Professor David Hilbert

A German mathematician, he is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis. He adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century. He and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. He is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics. He was born in the Province of Prussia - either in K?nigsberg (according to Hilbert's own statement) or in Wehlau (known since 1946 as Znamensk) near K?nigsberg where his father worked at the time of his birth. In the fall of 1872, he entered the Friedrichskolleg Gymnasium (Collegium fridericianum, but after an unhappy duration he transferred (fall 1879) to and graduated from (spring 1880) the more science-oriented Wilhelm Gymnasium. Upon graduation he enrolled (autumn 1880) at the University of K?nigsberg, the "Albertina". He obtained his Doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled ?ber invariante Eigenschaften spezieller bin?rer Formen, insbesondere der Kugelfunktionen ("On the invariant properties of special binary forms, in particular the spherical harmonic functions"). He remained at the University of K?nigsberg as a professor from 1886 to 1895. In 1892, He married K?the Jerosch (1864?1945), "the daughter of a Konigsberg merchant, an outspoken young lady with an independence of mind that matched his own". While at K?nigsberg they had their one child Franz Hilbert (1893?1969). In 1895, as a result of intervention on his behalf by Felix Klein he obtained the position of Chairman of Mathematics at the University of G?ttingen, at that time the best research center for mathematics in the world and where he remained for the rest of his life. He and the mathematicians who worked with him in his enterprise were committed to the project. His attempt to support axiomatized mathematics with definitive principles, which could banish theoretical uncertainties, was however to end in failure. G?del demonstrated that any non-contradictory formal system, which was comprehensive enough to include at least arithmetic, cannot demonstrate its completeness by way of its own axioms. In 1931 his incompleteness theorem showed that Hilbert's grand plan was impossible as stated. The second point cannot in any reasonable way be combined with the first point, as long as the axiom system is genuinely finitary. Nevertheless, the subsequent achievements of proof theory at the very least clarified consistency as it relates to theories of central concern to mathematicians. His work had started logic on this course of clarification; the need to understand G?del's work then led to the development of recursion theory and then mathematical logic as an autonomous discipline in the 1930s. The basis for later theoretical computer science, in Alonzo Church and Alan Turing also grew directly out of this 'debate'. Around 1909, he dedicated himself to the study of differential and integral equations; his work had direct consequences for important parts of modern functional analysis. In order to carry out these studies, he introduced the concept of an infinite dimensional Euclidean space, later called Hilbert space. His work in this part of analysis provided the basis for important contributions to the mathematics of physics in the next two decades, though from an unanticipated direction. Later on, Stefan Banach amplified the concept, defining Banach spaces. Hilbert spaces are an important class of objects in the area of functional analysis, particularly of the spectral theory of self-adjoint linear operators that grew up around it during the 20th century. He lived to see the Nazis purge many of the prominent faculty members at University of G?ttingen in 1933. Those forced out included Hermann Weyl (who had taken his chair when he retired in 1930), Emmy Noether and Edmund Landau. One who had to leave Germany, Paul Bernays, had collaborated with him in mathematical logic, and co-authored with him the important book ?Grundlagen der Mathematik? (which eventually appeared in two volumes, in 1934 and 1939). This was a sequel to the Hilbert-Ackermann book, ?Principles of Mathematical Logic? from 1928. In Turing?s Cathedral by George Dyson it is noted, ?Turing, like von Neumann, grew up under the influence of David Hilbert, whose ambitious program of formalization set the course for mathematics between World War I and World War II.?