Definition
Plain language
A mathematical statement that has been proved to be true.
As stated in the literature
A proposition together with a derivation from axioms and prior results; in a proof assistant, the statement is a type and the proof is a term inhabiting it.
Also called: theorems
Why it matters: A theorem's value lies entirely in the pairing of what it claims with the argument backing it, so a valid proof of a weakened statement is worth much less than it looks.
For example, the statement that the angles inside any triangle add up to a half-turn is a theorem, because there is an argument establishing it from more basic assumptions.
Heard on the show
“The paper's first theorem says: actually, no.”Episode 020 — The Compliance Gap: Why AI Says Yes and Does No