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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
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
23 mathematical problems stated in 1900
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. He intended to rival the master of French mathematics
Hilbert's_problems
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
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
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
System of formal deduction in logic
a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann
Hilbert_system
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
Topic in mathematical analysis
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
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
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
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
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
German philosopher (1891–1953)
known as the "Berlin Circle". Carl Gustav Hempel, Richard von Mises, David Hilbert and Kurt Grelling all became members of the Berlin Circle. In 1930,
Hans_Reichenbach
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
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
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
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
American mathematician (1878–1932)
Integralgleichungen und des Dirichlet'schen Prinzips under the direction of David Hilbert. After completing his thesis, Kellogg became an instructor at Princeton
Oliver_Dimon_Kellogg
Austrian mathematician and theoretical physicist (1844–1906)
function f. The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success. The form of
Ludwig_Boltzmann
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
Conjecture in topology
of the conjecture is for David Hilbert, and Paul A. Smith. It is considered by some to be a better formulation of Hilbert's fifth problem, than the characterisation
Hilbert–Smith_conjecture
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
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
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
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
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
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
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
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
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
Mathematician (1845–1918)
Sylvester Medal, the highest honor it can confer for work in mathematics. David Hilbert defended Cantor's work from its critics by declaring, "No one shall
Georg_Cantor
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
1660 textbook
a counter-argument to a psychologistic view of language and logic. David Hilbert and Rudolph Carnap further developed Husserl's model, leading to the
Port-Royal_Grammar
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
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
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
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
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
Karl Herberstein Maximilian Herzberger Edmund Hess Karl Hessenberg David Hilbert Friedrich Hirzebruch Eberhard Hopf Heinz Hopf Wolfgang Johannes Höppner
List_of_German_mathematicians
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
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
Swiss mathematician (1885–1970)
science. Speiser studied in Göttingen, starting in 1904, notably with David Hilbert, Felix Klein, Hermann Minkowski. In 1917 he became full-time professor
Andreas_Speiser
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
Graphical symbol or pictogram used to point or indicate direction
mathematical notation developed in the first half of the 20th century. David Hilbert in 1922 introduced the arrow symbol representing logical implication
Arrow_(symbol)
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
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
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
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)
Polish mathematician (1887–1972)
Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the
Hugo_Steinhaus
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
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
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
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
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
1924–1936 group of philosophers and scientists
logical positivism or neopositivism. It was influenced by Ernst Mach, David Hilbert, French conventionalism (Henri Poincaré and Pierre Duhem), Gottlob Frege
Vienna_Circle
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
Excess growth of certain parts of the body
singer. Jacob Grommer (1879–1933), Belarusian mathematician. Student of David Hilbert and assistant to Albert Einstein. A number of notable historical figures
Acromegaly
On solutions of 7th-degree equations
Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether
Hilbert's_thirteenth_problem
Mathematical ring with well-behaved ideals
recognized earlier by David Hilbert, with the proof of Hilbert's basis theorem (which asserts that polynomial rings are Noetherian) and Hilbert's syzygy theorem
Noetherian_ring
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
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
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
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
Field of knowledge
list of 23 open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list has achieved great celebrity
Mathematics
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DAVID HILBERT
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