Elliott drank the hot coffee, Raj watching him curiously. “What happened last night?” Raj asked.
“Nothing. I dreamed about a function to factor large numbers. Over two hundred digits.”
“Only God can do that.”
“The discrete has to be made continuous first. Cantor was close. Grothendieck…”
“Later. You have your car keys?”
Elliott felt them jingle in his pocket.
“Go.”
“I’m not sure I’ll ever come back,” Elliott said. “I think I’m going to lose all this.”
After that Elliott worked on the Riemann Hypothesis, staying at his apartment.
He ate his cold cereal and drank a lot of coffee. He sat at his kitchen table twisting bits of paper into dough.
His father called claiming to be fine, always a bad sign. He only talked of his health when he’d had an episode, but Elliott’s probing yielded no further information about any deterioration in his condition. Every few days Raj came by. Once he brought lentils and rice in a big pot. Elliott lived on that for a week, spooning portions into a bowl each night, no longer caring that it was cold food.
The problem with Raj was that he didn’t love math enough, not like Elliott did. Raj didn’t
With a few thousand in the bank, his tuition and rent paid, he closed the blinds. He stopped answering his phone.
Raj brought Professor Braun to see Elliott. Braun had contributed several original papers on differentiable manifolds before the age of twenty-two, and at the age of twenty-nine had been made the youngest full professor in the history of MIT. He taught the advanced number-theory course.
“You’re wet,” Elliott said as Raj and Braun took off their jackets and hung them on chairs.
“It’s pouring outside,” Braun said. “Didn’t you notice?”
“Did you come to see my work? Because it’s not ready yet. You know Erdos’s proof that a prime can always be found between an integer and its double? It has to do with the number One. The Stick. One is an integer. I don’t care if you won’t call it a prime number, you have to admit it’s an integer. Why doesn’t the proof work with One? There is no prime between One and Two. How can it be said that Erdos proved anything? Have you thought about this problem?”
“We want to take you out to lunch,” Raj said. “And Professor Braun wants you to return to class.”
“Wait, I want you to think about it. The way there’s no integer between One and Two, but where the prime should be, there is one-half. What does that remind you of, Raj?”
“Real part one-half,” Raj said softly. “Riemann’s critical line.”
“Yes! Yes! The Riemann Hypothesis! There’s a link, but I haven’t been able to prove it. Shall we talk about that?”
“We’ll talk about anything you want if you’ll come have a meal with us,” Dr. Braun said.
“Okay. I’m out of food anyway.”
They walked out into the rain, to a grubby pizza place on Mass Avenue. Drinking beer fast, eating a large salad, Elliott talked about his new suspicion that the Riemann Hypothesis was undecidable, unprovable either way. He talked about Cantor, about the discrete integers and the continuum. He explained how he had tried the algebraic approach through finite fields; how he had used Cramer’s model, treating it as a perturbation problem, trying to get a set of wobble frequencies. He talked about Sarnak and Wiles and Bump.
But mostly he talked about Cantor, the master of infinity. “I need a math that will operate with divergent series,” he explained, “comfortable with infinity. That happens if you permit division by zero.”
Raj groaned.
“Yeah, that again,” Elliott said.
They pumped him, or did they? Maybe they were just curious. He couldn’t tell. They wanted to know about his work on factoring large numbers, and he told them he had been trying a variation on the Pollard-Strassen method on his computer. He told them that Dixon ’s method using the quadratic sieve was inferior. He talked, because he hadn’t talked for so long, he had no choice. He knew he had no perspective anymore, but drunk or not, he didn’t go into detail.
He didn’t talk about his new idea, for a function that seemed to predict the location of large primes. He had to work alone. The function had some flaw he couldn’t find yet, some error in the calcs. If his idea got around the campus, it might be stolen, published half-baked in some journal under someone else’s name.
He promised Dr. Braun that he would return to class the next morning. The professor gave him some class materials and said he’d pass Elliott if he turned in some work. Raj kept talking about eating better. The two of them and the other people in the restaurant seemed to be talking in some other universe, their minds occupied with all the wrong things.
