Kurt Godel

Austrian-American logician and mathematician — author of the Incompleteness Theorems (1931) — who proved that any consistent formal system capable of expressing arithmetic contains true statements that cannot be proved within the system — the most significant result in the foundations of mathematics.

Creates the Incompleteness Theorems — Gödel's proof (that no consistent formal system of arithmetic can prove all truths about arithmetic from within itself; and that such a system cannot prove its own consistency) demonstrated that Hilbert's formalist program was impossible and transformed the philosophy of mathematics.