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German mathematician (1862–1943)
David Hilbert (/ˈhɪlbərt/; German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and
David_Hilbert
23 mathematical problems stated in 1900
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several
Hilbert's_problems
Type of vector space in math
techniques of calculus to be used. Hilbert spaces were studied beginning in the first decade of the 20th century by David Hilbert (after whom they are named)
Hilbert_space
Annual mathematics award
The David Hilbert Award, named after David Hilbert, was established by the World Federation of National Mathematics Competitions (WFNMC) to acknowledge
David_Hilbert_Award
Space-filling curve
fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by
Hilbert_curve
Axiomatic system of formal deduction in logic
In logic and proof theory, a Hilbert system, Hilbert calculus, or Hilbert-style proof system is a type of formal proof system in which logical principles
Hilbert_system
Integral transform and linear operator
introduced by David Hilbert in this setting, to solve a special case of the Riemann–Hilbert problem for analytic functions. The Hilbert transform of u
Hilbert_transform
Thought experiment of infinite sets
David Hilbert in a 1924–1925 lecture "Über das Unendliche", and was popularized through George Gamow's 1947 book One Two Three... Infinity. Hilbert imagines
Hilbert's paradox of the Grand Hotel
Hilbert's_paradox_of_the_Grand_Hotel
Foundational controversy in twentieth-century mathematics
a proponent of the constructivist school of intuitionism, opposed David Hilbert, a proponent of formalism. Much of the controversy took place while
Brouwer–Hilbert_controversy
Mathematical problems related to differential equations
In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential
Riemann–Hilbert_problem
Axiomatization of probability and physics
which lead from the atomistic view to the laws of motion of continua. David Hilbert himself devoted much of his research to the sixth problem; in particular
Hilbert's_sixth_problem
Debate about credit for general relativity
discovery of the gravitational field equations of general relativity and David Hilbert's almost simultaneous derivation of the theory using an elegant variational
General relativity priority dispute
General_relativity_priority_dispute
Impossible task in computing
problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers
Entscheidungsproblem
Type of topological space
In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore
Hilbert_cube
Function used in local class field theory related to reciprocity laws
of the Artin symbol of local class field theory. The Hilbert symbol was introduced by David Hilbert (1897, sections 64, 131, 1998, English translation)
Hilbert_symbol
Attempt to formalize all of mathematics, based on a finite set of axioms
In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early 1920s, was a proposed solution to the foundational crisis
Hilbert's_program
Topic in mathematics
In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator A : H → H {\displaystyle A\colon H\to
Hilbert–Schmidt_operator
Topics referred to by the same term
David Hilbert (1862–1943) was a German mathematician. Hilbert may also refer to: 12022 Hilbert, an asteroid Hilbert (crater), on the Moon Hilbert, West
Hilbert_(disambiguation)
mathematicians like Gauss, Riemann, David Hilbert, Dirichlet, Hermann Minkowski, and Felix Klein. Abraham Fraenkel has written that Hilbert was "the most significant
Mathematics_in_Nazi_Germany
German mathematician (1882–1935)
time, women were largely excluded from academic positions. In 1915, David Hilbert and Felix Klein invited her to join the mathematics department at the
Emmy_Noether
2008 British TV series or programme
achievements of David Hilbert were now considered. In addition to Hilbert's problems, Hilbert space, Hilbert Classification and the Hilbert Inequality, du
The_Story_of_Maths
Two-volume work by David Hilbert and Paul Bernays
Mathematik (English: Foundations of Mathematics) is a two-volume work by David Hilbert and Paul Bernays. Originally published in 1934 and 1939, it presents
Grundlagen_der_Mathematik
On solvability of Diophantine equations
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge
Hilbert's_tenth_problem
Relation between algebraic varieties and polynomial ideals
proven by David Hilbert in his second major paper on invariant theory in 1893 (following his seminal 1890 paper in which he proved Hilbert's basis theorem)
Hilbert's_Nullstellensatz
View that mathematics does not necessarily represent reality, but is more akin to a game
formalism was David Hilbert, whose program was intended to be a complete and consistent axiomatization of all of mathematics. Hilbert aimed to show the
Formalism (philosophy of mathematics)
Formalism_(philosophy_of_mathematics)
Conjecture in topology
conjecture is for David Hilbert, and the American topologist Paul A. Smith. It is considered by some to be a better formulation of Hilbert's fifth problem
Hilbert–Smith_conjecture
