Monday, October 31, 2011

David Hilbert

Jan 23 1862 - Feb 14 1943
Born Königsberg, Germany (now Kaliningrad, Russia).
Died Göttingen, Germany.

David Hilbert received his Ph.D. from the University of Königsberg and was a member of staff there from 1886 to 1895 In 1895 he was appointed to the chair of mathematics at the University of Göttingen, where he continued to teach for the rest of his life.

Hilbert's first work was on invariant theory, in 1888 he proved his famous Basis Theorem. First he gave an existence proof but, after Cayley, Gordan, Lindemann and others were baffled, in 1892 Hilbert produced a constructive proof which satisfied everyone.

In 1893 while still at Königsberg he began a work "Zahlbericht" on algebraic number theory. The "Zahlbericht" (1897) is a brilliant synthesis of the work of Kummer, Kronecker and Dedekind but contains a wealth of Hilbert's own ideas. The ideas of the present day subject of 'Class field theory' are all contained in this work.

Hilbert's work in geometry had the greatest influence in that area after Euclid. A systematic study of the axioms of Euclidean geometry led Hilbert to propose 21 such axioms and he analysed their significance.

He published "Grundlagen der Geometrie" in 1899 putting geometry on a formal axiomatic setting. His famous 23 Paris problems challenged (and still today challenges) mathematicians to solve fundamental questions.

In 1915 Hilbert discovered the correct field equation for general relativity before Einstein but never claimed priority.

In 1934 and 1939 two volumes of "Grundlagen der Mathematik" were published which were intended to lead to a 'proof theory' a direct check for the consistency of mathematics. Göde's paper of 1931 showed that this aim is impossible.

Hilbert contributed to many branches of mathematics, including invariants, algebraic number fields, functional analysis, integral equations, mathematical physics, and the calculus of variations.

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