Fermat’s Lost Theorem
by Jerry Oltion
Illustration by Janet Aulisio Dannheiser
When Rick Hopkins met the new math professor, he felt the sudden conviction that he’d slept with her. Trouble was, he couldn’t remember when.
The faculty lounge was abuzz with people milling about, cocktail glasses and colored napkins in hand. Marsha Selwood stood amid a small knot of professors and assistant profs near the punch bowl while Vince Gardoni, the department head, introduced her around. Tall, blonde, with high cheekbones and green eyes, she would have been the center of attention even if she hadn’t been the guest of honor. The only people in the room who weren’t fawning over her were the other women, and the dozen or so grad students who hovered over the hors d’œuvres, nervously packing away rumaki and canapes as if they were french fries. Rick didn’t recognize half of them, but he supposed their formal clothing accounted for that. Put them in baggy jeans and flannel shirts and they would suddenly become familiar again.
Maybe that was the problem with Marsha. Rick must have met her under different circumstances, and he just wasn’t making the connection.
Had he really slept with her? A moment ago he’d have sworn he had, but now he wasn’t sure. There’d been that flash of recognition, a momentary glimpse of the two of them entwined in an unfamiliar bed, but nothing after that, and now even the flash was gone. He couldn’t remember anything about the actual act, where it had been, or when. It couldn’t have been recently; he’d been away all through the holidays, and she’d been teaching halfway across the country during the fall semester. Maybe it had just been wishful thinking.
Then again, maybe not. That look on her face was unmistakable. She was waiting for him to say something, to acknowledge their special secret, and Rick had about two seconds to come up with the right response or he was dead meat.
When in doubt, go for the truth. Rick smiled at her and said, “I just had the strongest sensation of déjà vu,” putting as much spin into the words as he could without alerting Vince to the subtext.
Marsha blinked her green eyes at him and said, “Now that’s odd, so did I.”
Not to be outdone, Vince said, “You’re kidding. I did too.”
Rick and Marsha exchanged a knowing glance, then Marsha turned to Vince. “Oh really? What about?”
Three more grad students entered the lounge, two guys flanking a woman, all three of them wearing the same style suit. Gray, wide lapels, red ties. They stomped the snow from their shoes—black running shoes, it looked like—and made straight for the punch bowl. When they drew close, Rick could see that the woman’s oversized glasses had tiny winking lights around the rims, but facing inward, where she could see them better than anyone else could. Rick smiled at the odd trio and sipped his wine while Vince said, “It was really strange, but for just a second there I was sure we were holding an awards ceremony for Rick.”
Rick tried not to snort Chablis through his nose. The idea of Vince awarding him anything was laughable. Vince had barely spoken to him since their run-in with the NSA over Rick’s code-breaking algorithm. Marsha didn’t seem to realize that, though, because she asked seriously, “Oh really, what for?”
Vince laughed. “Oh, nothing much. Just solving Fermat’s last theorem.”
“That’s been done,” Rick said. “Andrew Wiles, at Princeton.”
Waving a green napkin in dismissal, Vince said, “No no, Wiles’s proof was a big, ugly, two-hundred page thing. I mean Fermat’s proof, the elegant one he didn’t bother to write down.”
Marsha’s eyes glittered with mischief. “Well, Rick,” she said, “Looks like we know what you’ll be doing for the next couple of years, eh?”
“What?” Rick frowned. Both Marsha and Vince were watching him like vultures. Like mathematicians who’d just laid down a challenge. “Oh no,” he said. “If you think I’m going to waste my time on that, you’re nuttier than Fermat.”
But as he said that, he felt a flash of insight, a tantalizing glimpse of the proof, as if he’d already solved it. The moment he focused his attention on it, though, it was gone, just like his night in the sack with Marsha.
On the way home, while he was giving a ride to Nigel, one of the other single men in the department, Nigel said, “I didn’t realize you were so popular. I had three different people ask me about you tonight.”
“Oh really?” Rick concentrated on keeping the Volkswagen from sliding on the icy streets. It had snowed on New Year’s Eve, and traffic had packed it all down before the plows could clear it away. Now they would be stuck with it for months.
“Yeah, they kept asking about your work, and what you were planning next.”
Rick groaned. “It wasn’t those bastards from the NSA again, was it? I gave up cryptography over a year ago.”
“No, I don’t think so,” Nigel said. “These guys weren’t near as slick.”
The National Security Agency people had definitely been slick. When Rick had inadvertently stepped on federal toes with his code-breaking project, they had materialized like dark wraiths. A few soft words to the dean of the college, a midnight visit to his office to clean off his hard drive—they’d even found his backup disks in the closet at home, though Rick had found no evidence of forced entry to the house. They had swept through his life in a single night, and Rick had suddenly found himself without a project. A whole year down the tubes, and strict orders from Vince to lay off cryptography.
Now he realized what tonight’s little exchange had been all about. Rick hadn’t picked a new project yet. He wasn’t doing anything exciting, and he hadn’t written any papers for over a year. Vince’s little bit about Fermat’s last theorem hadn’t been one-upmanship in the presence of a beautiful new colleague; it had been a hint. Do something or wind up teaching remedial algebra for the rest of your life.
An oncoming car seemed to materialize out of nowhere, sliding into their lane. Rick dodged to the right, narrowly missing a parked delivery van. “Jeez, where did that guy come from?” he said as the headlights swept past, but as he spoke, his mind was already leaping off on a tangent.
“Graphically,” he whispered. “I can solve it graphically.”
“What?” Nigel asked.
“Nothing,” Rick said.
He lay awake that night, the yellow sodium vapor glow from the streetlight casting shadows of tree branches on the wall. They curved and zagged in the illuminated square, and Rick tried to envision them as lines on a graph. How could they illustrate Fermat’s last theorem?
Fermat’s was one of the oldest—and simplest—unproved theorems in mathematics. Pythagoras had proved that the sides of a right triangle added up by the relationship A2 + B2 = C2, and it was easy to show that there were an infinite number of integer solutions to the equation, but no one had been able to find an integer situation in which A3 + B3 = C3, or for any higher powers either. Nearly everyone believed that no such solutions existed, but nobody had been able to prove it.
Nobody except Pierre de Fermat. He had been more of a hobbyist than a mathematician, but he was good at it. He had made some big advances in probability theory, and had nearly invented calculus. And in the margin of Diophantus’s Arithmetics, beside the section discussing integer solutions to A2 + B2 = C2, he had written his theorem, adding, “I have discovered a truly remarkable proof which this margin is too small to contain.”
Mathematicians had been trying for over three centuries to figure out what the Frenchman had had in mind, but so far without success. Andrew Wiles had come up with a proof in 1993, but it wasn’t elegant and it used semistable elliptic curves and hyperbolic planes—math that Fermat couldn’t have known about. Fermat’s proof had to be simpler, maybe even visual.