Definition
Plain language
A formal theorem-proving system used as a comparison point that solves proofs by diving in and breaking the goal into smaller pieces from the top down.
As stated in the literature
A recursive-decomposition formal proving system used as the head-to-head baseline for Goedel-Architect; reported to be far more compute-expensive per problem than blueprint-based approaches.
Why it matters: It serves as a yardstick for comparing proving strategies, highlighting how much computing power a top-down approach burns versus alternatives.
For example, given a hard theorem, Hilbert dives straight in and keeps splitting the goal into smaller and smaller sub-goals until each piece is provable.
Heard on the show
“And the comparison system — the recursive-decomposition one, called Hilbert — came in around two hundred and forty-four dollars *per problem*.”Episode 117 — How an Open AI System Verified 672 Hard Math Proofs for Under $300