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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
Geometry without the parallel postulate
now known to be an insufficient basis for Euclidean geometry, so other systems (such as Hilbert's axioms without the parallel axiom) are used instead
Absolute_geometry
Geometry without using coordinates
characterizing geometry. The first complete axiom system for geometry was given only at the end of the 19th century by David Hilbert. At the same time
Synthetic_geometry
German mathematician (1862–1943)
David Hilbert Foundations of geometry Hilbert C*-module Hilbert cube Hilbert curve Hilbert matrix Hilbert metric Hilbert–Mumford criterion Hilbert number
David_Hilbert
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
Type of vector space in math
mathematical concept of a Hilbert space generalizes the notion of Euclidean space. It extends the methods of Euclidean geometry and calculus from the two-dimensional
Hilbert_space
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
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
Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor
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
Hilbert_scheme
Thought experiment of infinite sets
Hilbert's paradox of the Grand Hotel (colloquially the Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive
Hilbert's paradox of the Grand Hotel
Hilbert's_paradox_of_the_Grand_Hotel
Study of geometries as axiomatic systems
mathematician David Hilbert (1862–1943) presented a course of lectures on the foundations of geometry. At the request of Felix Klein, Professor Hilbert was asked
Foundations_of_geometry
On topology of algebraic curves and surfaces
problem is what usually is meant when talking about Hilbert's sixteenth problem in real algebraic geometry. The second problem also remains unsolved: no upper
Hilbert's_sixteenth_problem
Mathematics of varieties with integer coordinates
Mordell's Diophantine Equations (1969). The Hilbert–Hurwitz result from 1890 reducing the Diophantine geometry of curves of genus 0 to degrees 1 and 2 (conic
Diophantine_geometry
Distance function
introduced by David Hilbert (1895) as a generalization of Cayley's formula for the distance in the Cayley–Klein model of hyperbolic geometry, where the convex
Hilbert_metric
Geometry where the axiom of Archimedes is negated
"accumulate". Robin Hartshorne, Geometry: Euclid and beyond (2000), p. 158. Hilbert, David (1902), The foundations of geometry (PDF), The Open Court Publishing
Non-Archimedean_geometry
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
Branch of mathematics
notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through Hilbert's Nullstellensatz, with a maximal ideal
Algebraic_geometry
Tool in mathematical dimension theory
of a graded vector space. The Hilbert polynomial and Hilbert series are important in computational algebraic geometry, as they are the easiest known
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
Points and lines with equal incidences
American Mathematical Society, ISBN 978-0-8218-4308-6. Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination (2nd ed.), Chelsea, pp. 94–170
Configuration_(geometry)
On dissections between polyhedra
the area of two-dimensional polygons, in connection with Hilbert's axioms for Euclidean geometry. He later formulated a 20th-century influential set of
Hilbert's_third_problem
Mathematical model of the physical space
Euclidean geometry is a model. Absolute geometry Analytic geometry Birkhoff's axioms Cartesian coordinate system Hilbert's axioms Incidence geometry List of
Euclidean_geometry
Branch of mathematics
to infinite dimension (Hilbert spaces, for example) and positive real numbers (in fractal geometry). In algebraic geometry, the dimension of an algebraic
Geometry
Euclidean geometry without distance and angles
of affine geometry over the field of real numbers. The first non-Desarguesian plane was noted by David Hilbert in his Foundations of Geometry. The Moulton
Affine_geometry
On Schubert's enumerative calculus
enumerative geometry. Justifying this calculus was the content of Hilbert's 15th problem, and was also the major topic of the 20 century algebraic geometry. In
Hilbert's_fifteenth_problem
Branch of mathematics
Noncommutative geometry (NCG) is a branch of mathematics that studies geometric ideas through noncommutative algebras. In ordinary geometry, a space can
Noncommutative_geometry
1932 book by David Hilbert and Stefan Cohn-Vossen
Geometry and the Imagination is the English translation of the 1932 book Anschauliche Geometrie by David Hilbert and Stefan Cohn-Vossen. The book was based
Geometry_and_the_Imagination
No complete regular surface of constant negative gaussian curvature immerses in R3
In differential geometry, Hilbert's theorem (1901) states that there exists no complete regular surface S {\displaystyle S} of constant negative gaussian
Hilbert's theorem (differential geometry)
Hilbert's_theorem_(differential_geometry)
Type of geometry
projective geometry. Many alternative sets of axioms for projective geometry have been proposed (see, for example, Coxeter 2003, Hilbert & Cohn-Vossen
Projective_geometry
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
Overview of and topical guide to geometry
Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive
Outline_of_geometry
Topics referred to by the same term
Hilbert's theorem may refer to: Hilbert's theorem (differential geometry), stating there exists no complete regular surface of constant negative gaussian
Hilbert's_theorem
Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Differential_geometry
Mathematical set with some added structure
of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space"
