The Last Theorem

28 MAKING A LIFE

Well, the job was. Whatever faults Dr. Dhatusena Bandara might be charged with, vindictiveness was not among them. The university would be delighted to welcome Dr. (if only honorary) Ranjit Subramanian to the faculty as a full and tenured professor, with his employment (and thus his pay) to begin at once, actual work to start when the professor found it quite convenient. More than that, the university would be pleased to find a faculty position for Dr. (this time not honorary but fully earned) Myra de Soyza Subramanian as well. Of course, it went without saying, her title wouldn’t be as elevated as her husband’s, and neither would her pay scale. But still…

But still, they were going back to Sri Lanka!

If the president of the United States objected to Ranjit’s walking out on the job offer, he didn’t say anything about it. Neither did anyone else. Ranjit cleared out his few personal belongings at the office; true, there was a maintenance man, who happened also to be a security man, to help him pack everything up. True, he was required to turn in his passes and badges and IDs. But no one bothered them in their apartment, or at the air terminal, or on the planes they took. And Natasha rode in her cradle-seat between the two of them without a whimper.

Mevrouw Vorhulst, of course, was waiting for them at the Colombo airport, since it was obvious that the best thing was for them all to stay at her house again. “Just until we find an apartment,” Myra said, while being hugged by her.

“As long as you like,” said Mevrouw Vorhulst. “Joris wouldn’t have it any other way.”

There was a strange thing about those classrooms at the university, Ranjit found. When his principal dearest wish had been to get out of them, they had seemed oppressively small. Not now, not to a brand-new professor who had never faced a class before. Now the room was a vast jury box, packed with young men and women sitting in judgment on him. Their eyes were unerringly focused on his every move, their ears impatient for the great revelations Professor Subramanian would have for them of the innermost secrets of the world of mathematicians.

It wasn’t just how to nurture this nest of hungry hatchlings that baffled Ranjit. It was what to nurture them with. When the university’s search committee had welcomed him to the faculty, they had generously left the exact nature of his duties to his own good plan.

He didn’t have one.

Ranjit was aware that he needed help. He even had a hope of finding it in the person of Dr. Davoodbhoy, the man who had behaved so exemplarily in the matter of the stolen math teacher’s password.

He was not only still at the university. He had, in the natural attrition of deaths and retirements, already moved up a terrace or two along the slope of authority. All the same, when Ranjit applied to him for help, there wasn’t much available. “Oh, Ranjit,” he said. “May I still call you Ranjit? You know how it is. Our little university doesn’t have many world-famous stars. The search committees want you here very much, but they don’t have a clue about what to do with you. You do realize that you don’t actually have to do much teaching? We don’t have many faculty members who specialize in research instead, but that is a possibility.”

“Huh,” Ranjit said thoughtfully. He went on thinking for a moment, then said, “I suppose I might take a look at some of the famous old problems like Riemann, Goldbach, Collatz—”

“Certainly,” Davoodbhoy said, “but don’t give up on teaching until you try it. Why don’t we set up a couple of quick seminars for practice? That sort of thing we can do on short notice.” And then as Ranjit prepared to leave, turning that idea over in his mind, Davoodbhoy said, “Oh, and one more thing, Ranjit. You were right about Fermat and I was wrong. I haven’t had to say that very often in my life. It leads me to want to trust your judgment.”

It was pleasing for Ranjit to know that the provost trusted his judgment. Ranjit himself, however, was not quite as trusting. His first seminar was called Foundations of Number Theory. “I’ll give them a sort of overview of the whole subject,” he promised Davoodbhoy, who immediately started the wheels in motion. It would run for six weeks, four-hour classes, limited to juniors, seniors, and graduate students and a class size no larger than twenty-five.

The subject, of course, was one Ranjit had paid little attention to since he was fourteen and just beginning his fascination with Fermat’s jotting. So he mined the university library for texts and taught out of them, trying to keep at least a dozen pages ahead of the dismayingly bright and worrisomely quick students who had signed up for the seminar.

Unfortunately, it didn’t take them long to figure out what he was doing. That night he confessed to Myra, “I’m boring them. They can read from the book as well as I can.”

“That,” she said loyally, “is ridiculous.” But then, as he repeated some of the quite respectful but unimpressed comments students had made, she thought more carefully. “I know,” she said. “You need to make a little more personal contact with them. Do some of those binary arithmetic tricks for them, why don’t you?”

Ranjit, having no better idea of his own, did. He did the Russian multiplication and the finger-counting and the one where he wrote down the heads-tails permutations of a row of coins of unknown length—he used actual coins, and let the students blindfold him while someone covered up a part of the row. Myra had been right. The students were amused. One or two of them begged for more, which sent Ranjit to the library’s stacks, where he found an ancient copy of a Martin Gardner book on mathematical games and puzzles, and so he got through the six weeks of the seminar unscathed.

