David Hilbert was a German mathematician, He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics. Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. Hilbert is known as one of the founders of proof theory and mathematical logic.