David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

(1862–1943), a mathematician, is the eponym of all of the things (and topics) listed below.

Mathematics and physics

Brouwer–Hilbert controversy In a controversy over the foundations of mathematics, in twentieth-century mathematics, L. E. J. Brouwer, a proponent of the constructivist school of intuitionism, opposed David Hilbert, a proponent of formalism. The debate concerned fundamental ...

Einstein–Hilbert action The Einstein–Hilbert action (also referred to as Hilbert action) in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the metric signature, the gravitational part of the act ...

* Einstein–Hilbert equations * Hilbert algebra * Hilbert C*-module *

Hilbert basis (linear programming) The Hilbert basis of a convex cone ''C'' is a minimal set of integer vectors such that every integer vector in ''C'' is a conical combination of the vectors in the Hilbert basis with integer coefficients. Definition Given a lattice L\subset\mat ...

Hilbert class field In algebraic number theory, the Hilbert class field ''E'' of a number field ''K'' is the maximal abelian unramified extension of ''K''. Its degree over ''K'' equals the class number of ''K'' and the Galois group of ''E'' over ''K'' is canonicall ...

Hilbert cube In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore, many interesting topological spaces can be embedded in the Hilbert cube; that is, c ...

Hilbert curve The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous 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 Giuseppe ...

Hilbert curve scheduling In parallel processing, the Hilbert curve scheduling method turns a multidimensional task allocation problem into a one-dimensional space filling problem using Hilbert curves, assigning related tasks to locations with higher levels of proximity.''S ...

* Hilbert field *

Hilbert function In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homoge ...

Hilbert manifold In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold ...

Hilbert matrix In linear algebra, a Hilbert matrix, introduced by , is a square matrix with entries being the unit fractions : H_ = \frac. For example, this is the 5 × 5 Hilbert matrix: : H = \begin 1 & \frac & \frac & \frac & \frac \\ \frac & \frac & \f ...

Hilbert metric In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the ''n''-dimensional Euclidean space R''n''. It was introduced by as a generalization of Ca ...

Hilbert modular form In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function on the ''m''-fold product of upper half-planes \mathcal satisfying a certain kind of functional e ...

Hilbert modular variety In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular variet ...

Hilbert–Mumford criterion In mathematics, the Hilbert–Mumford criterion, introduced by David Hilbert and David Mumford, characterizes the semistable and stable points of a group action on a vector space in terms of eigenvalues of 1-parameter subgroups . Definition of s ...

Hilbert number In number theory, a branch of mathematics, a Hilbert number is a positive integer of the form (). The Hilbert numbers were named after David Hilbert. The sequence of Hilbert numbers begins 1, 5, 9, 13, 17, ... ) Properties *The Hilbert number ...

* Hilbert plane *

Hilbert polynomial In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homoge ...

Hilbert series In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homoge ...

Hilbert ring In algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals. For commutative rings primitive ideals are the same as maximal ideals so in this case a Jacobson ring is one in which ever ...

Hilbert–Samuel function In commutative algebra the Hilbert–Samuel function, named after David Hilbert and Pierre Samuel,H. Hironaka, Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I. Ann. of Math. 2nd Ser., Vol. 79, No. 1. (Jan., ...

Hilbert projection theorem In mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector x in a Hilbert space H and every nonempty closed convex C \subseteq H, there exists a unique vector m \in C for which \, c - x\, ...

Hilbert R-tree Hilbert R-tree, an R-tree variant, is an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric objects. It can be thought of as an extension to B+-tree for multidimensional objects. Th ...

* Hilbert reciprocity *

Hilbert scheme In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a d ...

Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...

** Hilbert dimension **

Projective Hilbert space In mathematics and the foundations of quantum mechanics, the projective Hilbert space P(H) of a complex Hilbert space H is the set of equivalence classes of non-zero vectors v in H, for the relation \sim on H given by :w \sim v if and only if v = \ ...

Reproducing kernel Hilbert space In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions f and g in ...

Rigged Hilbert space In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis. Such spaces were introduced to study s ...

** Semi-Hilbert space *

Hilbert spectrum The Hilbert spectrum (sometimes referred to as the Hilbert amplitude spectrum), named after David Hilbert, is a statistical tool that can help in distinguishing among a mixture of moving signals. The spectrum itself is decomposed into its compo ...

Hilbert symbol In mathematics, the Hilbert symbol or norm-residue symbol is a function (–, –) from ''K''× × ''K''× to the group of ''n''th roots of unity in a local field ''K'' such as the fields of reals or p-adic numbers . It is related to reciprocity l ...

Hilbert system :''In mathematical physics, ''Hilbert system'' is an infrequently used term for a physical system described by a C*-algebra.'' In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive ...

Hilbert transform In mathematics and in signal processing, the Hilbert transform is a specific linear operator that takes a function, of a real variable and produces another function of a real variable . This linear operator is given by convolution with the functi ...

