Kurt Gödel

Kurt Gödel

An Austrian-American logician whose 1931 incompleteness theorems showed that any consistent formal system rich enough to express arithmetic must contain true statements it cannot prove, and cannot prove its own consistency. The result ended the programme of putting all of mathematics on a complete mechanical footing, and his work on general recursive functions helped define what "computable" means at all. For AI, Gödel marks the boundary of the field's ambitions: some limits on what a formal system can establish about itself are mathematical facts, not engineering problems. (See also: Alan Turing, Alonzo Church, Symbolic AI)