David Hilbert

David Hilbert was born on January 23, 1862, in Wehlau (near modern-day Kaliningrad) in what was then East Prussia. He received his doctorate from the University of Königsberg in 1884. He taught at Königsberg from 1886 to 1895, and then moved to Göttingen, where he taught until his death in 1943.

Hilbert made deep and fundamental contributions to algebra, number theory, and geometry. In 1900 he was invited to give an address at the International Congress of Mathematicians in Paris. His address, entitled Mathematical Problems, listed 23 important problems he felt deserved the attention of mathematicians of the coming century.

Hilbert's Tenth Problem asked if there was a "process" by which "it can be deterined by a finite number of operations whether [a Diophantine] equation can be solved in ... integers". (A Diophantine equation is a multivariate polynomial equation.) In his later career, Hilbert became more interested in the foundations of mathematics and the possibility of resolving, by completely mechanical means, any well-posed mathematical problem. In 1928 he asked:

Hilbert believed that the answer to all these questions was "yes". But in 1931 the Czech mathematician Kurt Gödel proved that any sufficiently powerful mathematical system must be either inconsistent or incomplete. Also, such a system cannot be proved consistent within its own axiom system. But the third question remained open, with "provability" substituted for "truth". This was finally resolved negatively by Alan Turing in 1936.

Hilbert died in Königsberg on February 14, 1943.


  1. Constance Reid, Hilbert, Springer-Verlag, New York, 1970.
  2. David Hilbert, (transl. Mary Winston Newson), Mathematical problems, Bull. Amer. Math. Soc. 8 (1902), 437-479.
  3. Andrew Hodges, Alan Turing: The Enigma, Simon and Schuster, 1983.

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September 10 1997