The Gödel Incompleteness

At the turn of the century, the world-famous German mathematician David Hilbert proposed a programme for the development of all of mathematics within the strict formalization of the axiomatic method. According to Hilbert's belief, all of mathematics could be regarded as the formal, logical manipulation of symbols based on prescribed axioms. (This would mean that, in principle, a computer could be programmed to 'do all of mathematics'.) But in 1930, with two startling and totally unexpected theorems, the young Austrian mathematician Kurt Gödel demonstrated that Hilbert's programme could not possibly succeed.