Hilbert spectroscopy Hilbert Spectroscopy uses Hilbert transforms to analyze broad spectrum signals from gigahertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz ...

Hilbert–Huang transform The Hilbert–Huang transform (HHT) is a way to decompose a Signal processing, signal into so-called intrinsic mode functions (IMF) along with a trend, and obtain instantaneous frequency data. It is designed to work well for data that is Station ...

** Hilbert spectral analysis *

Hilbert-style deduction system :''In mathematical physics, ''Hilbert system'' is an infrequently used term for a physical system described by a C*-algebra.'' In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive s ...

Hilbert–Bernays paradox The Hilbert–Bernays paradox is a distinctive paradox belonging to the family of the paradoxes of reference (like Berry's paradox). It is named after David Hilbert and Paul Bernays. History The paradox appears in Hilbert and Bernays' ''Grundlag ...

Hilbert–Bernays provability conditions In mathematical logic, the Hilbert–Bernays provability conditions, named after David Hilbert and Paul Bernays, are a set of requirements for formalized provability predicates in formal theories of arithmetic (Smith 2007:224). These conditions are ...

Hilbert–Burch theorem In mathematics, the Hilbert–Burch theorem describes the structure of some free resolutions of a quotient of a local or graded ring in the case that the quotient has projective dimension 2. proved a version of this theorem for polynomial ...

* Hilbert–Kunz function *

Hilbert–Poincaré series In mathematics, and in particular 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 of the notion of dimension to the context of grade ...

Hilbert–Pólya conjecture In mathematics, the Hilbert–Pólya conjecture states that the non-trivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint operator. It is a possible approach to the Riemann hypothesis, by means of spectral theor ...

Hilbert–Schmidt inner product In mathematics, Hilbert–Schmidt may refer to * a Hilbert–Schmidt operator; ** a Hilbert–Schmidt integral operator In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform. Specifically, given a domain (an open an ...

** Hilbert–Schmidt norm **

Hilbert–Schmidt operator In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator A \colon H \to H that acts on a Hilbert space H and has finite Hilbert–Schmidt norm \, A\, ^2_ \ \stackrel\ \sum_ \, Ae_i\, ^2_ ...

Hilbert–Schmidt integral operator In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform. Specifically, given a domain (an open and connected set) Ω in ''n''-dimensional Euclidean space R''n'', a Hilbert–Schmidt kernel is a function ''k'' ...

Hilbert–Schmidt theorem In mathematical analysis, the Hilbert–Schmidt theorem, also known as the eigenfunction expansion theorem, is a fundamental result concerning compact, self-adjoint operators on Hilbert spaces. In the theory of partial differential equations, it is ...

* Hilbert–Serre theorem *

Hilbert–Smith conjecture In mathematics, the Hilbert–Smith conjecture is concerned with the transformation groups of manifolds; and in particular with the limitations on topological groups ''G'' that can act effectively (faithfully) on a (topological) manifold ''M''. Re ...

Hilbert–Speiser theorem In mathematics, the Hilbert–Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of , which by the Kronecker–Weber theorem are isomorph ...

* Hilbert–Waring theorem *

Hilbert's arithmetic of ends In mathematics, specifically in the area of hyperbolic geometry, Hilbert's arithmetic of ends is a method for endowing a geometric set, the set of ideal points or "ends" of a hyperbolic plane, with an algebraic structure as a field. It was introduc ...

Hilbert's axioms 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 the foundation for a modern treatment of Euclidean geometry. Other well-known modern ...

* Hilbert's basis theorem * Hilbert's epsilon calculus * Hilbert's inequality *

Hilbert's irreducibility theorem In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite number of variables and having rational number coefficients admit a common specialization o ...

* Hilbert's lemma *

Hilbert's Nullstellensatz In mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros," or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental relationship between geometry and algebra. This relationship is the basis of algebraic ge ...

Hilbert's paradox of the Grand Hotel Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely m ...

Hilbert's problems 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 proved to be very influential for 20th-century mathematics. Hilbert presented ten of the pro ...

Hilbert's program In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathema ...

Hilbert's syzygy theorem In mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in 1890, which were introduced for solving important open questions in invariant theory, and are at ...

Hilbert's theorem (differential geometry) In differential geometry, Hilbert's theorem (1901) states that there exists no complete regular surface S of constant negative gaussian curvature K immersed in \mathbb^. This theorem answers the question for the negative case of which surfaces in ...

Hilbert's Theorem 90 In abstract algebra, Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if ''L''/''K'' is an extension of fi ...

Riemann–Hilbert correspondence In mathematics, the term Riemann–Hilbert correspondence refers to the correspondence between regular singular flat connections on algebraic vector bundles and representations of the fundamental group, and more generally to one of several generaliz ...

Riemann–Hilbert problem In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential equations in the complex plane. Several existence theorems for Riemann–Hilbert problems h ...

Other

* David Hilbert Award * Hilbert (crater) {{DEFAULTSORT:List of things named after David Hilber Hilbert, David