Definition
Plain language
Writing mathematics in a strict code-like language so a computer can confirm every step.
As stated in the literature
Mathematics expressed in a machine-checkable logical language; correctness reduces to whether the proof term type-checks against the stated theorem, shifting trust from referees to the kernel and the statement itself.
Also called: formalization, formalized mathematics
Why it matters: It removes human error and hand-waving from proof-checking, but it shifts all the trust onto whether the statement you wrote down actually says what you meant.
For example, instead of writing "clearly this follows," you write out every step in a language the computer reads, and it either accepts the proof or refuses it.
Heard on the show
“There's a formalization team that takes the user's request — "simulate hypersonic flow around Apollo" — and turns it into a well-posed problem with explicit physics, geometry, and observables.”Episode 042 — An Agentic Scientific Computing System That Actually Remembers What It Learns