Gödel's Incompleteness Theorems
In any system of arithmetic strong enough to be useful, there are true statements it can never prove. Including this one.
193125 min read
Austrian-American mathematical logic
Kurt Gödel
1906 – 1978
Logician of the first rank. He proved the completeness of first-order logic (1929), then in 1931 the two incompleteness theorems that ended Hilbert's programme in its original form. He later proved the consistency of the continuum hypothesis and the axiom of choice with ZF (1938-40). A Platonist about mathematical truth, he resisted the subjectivist readings his theorems are still routinely given.