Or so he thought.

Then Dr. Davoodbhoy invited him to drop by for a chat. “I hope you won’t mind, Ranjit,” he said, pouring them each a stemmed glass of sherry, “but now and then, especially when we’re trying something new, we ask the students themselves for comments. I’ve just been going over the comment sheets on your seminar.”

“Huh,” said Ranjit. “I hope they’re all right.”

The provost sighed. “Not entirely, I’m afraid,” he said.

Indeed they were not entirely all right, Ranjit admitted that night at dinner. “Some of them said I was giving them nightclub magician tricks instead of math,” he told his wife and Mevrouw. “And nearly all of them didn’t like being taught right out of the book.”

“But I thought they enjoyed the tricks,” Mevrouw Vorhulst said, frowning.

“I suppose they did—in a way—but they said it wasn’t what they had signed up for.” He moodily peeled an orange. “I guess it wasn’t, either. I just don’t know what they want.”

Myra patted his hand, accepting an orange wedge. “Well,” she said, “that’s why you did this seminar, isn’t it? To see if this format would work? And apparently it didn’t, so now you’ll try something else.” She wiped the orange juice from her lips, leaned forward, kissed the top of his head. “So let’s give Tashy her bath, and then you and I can go for a swim in the pool to cheer ourselves up.”

All of which they did. It did cheer them up, too. When you came right down to it, just about everything about living in the Vorhulst household was cheering. The staff was visibly proud of their distinguished guests and, of course, quite infatuated with Natasha as well. True, Myra was still spending an hour or two most days searching for a flat for the three of them to move into, but no such flat appeared. Some seemed promising at first encounter, but Mevrouw Vorhulst helpfully pointed out the hidden flaws: bad neighborhood, long commute to the university, rooms that were tiny or dark or both. Oh, there were a thousand flaws a flat might have that would make it wrong for the Subramanians, and Beatrix Vorhulst was assiduous at finding them. “Of course,” Myra told her husband in one night’s pillow talk, “she really just wants us to stay, you know. With Joris away I think she’s lonely.”

Ranjit drowsily said, “Huh.” Then, yawning, “You know, there could be worse things than just staying here.”

Which was inarguably true. Chez Vorhulst their every need was met without effort on their part, and the price was certainly right. Ranjit had pleaded to be allowed to reimburse the Vorhulst family for at least the out-of-pocket expenses involved in housing them. Mevrouw declined. Declined affectionately and fondly, but definitely declined. “Oh, well,” Ranjit said to Myra as they lounged beside the pool that evening. “If it gives her pleasure to spoil us rotten, why should we deprive her?”

If Ranjit had a wish, it was that the outside world would be as pleasing. It wasn’t. The example of Korea notwithstanding, the globe of Earth was still pockmarked with small wars and acts of violence. There had been a sort of hiccupy pause right after Silent Thunder, while combatants worldwide hesitated in case they were next. They weren’t. Silent Thunder was not immediately repeated, and within a month the guns and the bombs outside North Korea were back to normal.

From time to time Ranjit wished that Gamini Bandara might drop by to give him the inside word on what was going on. He didn’t. Probably too busy straightening things out in the former North Korea, Ranjit supposed. Indeed, a great deal was going on there. Power was flowing back into the country’s struck transmission lines. Farms that had been abandoned because the men who would have worked them had been drafted into the army were being tilled once more. Even the actual manufacturing of consumer goods was beginning to happen. There were even puzzling reports of elections being planned. Curious ones, that neither the Subramanians nor anyone they spoke to could quite figure out. Computers seemed to be heavily involved, but in precisely what way no one could say.

Still, Myra and Ranjit admitted to each other, in their nightly wrapped-in-each-other’s-arms dialogues, most events seemed to be going at least a little better, or at least a little less badly, than before Silent Thunder had deposed a regime. Most things, that is. Not necessarily including Ranjit’s academic career.

The trouble with Ranjit’s academic career was that he couldn’t seem to get it started. After the dismal response to his first seminar, he was determined not to suffer a similar fate for his second attempt.

But what should it be? After much thought, he decided this one would be a recapitulation, step by step, of the long story of his involvement, and ultimate success, with Fermat’s legacy. Dr. Davoodbhoy agreed to schedule it, remarking temperately that it was at least worth a try.

The students, however, didn’t agree. Apparently, word had gotten around of his poor teaching skills, and although a few did sign up, a considerably larger number asked questions about it, temporized, and finally gave it a pass. Most seemed to think that Ranjit had already pretty well covered that ground, in speeches and interviews, anyway. The seminar was canceled.

