Researched
Gödel's Incompleteness
Gödel proves in 1931 that every sufficiently strong system of rules contains true statements it cannot prove.
Open in the interactive tree →Hilbert dreamed of a system that proves all mathematical truths and certifies its own consistency. The young Kurt Gödel showed this is impossible. His method of encoding statements as numbers became the model for the theory of computers.
Prerequisites
- Set Theory & Formal Logic1874
- Hilbert's Problems & Program1900Gödel's theorems answered Hilbert's programme to prove mathematics consistent
Unlocks
- Computability (Turing)1936
- Turing Machine1936Turing answered the decision problem that Goedel's theorem had opened
- Formal Proofs (Lean, Rocq)2005-2026
More in Mathematics · Machine Age
- Hilbert's Problems & Program1900
- Measure-Theoretic Probability1902-1933
- Markov Chains1906
- Abstract Algebra (Noether)1921-1931
- Computability (Turing)1936