Goldman (1951), who named them Hilbert rings after David Hilbert because of their relation to Hilbert's Nullstellensatz. Hilbert's Nullstellensatz of algebraic
Jacobson_ring
Basis for Euclidean geometry
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as
Hilbert's_axioms
Distance function
subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert (1895) as a generalization of Cayley's formula for the distance in the
Hilbert_metric
Historic German city, now Kaliningrad, Russia
Immanuel Kant, Johann Georg Hamann, Käthe Kollwitz, E. T. A. Hoffmann, David Hilbert, Agnes Miegel, Hannah Arendt, Michael Wieck, and others. It was the
Königsberg
demonstrated by David Hilbert with the constant 2π instead of π; the sharp constant was found by Issai Schur. It implies that the discrete Hilbert transform
Hilbert's_inequality
Subfield of mathematics
arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results
Mathematical_logic
Book by David Hilbert
around 1000 pages, published under the names of Richard Courant and David Hilbert. It was a comprehensive treatment of the "methods of mathematical physics"
Methoden der mathematischen Physik
Methoden_der_mathematischen_Physik
In mathematics, the Hilbert–Mumford criterion, introduced by David Hilbert and David Mumford, characterizes the semistable and stable points of a group
Hilbert–Mumford_criterion
German–British physicist (1882–1970)
in 1904, where he met the three renowned mathematicians Felix Klein, David Hilbert, and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of
Max_Born
Algebraic surface in mathematics
a Hilbert modular group. Hilbert modular surfaces were first described by Otto Blumenthal (1903, 1904) using some unpublished notes written by David Hilbert
Hilbert_modular_variety
Curve whose range contains the unit square
counterintuitive results. A year later, David Hilbert published in the same journal a variation of Peano's construction. Hilbert's article was the first to include
Space-filling_curve
Concept in general relativity
as the Euler–Lagrange equation of the Einstein–Hilbert action. The action was proposed by David Hilbert in 1915 as part of his application of the variational
Einstein–Hilbert_action
Swiss mathematician (1888–1977)
philosophy of mathematics. He was an assistant and close collaborator of David Hilbert. Bernays was born into a distinguished German-Jewish family of scholars
Paul_Bernays
Mathematician (1845–1918)
Sylvester Medal, the highest honor it can confer for work in mathematics. David Hilbert defended it from its critics by declaring, "No one shall expel us from
Georg_Cantor
German mathematician (1885–1955)
Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski. His research has had major significance for theoretical
Hermann_Weyl
Public university in Göttingen, Germany
center for mathematics and physics. During this period, scholars such as David Hilbert, Felix Klein, Max Born, and Ludwig Prandtl conducted influential research
University_of_Göttingen
The Hilbert–Bernays paradox is a distinctive paradox belonging to the family of the paradoxes of reference. It is named after David Hilbert and Paul Bernays
Hilbert–Bernays_paradox
In mathematical logic, the Hilbert–Bernays-Löb provability conditions, named after David Hilbert, Paul Bernays, and Martin Löb, are a set of requirements
Hilbert–Bernays-Löb provability conditions
Hilbert–Bernays-Löb_provability_conditions
On Schubert's enumerative calculus
Hilbert's fifteenth problem is one of the 23 Hilbert problems set out in a list compiled in 1900 by David Hilbert. The problem is to put Schubert's enumerative
Hilbert's_fifteenth_problem
Can all boundary value problems be solved
Hilbert's twentieth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether all boundary
Hilbert's_twentieth_problem
discoveries of German mathematicians like Carl Friedrich Gauss and David Hilbert. The origins of mathematical thought lie in the concepts of number,
History_of_mathematics
When are solutions in the calculus of variations analytic
Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled by David Hilbert in 1900. It asks whether the solutions of
Hilbert's_nineteenth_problem
Construct all metric spaces where lines resemble those on a sphere
In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry. In one statement derived from the
Hilbert's_fourth_problem
formalism. Some notable formalists include: David Hilbert: A leading mathematician of the early 20th century, Hilbert is one of the most prominent advocates
Mathematical_object
Mathematical term; concerning axioms used to derive theorems
Georg Cantor's abstract set theory, and Hilbert's revisionist axioms for Euclidean geometry. David Hilbert "was the first who explicitly adopted the
Axiomatic_system
On uniformization of analytic relations
Hilbert's twenty-second problem is the penultimate entry in the celebrated list of 23 Hilbert problems compiled in 1900 by David Hilbert. It entails the
Hilbert's twenty-second problem
Hilbert's_twenty-second_problem
1932 book by David Hilbert and Stefan Cohn-Vossen
book Anschauliche Geometrie by David Hilbert and Stefan Cohn-Vossen. The book was based on a series of lectures Hilbert made in the winter of 1920–21.