Space_(mathematics)
Set of mathematical concepts in quantum gravity
In quantum gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable
Quantum_geometry
Statement in plane geometry
Teubner Hilbert, David (1950) [1902], The Foundations of Geometry (PDF), translated by Townsend, E. J., LaSalle, IL: Open Court Publishing Hilbert, David
Pasch's_axiom
Fundamental object of geometry
point-free geometry Ohmer (1969), p. 34–37. Heath (1956), p. 153. Silverman (1969), p. 7. de Laguna (1922). Heath (1956), p. 154. "Hilbert's axioms", Wikipedia
Point_(geometry)
Branch of algebraic geometry
arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around
Arithmetic_geometry
Straight figure with zero width and depth
and geometry is established analytically in terms of numerical coordinates. In an axiomatic formulation of Euclidean geometry, such as that of Hilbert (modern
Line_(geometry)
Algebraic surface in mathematics
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
Hilbert_modular_variety
Type of metric geometry
axis-aligned reflections. Taxicab geometry satisfies all of Hilbert's axioms (a formalization of Euclidean geometry) except that the congruence of angles
Taxicab_geometry
Type of non-Euclidean geometry
mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Property of a mathematical space
highly irregular sets and attain non-integer positive real values. Every Hilbert space admits an orthonormal basis, and any two such bases for a particular
Dimension
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
Expression of polynomials as sum of squares
Hilbert's seventeenth problem is one of the 23 of Hilbert's problems set out in a celebrated list compiled in 1900 by David Hilbert. It concerns the expression
Hilbert's_seventeenth_problem
Infinitely detailed mathematical structure
in the Menger sponge, the shape is called affine self-similar. Fractal geometry relates to the mathematical branch of measure theory by their Hausdorff
Fractal
Branch of differential geometry and differential topology
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds
Symplectic_geometry
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
Mathematical treatise by Euclid
Mathematics. Courier Corporation. ISBN 9780486152325. Hilbert, David (1902). Foundations of Geometry (PDF). Translated by Townsend, E. J. Open Court. Hoppen
Euclid's_Elements
Part of a straight line that is bounded by two distinct end points
Analysis, pages 2 & 3, Marcel Dekker ISBN 0-8247-6671-7 David Hilbert The Foundations of Geometry. The Open Court Publishing Company 1950, p. 4 Wikimedia Commons
Line_segment
Mathematical conjecture about the Riemann zeta function
noncommutative geometry of Adele classes. A possible connection of Hilbert–Pólya operator with quantum mechanics was given by Pólya. The Hilbert–Pólya conjecture
Hilbert–Pólya_conjecture
Foundational controversy in twentieth-century mathematics
board of Mathematische Annalen. The controversy started with Hilbert's axiomatization of geometry in the late 1890s. In his biography of Kurt Gödel, John W
Brouwer–Hilbert_controversy
Manifold modelled on Hilbert spaces
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
Hilbert_manifold
Einstein–Hilbert equations Hilbert algebra Hilbert C*-module Hilbert basis (linear programming) Hilbert class field Hilbert cube Hilbert curve Hilbert curve
List of things named after David Hilbert
List_of_things_named_after_David_Hilbert
Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension of an algebraic variety Hilbert's Nullstellensatz Complete variety Elimination theory
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Study of geometry using a coordinate system
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts
Analytic_geometry
German mathematician (1826–1866)
made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous
Bernhard_Riemann
Mathematics book
Göttsche, Lothar (2005), "Local properties and Hilbert schemes of points", Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Providence,
Fondements de la Géometrie Algébrique
Fondements_de_la_Géometrie_Algébrique
Criteria of simplicity for mathematical proofs
Hilbert's twenty-fourth problem is a mathematical problem that was not published as part of the list of 23 problems (known as Hilbert's problems) but
Hilbert's twenty-fourth problem
Hilbert's_twenty-fourth_problem
Field of mathematics which studies incidence structures
Introduction to Geometry, New York: John Wiley & Sons, p. 233, ISBN 978-0-471-50458-0 Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination
Incidence_geometry
Mathematical term; concerning axioms used to derive theorems
included non-Euclidean geometry, Georg Cantor's abstract set theory, and Hilbert's revisionist axioms for Euclidean geometry. David Hilbert "was the first who
Axiomatic_system
Result in number theory, concerning irreducible polynomials
In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite
Hilbert's irreducibility theorem
Hilbert's_irreducibility_theorem
Historical development of geometry
now known as Hilbert's axioms, were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie (Foundations of Geometry). In the mid-18th
History_of_geometry
Non-Euclidean geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel
Elliptic_geometry
On curvature of surfaces
number. Hilbert's theorem (differential geometry) Gray, Mary (1997), "28.4 Hilbert's Lemma and Liebmann's Theorem", Modern Differential Geometry of Curves
Hilbert's_lemma
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
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
On lattices and sphere packing in Euclidean space
Hilbert's eighteenth problem is one of the 23 problems set out in a celebrated list compiled in 1900 by mathematician David Hilbert. It asks three separate
