# Hilbert Program **Domain:** Foundations of Mathematics / Proof Theory **Doc Type:** Historical Research Program **Maturity:** Developed **Related:** [[David Hilbert]], [[Gödel's Incompleteness Theorems]], [[Mathematical Foundations]], [[Formal Systems]], [[Proof Theory]] ## Definition The **Hilbert Program** sought a secure formal foundation for mathematics, including finitary demonstrations of the consistency of formalized mathematical theories. ## Gödel Context The incompleteness theorems placed decisive limits on the program's general ambitions. The result was not the destruction of formal mathematics; it redirected foundational work toward relative consistency, proof theory, model theory and explicit study of formal strength. ## Corpus Context The program is important to machine intelligence because it supplies the historical background for recurring hopes that a sufficiently explicit symbolic architecture could certify itself completely from within. ## Sources / Provenance - [Stanford Encyclopedia of Philosophy — Hilbert's Program](https://plato.stanford.edu/entries/hilbert-program/) - [[Gödel's Incompleteness Theorems]]