Ranjit considered the research option. There were, to start, the famous seven unsolved problems proposed by the Clay Mathematics Institute at the dawn of the twenty-first century—not only interesting problems in themselves but, through the generosity of the institute, each one coming with a million-dollar reward for a solution.

So Ranjit accessed the list and thoughtfully pondered it. Some were pretty abstruse, even for him. Still, there was the Hodge conjecture and the Poincaré, the Riemann hypothesis—no, no, at least some of them had been solved and the prize collected. And, of course, the biggest of all: P = NP.

No matter how much Ranjit pondered over them, they remained remote. He could not work up the feeling that had gripped him the first time he’d seen what Fermat had scribbled in his margin. Myra offered one theory: “Maybe you just aren’t fourteen anymore.”

But that wasn’t it. Fermat’s proof had been an entirely different matter. It hadn’t ever been presented to him as a problem that he should try to solve. One of the greatest minds in the history of mathematics had boasted that he had a proof for that final theorem. All Ranjit had to do was figure it out.

He tried to explain to Myra. “Did you ever hear of a man named George Dantzig? He was a graduate student at UC Berkeley in 1939. He came late to a class and saw two equations that the professor had written on the blackboard. Dantzig thought they were a homework assignment, so he copied them down and took them home and solved them.

“Only,” he told her, “they weren’t homework. The professor had put them up there as two problems in statistical mathematics that no one had been able to solve.”

Myra pursed her lips. “So what you’re saying,” she said, “is if Dantzig had known that, he might not have been able to solve them. Is that right?”

Ranjit shrugged. “Maybe.”

Myra availed herself of her husband’s favorite reply to puzzling remarks. “Huh,” she said.

Which made him grin. “Good,” he said. “So now let’s give Tashy a swimming lesson.”

No one who knew little Natasha de Soyza Subramanian thought for one instant that she was not an exceptionally bright child. Toilet trained at under a year, first steps a month later, first clearly articulated word—it was “Myra”—less than a month after that. And all of those things Tashy had accomplished on her own.

It wasn’t that her mother didn’t have things she yearned to teach her daughter. She had many of them, but Myra was too intelligent to try to teach them all at once. So she limited parental lessons for her less-than-two-year-old to two subjects. One was singing, or at least vocalizing sounds that matched the ones Myra sang for her. The other was how to swim.

From the edge of the Vorhulst pool, his feet dangling in the water, Ranjit beamed at the two of them. He had learned not to rush to rescue his child whenever she slipped under the surface for a moment. “She’ll always come up by herself,” Myra promised, as indeed Natasha always did. “And anyway, I’m right here.”

Later, when Tashy was dry and contentedly playing with her toes in her playpen beside the pool, while her mother frowned over the news reports on her portable screen, Ranjit peeked over Myra’s shoulder. Of course the news was bad. When had it not been?

“It would be so nice,” he said thoughtfully, “if something nice happened.” And then something did.

Its name was Joris Vorhulst. When Ranjit walked in the door after another day of sitting in his little university office and trying to figure out how to earn his salary, he heard sounds of laughter. The ladylike elderly chuckle he quickly identified as Mevrouw Vorhulst, the less restrained giggles were his own dear wife, while the baritone and definitely male one was—

Ranjit very nearly ran the dozen meters to where they were gathered on the sunporch. “Joris!” he cried. “I mean, Dr. Vorhulst! I can’t tell you how glad I am to see you!”

As soon as he said it, he realized how true it was. For days he had been wishing for someone like his old Astronomy 101 teacher—no, not someone like him! That specific person! That Joris Vorhulst who had made his astronomy course the only class in Ranjit’s experience that he’d yearned to have taken sooner. And who—maybe—could help Ranjit solve his own teaching problems.

The first thing to be settled was that it wasn’t to be “Dr. Vorhulst” anymore. “After all,” he said, “it’s one full professor talking to another now, even if I’m on extended leave to work on the Skyhook.”

Which, of course, demanded that Vorhulst give everyone a report on just how the space ladder was getting along. Very well, he assured them. “We’ve already begun deploying the micron-size cable. Once we get a decent start on that, we’ll start doubling up, and then things will really begin to move because we’ll be able to start using the ladder itself to lift material to LEO instead of all those damn rockets…. Not,” he added quickly, “that they’re not doing a hell of a job. It moves fast because the big boys are all moving it. Russia, China, America—they’ve just about turned their whole space programs over to getting the ladder going. I’ve been checking all their launch sites for two months now.” He held out his glass for a refill. “And they’ve already got started on the ground terminal down on the southeast coast. That’s why I’m in Lanka today; I’ve got to go down there and prepare a report for the three presidents.”

“I’d love to see that myself,” Ranjit said wistfully.

