On Invariant Properties of Special Binary Forms, Especially of Spherical Functions (1885)
Doctoral advisor
Ferdinand von Lindemann[2]
Doctoral students
Wilhelm Ackermann
Heinrich Behmann
Felix Bernstein
Otto Blumenthal
Anne Bosworth
Werner Boy
Ugo Broggi
Richard Courant
Haskell Curry
Max Dehn
Ludwig Föppl
Rudolf Fueter
Paul Funk
Kurt Grelling
Alfréd Haar
Erich Hecke
Earle Hedrick
Ernst Hellinger
Wallie Hurwitz
Margarete Kahn
Oliver Kellogg
Hellmuth Kneser
Robert König
Emanuel Lasker
Klara Löbenstein
Charles Max Mason
Alexander Myller
Erhard Schmidt
Kurt Schütte
Andreas Speiser
Hugo Steinhaus
Gabriel Sudan
Teiji Takagi
Hermann Weyl
Ernst Zermelo
Other notable students
Edward Kasner John von Neumann Carl Gustav Hempel
David Hilbert (/ˈhɪlbərt/;[3]German:[ˈdaːvɪtˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).
Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century.[4][5]
Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. Hilbert was one of the founders of proof theory and mathematical logic.[6]
^Weyl, H. (1944). "David Hilbert. 1862–1943". Obituary Notices of Fellows of the Royal Society. 4 (13): 547–553. doi:10.1098/rsbm.1944.0006. S2CID 161435959.
^David Hilbert at the Mathematics Genealogy Project
^"Hilbert". Random House Webster's Unabridged Dictionary.
^Joyce, David. "The Mathematical Problems of David Hilbert". Clark University. Retrieved 15 January 2021.
^Hilbert, David. "Mathematical Problems". Retrieved 15 January 2021.
^Zach, Richard (31 July 2003). "Hilbert's Program". Stanford Encyclopedia of Philosophy. Retrieved 23 March 2009.
DavidHilbert (/ˈhɪlbərt/; German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians...
In mathematics, Hilbert spaces (named after DavidHilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)...
fractal space-filling curve first described by the German mathematician DavidHilbert in 1891, as a variant of the space-filling Peano curves discovered by...
introduced by DavidHilbert in this setting, to solve a special case of the Riemann–Hilbert problem for analytic functions. The Hilbert transform of u...
problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by DavidHilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that...
The DavidHilbert Award, named after DavidHilbert, was established by the World Federation of National Mathematics Competitions to acknowledge mathematicians...
mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal...
In mathematics, the Hilbert cube, named after DavidHilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore...
achievements of DavidHilbert were now considered. In addition to Hilbert's problems, Hilbert space, Hilbert Classification and the Hilbert Inequality, du...
discovery of the gravitational field equations of general relativity and DavidHilbert's almost simultaneous derivation of the theory using an elegant variational...
a Hilbert modular group. Hilbert modular surfaces were first described by Otto Blumenthal (1903, 1904) using some unpublished notes written by David Hilbert...
of the Artin symbol of local class field theory. The Hilbert symbol was introduced by DavidHilbert (1897, sections 64, 131, 1998, English translation)...
mathematicians like Gauss, Riemann, DavidHilbert, Dirichlet, Hermann Minkowski and Felix Klein. Abraham Fraenkel has written that Hilbert was "the most significant...
Goldman (1951), who named them Hilbert rings after DavidHilbert because of their relation to Hilbert's Nullstellensatz. Hilbert's Nullstellensatz of algebraic...
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