âJude,â Laurence said, whose voice was even lower than Haroldâs, âHarold tells me you're also getting your master's at MIT. What in?â
âPure math,â he replied. âHow is that different fromââshe laughedââregular math?" Gillian asked.
âWell, regular math, or applied math, is what I suppose you could call practical math,â he said. âIt'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 willâthe 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.â
âDo you mean imaginary geometries, stuff like that?â Laurence asked.
"It can be, sure. But it's not just that. Often, it's merely proof ofâof 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."
âWhich is what?â Laurence asked.
He thought. âMathematical logic, or pure logic, is essentially a conversation between truths and falsehoods. So for example, I might say to you âAll positive numbers are real. Two is a positive number. Therefore, two must be real.â 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.â He stopped. âDoes that make sense?â
âVideo, ergo est,â said Laurence, suddenly. I see it, therefore it is. He smiled. âAnd that's exactly what applied math is. But pure math is moreââhe thought againââImaginor, ergo est.â
[...]
â[The] law isn't so unlike pure math, reallyâI 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. âI 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 managerialâit only has to be true.
âBut I suppose the other way in which they're alike is that in mathematics, as well as in law, what matters moreâor, more accurately, what's more memorableâis not that the case, or proof, is won or solved, but the beauty, the economy, with which it's done."
âWhat do you mean?â asked Harold.
âWell,â he said, âin 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."
âWhat about something like Fermat's last theorem?" asked Julia.
âThat's a perfect example of a non-beautiful proof. Because while it was important that it was solved, it was, for a lot of peopleâlike my adviserâa disappointment. The proof went on for hundreds of pages, and drew from so many disparate fields of mathematics, and was soâtortured, jigsawed, really, in its execution, that there are still many people at work trying to prove it in more elegant terms, even though itâs 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.â 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. âI'm sorry," he apologized. "I'm sorry. I didn't mean to ramble on.â
âAre you joking?â said Laurence. âJude, I think that was the first truly revelatory conversation Iâve had in Haroldâs house in probably the last decade or more: thank you.â
A Little Life by Hanya Yanagihara
Part II: The Postman. Chapter 1, pgs. 124-126








