The David Hilbert reference article from the English Wikipedia on 24-Jul-2004
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David Hilbert

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Table of contents
1 Bio
2 Major Contributions
3 Miscellaneous talks, essays, and contributions
5 Further reading
6 External links


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David Hilbert

David Hilbert (January 23, 1862February 14, 1943) was a German mathematician born in Königsberg, Prussia (now 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.

Major Contributions

Hilbert solved several important problems in the theory of invariants. Hilbert's basis theorem solved the principal problem in the 1800s 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.

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

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").

He also laid the foundations of functional analysis by studying integral equations and Hilbert spaces.

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

Miscellaneous talks, essays, and contributions

Hilbert presented the paradox of the Grand Hotel, a musing about strange properties of the infinite.

He put forth an influential list of 23 unsolved problems in the Paris conference of the International Congress of Mathematicians in 1900.

Additionally, Hilbert is responsible for assisting several advances in the mathematics of quantum mechanics. These include his integral calculations of hilbert spaces and proving the mathematical equivalency of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation.

Hilbert's Program

In 1920 he proposed a program that became known as Hilbert's program. He wanted mathematics be formulated on a solid and complete logical foundation (by showing that all of mathematics follows from a finite system of axioms, and that that axiom system is consistent). Called Hilbert's Program, this is still the most popular philosophy of mathematics usually called formalism. However, Gödel's Incompleteness Theorem showed in 1931 that his grand plan was impossible.


The following quote from Hilbert is engraved into his tombstone

Further reading

External links