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Later, Hilbert did work in algebraic number theory and geometry, and he helped create the general [[theory of relativity]] by first publishing a derivation of the field equations. His work on ''Hilbert spaces'' was also crucial for the development of [[quantum mechanics]]. In 1934 and 1939 he published two works attempting to develop a "proof theory," which is a direct check for the consistency of mathematics. But in 1931 [[Kurt Godel|Kurt Gödel]] had already proved that this goal was impossible.