David Hilbert

David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. His own discoveries alone would have given him that honor, yet it was his leadership in the field of mathematics throughout his later life that distinguishes him. He held a professorship in mathematics at the University of Göttingen for most of his life.

Major contributions

Hilbert solved several important problems in the theory of invariants. Hilbert's basis theorem solved the principal problem in nineteenth century invariant theory by showing that any form of a given number of variables and of a given degree has a finite, yet complete system of independent rational integral invariants and covariants.

Related Topics:
Theory of invariants - Hilbert's basis theorem

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He also unified the field of algebraic number theory with his 1897 treatise Zahlbericht (literally "report on numbers").

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Famous for his ability to make discoveries in various mathematical fields, Hilbert went on to provide the first correct and complete axiomatization of Euclidean geometry to replace Euclid's axiomatization of geometry, in his 1899 book Grundlagen der Geometrie ("Foundations of Geometry"). See Hilbert's axioms.

Related Topics:
Axiomatization - Euclidean geometry - Euclid - Geometry - 1899 - Hilbert's axioms

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He also laid the foundations of functional analysis by studying integral equations and formulating a first version, in terms of quadratic forms in infinitely many variables, of what would be called Hilbert space. This work turned out in the 1920s to be foundational for quantum mechanics.

Related Topics:
Functional analysis - Integral equation - Quadratic form - Hilbert space - Quantum mechanics

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His interest in physics, in the decade 1900-1910, was not as important as later contacts with Albert Einstein and formulations of general relativity that helped its mathematical respectability (see also Einstein-Hilbert action).

Related Topics:
Albert Einstein - General relativity - Einstein-Hilbert action

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Hilbert helped provide the basis for the theory of automata which was later built upon by computer scientist Alan Turing.

Related Topics:
Theory of automata - Computer scientist - Alan Turing

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