Kurt Friedrich Godel (1906-1978) was, in the words of the Stanford Encyclopedia of Philosophy, “one of the principal founders of the modern, metamathematical era in mathematical logic.” He was born in Brunn (now Brno) and spent the later part of his career at the Institute for Advanced Study in Princeton, where he died in 1978.
Godel’s best known work is the pair of incompleteness theorems he published in 1931, which the Stanford Encyclopedia describes as “among the handful of landmark theorems in twentieth century mathematics.” The first theorem shows that any consistent formal system strong enough to express elementary arithmetic must contain statements that can neither be proved nor disproved within it; the second shows that such a system cannot prove its own consistency.
These results closed off a hope, associated with David Hilbert’s program, that all of mathematics could be placed on a complete and provably consistent formal footing. By demonstrating intrinsic limits on what formal systems can establish, Godel reframed the questions that logicians asked about proof and truth.
His work also fed directly into the theory of computation. The techniques and questions raised by incompleteness were closely tied to the work of Alan Turing and Alonzo Church a few years later on what can and cannot be decided by a mechanical procedure, making Godel a foundational figure for computer science as well as logic.