Gödel’s proof
a proof that in any logic system at least as powerful as arithmetic it is possible to state theorems that can be proved to be neither true nor false, using only the proof rules of that system. Published in 1931, this incompleteness result was very challenging to the mathematics of the time. British mathematician Alan Turing (1912–1954), with his proof of the undecidability of the halting problem, extended this result to computation (see Turing machine). [Kurt Gödel (1906–1978), Austrian-born U.S. mathematician]