“Carleen moved out of Everett Street,” Raj announced. “She claims she’s forgiven you, but she won’t hang with us anymore.”
“And Silke?”
“Did Silke have something to forgive you for?”
“Are you and Silke still taking trips?”
Raj cast a glance at Braun. “Sure,” he said. “You’re always welcome to join us again.”
“When I finish my work.”
“Do you sleep at night?” Professor Braun said, his blue eyes intent.
“I’ll sleep when I’m dead.”
“How old are you?”
“Twenty,” Elliott said. “How old are you?”
“Forty-two.”
“What have you discovered lately?”
“Don’t,” Raj said.
“You have to watch your health. I don’t like the look in your eye,” the professor went on.
“I don’t give a shit about my health.”
“Remember what happened to Cantor?”
Elliott thought of Cantor, alone in wartime at the asylum in Halle, begging his daughter to bring him home. She wouldn’t. He had always wondered how she put it: “Sorry, Father, but you’re too much trouble,” she must have said. Cantor had died swiftly after that.
“Don’t squander it,” the professor repeated, pushing the last piece of pizza away from himself. “ Wakefield, you have to pace yourself. It’s a question of balance. You should see people. Your friends are worried.”
“No, no,” Elliott said, draining his mug. “Accomplishment requires sacrifice, even pain. You have to set priorities. Right now, my work comes first. Friends, family, romps in the park, children, lovers, these things have to wait.” He stood up, carefully placing his chair under the table. “Thanks for the vitamins. I need to go.” He felt pressure to flee from their slowness and their compromises before they infected him.
“See you tomorrow, then,” said Dr. Braun.
“See you.” He gave them a friendly wave. He could afford the ten seconds it took to make them happy.
He didn’t go back to class the next day, or the next.
A week later, at four in the morning, Elliott finally fell into sleep, or something like sleep. He had been taking No-Doz and drinking a lot of coffee and hadn’t slept for a couple of days. He should have slept too hard for dreams to reach him.
But one did. It was early in the morning, he would remember later.
An angel appeared, her wings outspread, calling him to her and clasping him tight. He wasn’t afraid; he felt that he was already dead, and nothing worse could happen to him. In a way, he felt that this was his reward for dying. Maybe the angel was his mother.
They flew to a place at the dim limits. Here he found waves, rhythms, measures he had never known existed. All answers were here.
The angel generated a zeta landscape, infinitely dense. Even so, the mountains they flew over were porous, one or two stretching up into infinity. Between the mountains he saw deep holes, the points spiraling inward. The beauty of it made him weep.
They moved down to sea level and flew along the cross-section. The angel pointed. Then he saw it breaking through below: a huge prime, lonely and beautiful, its gray back shiny with spray. It had lost its way and was moving away from the other primes, spuming and slapping their tails in the limitless distance.
They moved into higher densities, Elliott now carrying his black notebook to write it all down. This rolling sequence, which looked like a field in Wisconsin, converged on both zero and infinity at the same time.
He looked at the angel, and the angel nodded its blazing head.
He didn’t really want to do it, but he felt he had to. He did the unthinkable. He divided by zero.
The white sky split and the rules gave way to random crime. The universe compressed into its basic reality, the four numbers surrounded by their clouds of probabilities. But Zero, staggering, was vanishing into the mist. One was a hard black branch beating the other integers. Two, the cop in blue, struggled to keep order, but it was outgunned by Three, red and bursting, rampaging all through the set.
The Three destroyed adelic space and time. Elliott, horrified, had to watch the gruesome factoring of the prime.
His angel faded away, leaving him to drift all alone in this disintegrating universe. It would all collapse into pure theory soon.
He became very frightened. Flying low across the sea, he found a hidden crater a few fathoms beneath: the square root of minus one, a geyser of fresh water rushing out of it into the saltiness.
He dove into the deep cold system.
