Gödel's incompleteness theorems
Kurt Gödel
Gödel’s 1931 incompleteness theorems show that no consistent, effectively axiomatized formal system capable of arithmetic can be both complete and self-consistent. They ended Hilbert’s program. Their method — Gödel numbering and diagonalisation — became foundational for computability theory. They do not apply outside formal systems satisfying strict technical conditions.
