Here is a question that sounds like it should have an obvious answer. Was mathematics invented or discovered? Did humans create the number two the way we created the word for it? Or did the number two exist before any human thought about it — a feature of reality we stumbled upon rather than constructed?

The obvious answer is that mathematics was invented. Humans made it up. The alternative sounds mystical: abstract objects existing in some Platonic realm, waiting to be found.

But the obvious answer runs into a problem almost immediately. If mathematics is a human invention — a useful fiction we constructed for our own purposes — then why does it describe the physical world with such uncanny precision? Why does mathematics developed to solve purely theoretical problems turn out, decades or centuries later, to be exactly what physicist ...