1906 – 1978
Kurt Gödel was an Austrian-American logician, mathematician, and philosopher whose incompleteness theorems transformed the foundations of mathematics and logic. His work demonstrated inherent limitations in formal axiomatic systems, reshaping philosophy of mathematics, epistemology, and debates about the nature of mind and computation.
Proved the Incompleteness Theorems (1931), showing any consistent formal system capable of arithmetic is incomplete
Proved the completeness theorem for first-order predicate logic (1929)
Demonstrated the consistency of the Axiom of Choice and the Generalized Continuum Hypothesis with ZF set theory
Formulated a modal ontological argument for the existence of God
Defended mathematical Platonism, arguing mathematical objects exist independently of the mind