What’s the opposite of mathematics?

A mathematician once sent me a draft of some writing he’d done for a general audience. I liked the ideas. I liked the storytelling. I liked being consulted as an expert (it’s very ego-soothing). But I gave one word of warning: don’t frame it as a “history.” Historians will object loudly, I said, for reasons X, Y, and Z.

Naturally, the author also ran his draft by a historian… who hated it, for reasons X, Y, and Z.

What’s the opposite of mathematics?

So what were X, Y, and Z?

X: History is not a tale of “progress.” Yes, new math depends and builds upon the mathematics of the past. But this does not mean past thinkers were benighted knaves. When mathematicians act as if humanity were a lone scholar perfecting her proofs, historians want to bang their heads against the wall (and by “their” I mean the mathematicians’).

Y: History is profoundly contextual. To know what is new and innovative in a document, you cannot rely on the document alone. When mathematicians attribute pivotal ideas to lone authors based on a single reading of a single document… well, again with the head-hanging.

And finally, Z: Historians get especially annoyed when mathematicians commit these errors, because they seem to do so with probability approaching 1.

“It’s almost impossible for mathematicians to tackle history,” I said to a friend recently. “History is the opposite of mathematics.”

My companion looked perplexed. “Explain.”

“Okay, not opposite. Dave Richeson and Jay Cummings can do it,” I clarified. (Totally changing my claim is my favorite kind of clarification.) “But in the high-dimensional space of academic subjects, the subject furthest from math—the one most different in methodology, nature of inquiry, and intellectual skills required—is history.”

“Not English literature?”

“No,” I said. “See, math is 100% theory, 0% empirics. Everything follows from first principles; think hard enough about something, and you reach the truth. In math, new data can never refute a beautiful idea.”

“And how is that like literature?”

“In literature, everything depends on the text. It’s a self-contained cosmos. Later texts can never refute it, only enrich it. And just like reading a proof, you approach the text word by word, excavating all the nuances that were carefully encoded there by an author.”


“But history is 1% text, 99% context. To understand a document, you’ve got to read a thousand others. Nothing means anything in isolation, nothing follows from first principles, and the primary role of theory is to keep us from drowning in oceans of detail. Historical truth is irreducibly complex, and all our conclusions are only tentative ways of compressing it to fit in a human brain.”


“More to the point, it’s messy, messy in a way that mathematical thinking is totally ill-equipped to handle. Mathematics is self-contained. History is uncontainable.”

Of course, I didn’t say any of these things precisely. A historian might be able to recreate the conversation more faithfully, or present the memory with sufficient vagueness instead of open fabrications—but alas, I’m the opposite of a historian. I remember the big idea, and I simply trust the details to fill in themselves.

Which might sound lazy of me. But if you consider the totality of mathematics—our culture of abstraction, the nature of our language, math’s uneasy interdependence with more “practical” sciences—in short, if you consider mathematicians in the rich, contextual way that a historian would… well, then my failures as a historian make perfect sense.