David Hilbert (1862-1943) was a German mathematician who attempted to formalize mathematics in a methodical manner. He is famous for listing the 23 greatest unsolved problems of mathematics in 1900, problems that included the Riemann hypothesis, the continuum hypothesis, Goldbach's conjecture, the well ordering of the reals, the transcendence of powers of algebraic numbers and the extension of Dirichlet's principle, in addition to his analogy for Cantorian infinite sets, known as 'Hilbert's Hotel'.
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.