Harold wanted to know how he had been raised, and if he had any siblings, and who his friends were, and what he did with them: he was greedy for information. At least he could answer the last questions, and he told him about his friends, and how they had met, and where they were: Malcolm in graduate school at Columbia, JB and Willem at Yale. He liked answering Harold’s questions about them, liked talking about them, liked hearing Harold laugh when he told him stories about them. He told him about CM, and how Santosh and Federico were in some sort of fight with the engineering undergrads who lived in the frat house next door, and how he had awoken one morning to a fleet of motorized dirigibles handmade from condoms floating noisily up past his window, up toward the fourth floor, each dangling signs that read SANTOSH JAIN AND FEDERICO DE LUCA HAVE MICRO-PENISES.
But when Harold was asking the other questions, he felt smothered by their weight and frequency and inevitability. And sometimes the air grew so hot with the questions Harold wasn’t asking him that it was as oppressive as if he actually had. People wanted to know so much, they wanted so many answers. And he understood it, he did—he wanted answers, too; he too wanted to know everything. He was grateful, then, for his friends, and for how relatively little they had mined from him, how they had left him to himself, a blank, faceless prairie under whose yellow surface earthworms and beetles wriggled through the black soil, and chips of bone calcified slowly into stone.
“You’re really interested in this,” he snapped at Harold once, frustrated, when Harold had asked him whether he was dating anyone, and then, hearing his tone, stopped and apologized. They had known each other for almost a year by then.
“This?” said Harold, ignoring the apology. “I’m interested in you. I don’t see what’s strange about that. This is the kind of stuff friends talk about with each other.”
And yet despite his discomfort, he kept coming back to Harold, kept accepting his dinner invitations, even though at some point in every encounter there would be a moment in which he wished he could disappear, or in which he worried he might have disappointed.
One night he went to dinner at Harold’s and was introduced to Harold’s best friend, Laurence, whom he had met in law school and who was now an appellate court judge in Boston, and his wife, Gillian, who taught English at Simmons. “Jude,” said Laurence, whose voice was even lower than Harold’s, “Harold tells me you’re also getting your master’s at MIT. What in?”
“Pure math,” he replied.
“How is that different from”—she laughed—“regular math?” Gillian asked.
“Well, regular math, or applied math, is what I suppose you could call practical math,” he said. “It’s used to solve problems, to provide solutions, whether it’s in the realm of economics, or engineering, or accounting, or what have you. But pure math doesn’t exist to provide immediate, or necessarily obvious, practical applications. It’s purely an expression of form, if you will—the only thing it proves is the almost infinite elasticity of mathematics itself, within the accepted set of assumptions by which we define it, of course.”
“Do you mean imaginary geometries, stuff like that?” Laurence asked.
“It can be, sure. But it’s not just that. Often, it’s merely proof of—of the impossible yet consistent internal logic of math itself. There’s all kinds of specialties within pure math: geometric pure math, like you said, but also algebraic math, algorithmic math, cryptography, information theory, and pure logic, which is what I study.”
“Which is what?” Laurence asked.
He thought. “Mathematical logic, or pure logic, is essentially a conversation between truths and falsehoods. So for example, I might say to you ‘All positive numbers are real. Two is a positive number. Therefore, two must be real.’ But this isn’t actually true, right? It’s a derivation, a supposition of truth. I haven’t actually proven that two is a real number, but it must logically be true. So you’d write a proof to, in essence, prove that the logic of those two statements is in fact real, and infinitely applicable.” He stopped. “Does that make sense?”
“Video, ergo est,” said Laurence, suddenly. I see it, therefore it is.
He smiled. “And that’s exactly what applied math is. But pure math is more”—he thought again—“Imaginor, ergo est.”
Laurence smiled back at him and nodded. “Very good,” he said.
“Well, I have a question,” said Harold, who’d been quiet, listening to them. “How and why on earth did you end up in law school?”
Everyone laughed, and he did, too. He had been asked that question often (by Dr. Li, despairingly; by his master’s adviser, Dr. Kashen, perplexedly), and he always changed the answer to suit the audience, for the real answer—that he wanted to have the means to protect himself; that he wanted to make sure no one could ever reach him again—seemed too selfish and shallow and tiny a reason to say aloud (and would invite a slew of subsequent questions anyway). Besides, he knew enough now to know that the law was a flimsy form of protection: if he really wanted to be safe, he should have become a marksman squinting through an eyepiece, or a chemist in a lab with his pipettes and poisons.
That night, though, he said, “But law isn’t so unlike pure math, really—I mean, it too in theory can offer an answer to every question, can’t it? Laws of anything are meant to be pressed against, and stretched, and if they can’t provide solutions to every matter they claim to cover, then they aren’t really laws at all, are they?” He stopped to consider what he’d just said. “I suppose the difference is that in law, there are many paths to many answers, and in math, there are many paths to a single answer. And also, I guess, that law isn’t actually about the truth: it’s about governance. But math doesn’t have to be convenient, or practical, or managerial—it only has to be true.
“But I suppose the other way in which they’re alike is that in mathematics, as well as in law, what matters more—or, more accurately, what’s more memorable—is not that the case, or proof, is won or solved, but the beauty, the economy, with which it’s done.”
“What do you mean?” asked Harold.
“Well,” he said, “in law, we talk about a beautiful summation, or a beautiful judgment: and what we mean by that, of course, is the loveliness of not only its logic but its expression. And similarly, in math, when we talk about a beautiful proof, what we’re recognizing is the simplicity of the proof, its … elementalness, I suppose: its inevitability.”
“What about something like Fermat’s last theorem?” asked Julia.
“That’s a perfect example of a non-beautiful proof. Because while it was important that it was solved, it was, for a lot of people—like my adviser—a disappointment. The proof went on for hundreds of pages, and drew from so many disparate fields of mathematics, and was so—tortured, jigsawed, really, in its execution, that there are still many people at work trying to prove it in more elegant terms, even though it’s already been proven. A beautiful proof is succinct, like a beautiful ruling. It combines just a handful of different concepts, albeit from across the mathematical universe, and in a relatively brief series of steps, leads to a grand and new generalized truth in mathematics: that is, a wholly provable, unshakable absolute in a constructed world with very few unshakable absolutes.” He stopped to take a breath, aware, suddenly, that he had been talking and talking, and that the others were silent, watching him. He could feel himself flushing, could feel the old hatred fill him like dirtied water once more. “I’m sorry,” he apologized. “I’m sorry. I didn’t mean to ramble on.”