A Little Life

by Hanya Yanagihara

“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...