing and now and then telling the world about it. Famous people like you, Ranjit. Do you think you might consider—?”

Ranjit didn’t let him finish. “Whatever you’re asking,” he said, “the answer is yes. After all, you’ve just saved my life!”

And “yes” it was… and years later Ranjit considered with wonder how that simple single word had changed his life.

Some light-years away the lives of the 140,000 One Point Fives in the Earth-depopulation fleet were also on the verge of a major change.

By the calculations of their Machine-Stored navigators the flotilla was within thirteen Earth years of their assault on the doomed human race. That was a meaningful point for the One Point Fives. It meant it was time for an important action to be taken.

So all over the fleet, in every corner of every ship, specially trained technical crews were checking every instrument or machine that was working, and turning most of them off. Basic drive, off; that meant the fleet was now simply drifting toward Earth—though already at such a great velocity that, under Einstein’s laws, further acceleration was very difficult and very nearly pointless. Airborne waste filters: off. So beginning at once the exhalations of the One Point Fives themselves would begin to contaminate the air they breathed. Power pack chargers, off. Search beams, off. The instruments that monitored the running of all the machinery that couldn’t be turned off even briefly—off.

Suddenly the armada of the One Point Fives was no longer a hard-driving fleet of warcraft aiming at a point of conflict; it had suddenly become a collection of derelicts, almost powerless and approaching the point where one ship might drift into another. The fleet could not maintain that condition for long.

The One Point Fives, however, didn’t need it to be for long. As soon as the last crew reported that everything that could be shut down was shut down, the One Point Fives began slipping out of the last vestiges of their protective armor and life supports. Then began the wildest orgy of sexual activity any One Point Five could imagine.

For about an hour.

Then the pallid creatures that were the organic One Point Fives hurriedly clambered back into their armor. In each ship the technical crews hastily retraced their steps, turning back on everything they had turned off, and the orgy was over.

Why did the One Point Fives do that?

For a reason that most human beings would have understood very easily. One Point Fives, whether armored or stripped to their wasted little organic bodies, did not look in the least like any humans, but they had some traits in common. No One Point Five wanted to die without leaving a live descendant to take his place. In the struggle that lay ahead there was a definite and nonzero chance that some or all of them would die. So in that collective mating, many—with luck, maybe most—of the females would become pregnant. The fifteen Earth years before that final conflict was the minimum time it would take for them to deliver their wretched little newborns to the nursery machines, and then for the infants to grow and mature to the stage of puberty.

With that knowledge, their parents could afford to launch the attack.

Of course, no human being knew this, so all nine billion of them went right on with their usual daily tasks, none of them knowing that, from that day forward, their own newborns could only expect to experience the first inklings of sexual maturity before being wiped from the face of the earth.

In the event, Ranjit did not begin his next seminar with Goldbach’s conjecture. Myra had a different suggestion, and he had learned to listen to Myra.

The first day he faced the class, he spent most of the opening hour on housekeeping matters—answering questions on his testing and grading policies, announcing what days of class would be skipped for higher-echelon reasons, getting to begin to know some of the students. Then he asked, “How many of you know what a prime number is?”

Nearly every hand in the room went up. Half a dozen of the students didn’t wait to be recognized but called out one version or another of the definition: a number that can be divided, without a remainder, only by one and itself.

It was a promising beginning. “Very good,” Ranjit told them. “So two is a prime number and three is a prime number, but four can be divided not only by itself and by one but also by two. It is not, therefore, a prime number. Next question: How do you generate prime numbers?”