“Oh, Elliott.” Her voice scolded him.
“You think there’s something more important?”
“Love, of course.”
“Oops. Forgot about that. Of course you’re right.”
“You’re teasing me, Wakefield,” she laughed. “You need a relationship. You deserve happiness. You’re not unattractive, you know.”
“Oh, don’t push Carleen again,” Elliott said, tracing his finger along the carving they had made, then he lifted his hand to her hair, as if to straighten it over her shoulders, stroking it. “We won’t happen.”
Silke didn’t push his hand away. Two red spots appeared on her cheeks. “Too bad. She cares for you.”
“Listen. I’m not attracted to her. I’d rather sleep with a Gila monster. She’s fine as a friend, but stop pushing her on me.”
Silke looked behind him, her eyebrows up high, so he turned around, sloshing the whiskey in his hand. Of course Carleen had come downstairs just at that instant. Her tartan robe was hanging open and she was wearing just underpants. Elliott’s eyes went to her pale rib cage, her short, skinny legs; he couldn’t help himself.
Carleen made a strangled sound and turned and ran. Rolling her eyes at him, Silke went after her.
Elliott drank down the whiskey. He would sleep on the lumpy couch and leave early. Silke did not come back down. It seemed his chance had fled, and just for a minute there, when he said, “Immortality,” he could have said, “You,” and Silke might still be talking to him. Now Carleen was mad and complications would ensue.
All external thoughts fled, and he fell gratefully into the rutted byways of his theories, like a junkie who knows it’s dangerous but can’t fight it anymore.
Back, back to Cantor’s Continuum. The central difficulty lies at the intersection of linguistics and math analysis, he thought, the intersection of what is discrete, like the integers, and what is continuous, like infinity. What is that intersection? Where is that intersection?
The Greeks had such a horror of infinity, and it still afflicted number theory, this need to make the infinite finite, these tortured reciprocals, these sequences that lead to the infinitely small, this strange reversal of the kingly truth…
The primes are discrete, but extend into infinity like any set of integers. They are discrete in some qualitatively different way. The integers are at equal intervals from each other by definition. What if I make a number line putting the primes at equal intervals… how is that function constructed… no damn imaginary numbers, not even reciprocals to make the series converge, forget the zeta function, I’ll invent my own…
“ Wakefield!” Whiskey-tinged breath blew into his face. He lay on his back on the couch, his neck at an impossible angle. His eyes refused to open. It was very late, or maybe very early?
“You have to go home. Carleen can’t see you here in the morning.”
He reached up and around Silke’s body, finding her waist. He drew her down to him.
“ Wakefield, no…”
“It’s you. It’ll always be you.”
“Stop!”
“You, not immortality.” He squeezed tighter. He loved holding warm, soft Silke against him. He felt hot tears on his face. Hers or his? She stopped struggling and lay exhausted on top of him.
“Please,” he said. “Just this once. I need you so much.”
“Idiot,” she said. “No.”
“Then kiss me. That’s all I ask. Silke, I need you more than he does. Please.” His lips already lay against her cheek. She turned her head slightly and her mouth caught his. He drank her in.
His arms relaxed and she rolled off the couch onto the floor and went away. He turned onto his side and went back to sleep.
Sun came through the curtains. “Old man,” Raj was saying, and shaking him none too gently. “Up you go.”
“What time is it?” Elliott mumbled.
“Eight-thirty.”
“I have class at nine.”
“The bathroom is clear. The women are upstairs, but the atmosphere up there is what my mother would describe as overspiced. Get up.”
Elliott borrowed Raj’s toothbrush and splashed cold water on his face.
Raj awaited him in the kitchen. “Drink.”
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 need math. As a result-his loss-he’d never be an immortal. And Silke… Elliott was glad now that she had rejected him; what a huge distraction.
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 Erdös’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 Erdös 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.”