“Sure you would. So would anybody from Astronomy 101, I hope, but don’t go just yet. What’s there now is a couple hundred pieces of earthmoving machinery, all going at once, and I think it’s up to nearly three thousand construction workers getting in one another’s way. Give it a few months and we’ll go down for a visit together. Anyway, it’s all top secret right now—I think the Americans are afraid the Bolivians or the Easter Islanders or somebody will steal their ideas and build a skyhook of their own. You would need really top security clearances to get in.”

Ranjit was about to assure his old teacher that he had the best security clearances a human being could possess, when he stopped himself, wondering if they had all been revoked. And by then Vorhulst was saying, “And what about you, Ranjit? Outside of finding the Fermat proof and marrying the best-looking AI scientist in Sri Lanka, what’ve you been doing?”

It turned out that Joris Vorhulst had heard a great deal about the adventures of his former pupil and wanted to hear a lot more. That took them right up to dinner. Ranjit was hesitant about asking for help in front of the whole household, and anyway Aunt Beatrix had been watching news programs and had a lot of questions. “They’re sending barges full of old tanks and self-propelled guns and things like that out into the China Sea and dumping them into the water,” she informed the group. “To make false reefs where fish will breed, they say. And they showed clips of a kind of guillotine they have, like the ones from the French Revolution only they’re five stories high, and they’re using those to chop up their ICBMs. I imagine they drain the fuel and the warheads first.”

“They strip them of recyclable metals first, too,” Joris informed his mother. “I saw trainloads of the stuff going west through Siberia; the Russians called it part of Korea’s reparations bill. And have you heard about the elections they’ve got scheduled?”

“Heard about them, certainly,” Myra responded. “Understand them, not a chance.”

Joris gave her a rueful grin. “Me, too. But in China I ran into a woman who’d been there, and she tried to explain it to me. The first thing is that the basic unit for voting isn’t the town or precinct the voter lives in. It’s an arbitrary group of ten thousand people, all over the country, who were born on the same day. And from those ten thousand there’s a group of thirty-five, randomly computer-selected, who will run the group. Those thirty-five do meet; they spend one week a month in session somewhere in Korea, and they elect from their own membership a presider—sort of like a mayor—and a legislature to take care of things like issuing permits and planning construction projects. And they name judges and elect representatives to the national legislature and so on.”

“Sounds complicated,” his mother commented. “Also, that part about selecting them at random by computer? That was suggested thirty years or so ago by a science-fiction writer.”

Joris nodded. “They have all the best ideas, don’t they? Anyway, the system can’t work until they get their communications back—at least another month or two, I think. Maybe by then we’ll understand it.”

After dinner the proud parents had to show Joris how well their infant could swim, and Mevrouw insisted that Joris go to bed when Tashy did. Since the last time he’d been in a bed, he had flown halfway around the world, and it was time he got some rest!

So there wasn’t any chance to ask for Joris’s help then, either. When both Natasha and his wife were sound asleep, Ranjit fretfully flipped on the news, sitting in their dressing room, volume too low to disturb the sleepers. The Security Council had issued a whole new bundle of stern warnings to countries that were engaging in, or seemed to be on the brink of, one of those brushfire wars; Silent Thunder was not mentioned but, Ranjit had no doubt, was present in the calculations of all the belligerents. It was possible, Ranjit told himself, that he had made a mistake in turning Gamini’s offer down. Pax per Fidem had every appearance of being where the action was, while Colombo did not.

Irritated, he turned off the news. He thought he might as well get some sleep and perhaps get a word with Joris first thing in the morning, before Joris was off again on his way to the terminal’s construction site.

But there was a faint sound of music coming from somewhere.

Ranjit pulled on a robe and investigated. There, on the balcony overlooking the gardens, Joris sat, sipping a tall drink and gazing at the moon while a radio softly played. When he saw Ranjit peering at him, he gave him a faintly embarrassed grin. “You caught me. I was just thinking where I’d like to land up there, oh, maybe five or six years from now, when the Skyhook’s operational and I can get there. Mare Tranquillitatis, or Crisium, or maybe something on the far side, just to show off. Sit down, Ranjit. Would you care for a nightcap?”

Ranjit certainly would, and Joris had the fixings all ready for them. As he accepted the glass, Ranjit nodded toward the moon, nearly full, bright enough, almost, to read by. “Do you really think you’ll be able to do that?” he asked.

“I don’t think it; I guarantee it,” Vorhulst promised. “Maybe it’ll take a little longer for your average man in the street to buy a ticket. Not me. I’m an executive in the program, and rank has its privileges.” He took note of a faintly quizzical expression on Ranjit’s face. “What is it? You never expected me to take advantage of a position to get something I wanted? Well, for most things I wouldn’t. But space travel is special. If the only way to get to the moon would be by robbing banks to finance the trip, I’d rob banks.”

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.