David Hilbert (1862-1943). Caricature of the German mathematician David Hilbert. Hilbert is regarded by many as one of the greatest mathematicians of all time. He was educated at Konigsberg and Heidelberg, taught at Konigsberg and became professor of mathematics at Gottingen in 1895. His first work was in number theory, creating a general theory of invariants. He later applied this to topology, developing the concept of infinite-dimensional Hilbert Space. This opened the way for quantum theorists such as Schrodinger, Heisenberg and Dirac. Hilbert also championed formalism in mathematical logic and philosophy, inspiring Godel to formulate his opposing theory of mathematical inconsistency.