Geometry_and_the_Imagination
Mathematician and philosopher (1906–1978)
century (at a time when Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics)
Kurt_Gödel
Baltic German mathematician
Dorpat), in the Governorate of Livonia (now Estonia). His advisor was David Hilbert and he was awarded his doctorate from University of Göttingen in 1905
Erhard_Schmidt
Promotes work on calculus of variations
Hilbert's twenty-third problem is the last of Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. In contrast with Hilbert's
Hilbert's twenty-third problem
Hilbert's_twenty-third_problem
Topics referred to by the same term
term Hilbert geometry may refer to several things named after David Hilbert: Hilbert's axioms, a modern axiomatization of Euclidean geometry Hilbert space
Hilbert_geometry
Dutch mathematician and logician
This position led to the Brouwer–Hilbert controversy, in which Brouwer sparred with his formalist colleague David Hilbert. Brouwer's ideas were subsequently
L._E._J._Brouwer
Polynomial ideals are finitely generated
Noetherian ring is also Noetherian. The theorem was stated and proved by David Hilbert in 1890 in his seminal article on invariant theory, where he solved
Hilbert's_basis_theorem
On polynomial rings over fields
mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in 1890,
Hilbert's_syzygy_theorem
Local and global geometry of the universe
was caused by the incompatibility of relativity with Euclidean space. David Hilbert (1925) thought the universe was determined finite by elliptical geometry
Shape_of_the_universe
Criteria of simplicity for mathematical proofs
list of 23 problems (known as Hilbert's problems) but was included in David Hilbert's original notes. The problem asks for a criterion of simplicity in mathematical
Hilbert's twenty-fourth problem
Hilbert's_twenty-fourth_problem
Axiom in Russell's ramified theory of types
from them, but not the antinomies. While he mentions the efforts of David Hilbert to prove the consistency of his axiomatisation of mathematics von Neumann
Axiom_of_reducibility
On curvature of surfaces
Hilbert's lemma was proposed at the end of the 19th century by mathematician David Hilbert. The lemma describes a property of the principal curvatures
Hilbert's_lemma
cube Hilbert curve Hilbert curve scheduling Hilbert field Hilbert function Hilbert manifold Hilbert matrix Hilbert metric Hilbert modular form Hilbert modular
List of things named after David Hilbert
List_of_things_named_after_David_Hilbert
Statistical tool used in distinguishing among a mixture of moving signals
The Hilbert spectrum (sometimes referred to as the Hilbert amplitude spectrum), named after David Hilbert, is a statistical tool that can help in distinguishing
Hilbert_spectrum
Algebraic structure with addition and multiplication
the 1870s to the 1920s, with key contributions by Richard Dedekind, David Hilbert, Abraham Fraenkel, and Emmy Noether. Rings were first formalized as
Ring_(mathematics)
German crystallographer and physicist (1888–1985)
of Göttingen: Felix Klein, David Hilbert, and Hermann Minkowski. While studying at Göttingen, Ewald was taken on by Hilbert as an Ausarbeiter, a paid position
Paul_Peter_Ewald
Mathematical model for deduction or proof systems
deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics
Formal_system
Mathematical study of invariants under symmetries
later paper of Hilbert (1893) dealt with the same questions in more constructive and geometric ways, but remained virtually unknown until David Mumford brought
Invariant_theory
Paradox in set theory
However, Zermelo did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other academics at the University of Göttingen
Russell's_paradox
American mathematician (1900-1982)
who were familiar with Schönfinkel's work. Curry was supervised by David Hilbert and worked closely with Bernays, receiving a Ph.D. in 1930 with a dissertation
Haskell_Curry
German mathematician and physicist (1864–1909)
decision. He also became a friend of another renowned mathematician, David Hilbert. His brother, Oskar Minkowski (1858-1931), was a well-known physician
Hermann_Minkowski
Formal power series in algebra
in the field of algebra, a Hilbert–Poincaré series (also known under the name Hilbert series), named after David Hilbert and Henri Poincaré, is an adaptation
Hilbert–Poincaré_series
German-American mathematician (1878–1952)
student of David Hilbert, and in his habilitation in 1900 Dehn resolved Hilbert's third problem, making him the first to resolve one of Hilbert's 23 problems
Max_Dehn
German-American mathematician (1888–1972)
the University of Zürich and the University of Göttingen. He became David Hilbert's assistant in Göttingen and obtained his doctorate there in 1910. He