Hilbert's_eighteenth_problem
Geometry of the surface of a sphere
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of
Spherical_geometry
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 polynomial rings over fields
invariant theory, and are at the basis of modern algebraic geometry. The two other theorems are Hilbert's basis theorem, which asserts that all ideals of polynomial
Hilbert's_syzygy_theorem
Statement that is taken to be true
axioms. An early success of the formalist program was Hilbert's formalization of Euclidean geometry, and the related demonstration of the consistency of
Axiom
Notable events in the history of geometry
the Klein bottle, 1899 – David Hilbert presents a set of self-consistent geometric axioms in Foundations of Geometry 1901 – Élie Cartan develops the
Timeline_of_geometry
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical
Computational_geometry
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
Hilbert's_arithmetic_of_ends
Study of systems of inequalitites
polynomials. (See Hilbert's 17th problem and the Krivine-Stengle Positivstellensatz.) The relation of real algebra to real algebraic geometry is similar to
Real_algebraic_geometry
American mathematician (born 1989)
Vincent Pardon (born June 1989) is an American mathematician who works on geometry and topology. He is primarily known for having solved Gromov's problem
John_Pardon
Index of articles associated with the same name
Dehn (1900) and discussed by Hilbert (1902, pp. 127–130, or pp. 42–43 in some later editions). To construct his geometries, Dehn used a non-Archimedean
Dehn_plane
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Form of geometry without distances
projective geometry). Moritz Pasch first defined a geometry without reference to measurement in 1882. His axioms were improved upon by Peano (1889), Hilbert (1899)
Ordered_geometry
Three dimensional analogue of uniformization conjecture
one of three geometries (Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological
Geometrization_conjecture
"The Geometry of Narrative" is a 1983 science fiction short story by American writer Hilbert Schenck. It was first published in Analog Science Fiction
The_Geometry_of_Narrative
Classical theory of gravitation
the Einstein–Hilbert action over Riemannian geometry by the Palatini action (see also Palatini variation) over Riemann–Cartan geometry; and second, removing
Einstein–Cartan_theory
Study of complex manifolds and several complex variables
geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
Axiom set used in first-order logic
first presented it in 1926. Other modern axiomizations of Euclidean geometry are Hilbert's axioms (1899) and Birkhoff's axioms (1932). Using his axiom system
Tarski's_axioms
Fundamental space of geometry
On the other hand, David Hilbert proposed a set of axioms, inspired by Euclid's postulates. They belong to synthetic geometry, as they do not involve any
Euclidean_space
Concept in general relativity
The Einstein–Hilbert action in general relativity yields the Einstein field equations through the principle of stationary action. With the ( − , + , +
Einstein–Hilbert_action
2008 British TV series or programme
be the first problem listed by Hilbert. Next Marcus discusses Henri Poincaré's work on the discipline of 'Bendy geometry'. If two shapes can be moulded
The_Story_of_Maths
Aspect of theoretical physics
Quantum geometry in condensed matter physics refers to gauge-invariant geometric properties of quantum states as functions of external parameters—most
Quantum geometry (condensed matter)
Quantum_geometry_(condensed_matter)
Set of points equidistant from a center
plane (the radical plane) in the pencil. In their book Geometry and the Imagination, David Hilbert and Stephan Cohn-Vossen describe eleven properties of
Sphere
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
Describes the structure of some free resolutions of a quotient of a local or graded ring
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
Hilbert–Burch_theorem
Local and global geometry of the universe
Euclidean space. David Hilbert (1925) thought the universe was determined finite by elliptical geometry or infinite by Euclidean geometry (i.e. flat). In the
Shape_of_the_universe
Belgian mathematician
and their extensions to Hilbert modular surfaces and p-adic L-functions form an important part of his work in arithmetic geometry. Other important research
Pierre_Deligne
Method of drawing geometric objects
impossibility of some constructions; only much later did Hilbert find a complete set of axioms for geometry. The most-used straightedge-and-compass constructions
Straightedge and compass construction
Straightedge_and_compass_construction
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric
Discrete_geometry
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
American mathematician
Robin (1963). Connectedness of the Hilbert scheme. Robin Hartshorne at the Mathematics Genealogy Project Algebraic Geometry. Springer Science+Business Media
Robin_Hartshorne
Theorem in algebraic geometry
algebraic geometry, given an ample line bundle L on a compact complex manifold X, Matsusaka's big theorem gives an integer m, depending only on the Hilbert polynomial
Matsusaka's_big_theorem
Relationship between two lines that meet at a right angle
In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of
Perpendicular
Polynomial ideals are finitely generated
interpreted in algebraic geometry as follows: every algebraic set is the set of the common zeros of finitely many polynomials. Hilbert's proof is highly non-constructive:
Hilbert's_basis_theorem
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