David Hilbert By: Camryn Messmore

Early Life David Hilbert was a German mathematician that is recognized as one of the most influential and well-known mathematicians of the 19th and some of the 20th centuries. He was born January 23, 1862 in Konigsberg, Germany. Hilbert married Kathe Jerosch in 1892 and had one child named Franz on August 11, 1893. He died on February 14, 1943 in Gottingen, Germany at the age of 81.

School David Hilbert went to the University of Konigsberg and got his Doctorate (Ph.D.) in 1885.

Work He became a member of staff at Konigsberg from 1886-1895, and privatdozent until 1892. Then he became a temporary professor for one year until becoming a full professor in 1893. In 1895, Hilbert was appointed to the chair of mathematics at the University of Gottingen.

Contributions Invariant Theory - An invariant is something that is left unchanged by some class of functions. Basic Theory (1888) – Every ideal in the ring of multivariate polynomials over a noetherian ring is finitely generated. Algebraic Number Theory (1893) – Algebraic number theory is a number theory studied without using methods like infinite series, convergent, etc. It contrasts with the analytic number theory. Published Grundlagen der Geometrie in 1899, putting geometry in a formal axiomatic setting. Grundlagen der Geometrie means ‘Fundamentals of Geometry’ in German.) Made 21 ‘Hilbert’s Axioms’ Hilbert Spaces- Analog of Euclidean space with an infinite dimension. This is one of the foundations of functional analysis. Hilbert’s Program- A proposed solution to the foundational crisis of mathematics.

Invariant Theorem Hilbert proved that all invariants can be expressed in terms of a finite number. More specifically, invariant theory studied quantities which were associated with polynomial equations and which were left invariant under transformations of the variables. Example: the discriminant: b2 - 4ac is an invariant of the quadratic form: ax2 + bxy + cy2.