Richard_Courant
Problem in Lie group theory
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization
Hilbert's_fifth_problem
Equation in differential geometry
mathematical physics (e.g., in models of 2D gravity) and was cited by David Hilbert in his formulation of the nineteenth problem, concerning the smoothness
Liouville's_equation
Limitative results in mathematical logic
philosophy of mathematics. The theorems are interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
algebraic structure as a field. It was introduced by German mathematician David Hilbert. In a hyperbolic plane, one can define an ideal point or end to be an
Hilbert's_arithmetic_of_ends
Fundamental mechanical principles
by Einstein's work on general relativity, the renowned mathematician David Hilbert applied the principle of least action to derive the field equations
Action_principles
On dissections between polyhedra
yield the second? Based on earlier writings by Carl Friedrich Gauss, David Hilbert conjectured that this was not always possible. His student Max Dehn
Hilbert's_third_problem
On topology of algebraic curves and surfaces
Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list
Hilbert's_sixteenth_problem
Consistency of the axioms of arithmetic
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent
Hilbert's_second_problem
Basic framework of mathematics
that formalists, such as David Hilbert (1862–1943), hold that mathematics is only a language and a series of games. Hilbert insisted that formalism, called
Foundations_of_mathematics
Hungarian mathematician
study at the University of Göttingen. His doctorate was supervised by David Hilbert. The Haar measure, Haar wavelet, and Haar transform are named in his
Alfréd_Haar
German mathematician (1896–1962)
honorary professor at the University of Münster. In 1928, Ackermann helped David Hilbert turn his 1917 – 22 lectures on introductory mathematical logic into
Wilhelm_Ackermann
In commutative algebra the Hilbert–Samuel function, named after David Hilbert and Pierre Samuel, of a nonzero finitely generated module M {\displaystyle
Hilbert–Samuel_function
On transcendence of certain numbers
Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence
Hilbert's_seventh_problem
Name list
politician Carl Aage Hilbert (1899–1953), Danish Prefect of the Faroe Islands David Hilbert (1862–1943), German mathematician Donna Hilbert (born 1946), American
Hilbert_(name)
Geometry without using coordinates
system for geometry was given only at the end of the 19th century by David Hilbert. At the same time, it appeared that both synthetic methods and analytic
Synthetic_geometry
Positive integer of the form 4n + 1
a Hilbert number is a positive integer of the form 4n + 1 (Flannery & Flannery (2000, p. 35)). The Hilbert numbers were named after David Hilbert. The
Hilbert_number
Branch of applied mathematics
infinite-dimensional vector space. That is called Hilbert space (introduced by mathematicians David Hilbert (1862–1943), Erhard Schmidt (1876–1959) and Frigyes
Mathematical_physics
German mathematician (1852–1939)
Lindemann acted as supervisor for the doctoral theses of the mathematicians David Hilbert, Hermann Minkowski, and Arnold Sommerfeld. In 1882, Lindemann published
Ferdinand_von_Lindemann
Fundamental space of geometry
given on the groups of translations and isometries. On the other hand, David Hilbert proposed a set of axioms, inspired by Euclid's postulates. They belong
Euclidean_space
French novelist and poet (1903–1976)
Les fondements de la littérature d'après David Hilbert (1976), alludes to the mathematician David Hilbert, and attempts to explore the foundations of
Raymond_Queneau
American mathematician (1878–1955)
Columbia. He spent 1899-1900 in Göttingen studying under Felix Klein and David Hilbert. Kasner was appointed tutor in Mathematics in the Columbia University
Edward_Kasner
Seven mathematical problems with a US$1 million prize for each solution
inspired by a set of twenty-three problems organized by the mathematician David Hilbert in 1900 which were highly influential in driving the progress of mathematics
Millennium_Prize_Problems
Self-intersecting compact surface, an immersion of the real projective plane
mathematician Werner Boy, who had been tasked by his doctoral thesis advisor David Hilbert to prove that the projective plane could not be immersed in three-dimensional
Boy's_surface
Hungarian-American physicist and mathematician (1902–1995)
Weissenberg and Richard Becker at the Kaiser Wilhelm Institute in Berlin, and David Hilbert at the University of Göttingen. Wigner and Hermann Weyl were responsible
Eugene_Wigner
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