Definition
Plain language
Getting a computer to find and check mathematical proofs, instead of a human writing them out by hand.
As stated in the literature
The use of software to search for and mechanically verify formal proofs; modern systems pair LLMs with proof assistants like Lean and search procedures, as in AlphaProof and Goedel-Architect.
Also called: theorem prover, theorem proving, automated theorem prover, theorem provers
Why it matters: It lets machines produce proofs that are guaranteed correct by construction, which can extend mathematics and verify software where human checking is too slow or error-prone.
For example, instead of a mathematician writing out every line of a proof, the software searches for the steps and a proof assistant checks that each one is airtight.
Heard on the show
“… particular subgoal looks routine and hands it off to AlphaProof — DeepMind's olympiad-level theorem prover — and you can see AlphaProof come back with "three quarters of this is proved, here's the bit …”Episode 067 — An AI Just Solved a 1996 Erdős Problem—and the Simplest Agent Won