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of George D. Birkhoff (crater) Birkhoff interpolation Birkhoff's axioms Birkhoff's theorem (disambiguation), multiple theorems Birkhoff decomposition
Birkhoff
American mathematician (1884–1944)
George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician. He is considered one of the top American mathematicians of his
George_David_Birkhoff
American mathematician (1911–1996)
Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician. He is best known for his work in lattice theory and universal algebra
Garrett_Birkhoff
Polytope
The Birkhoff polytope B n {\displaystyle B_{n}} is the convex polytope in R n 2 {\displaystyle \mathbb {R} ^{n^{2}}} whose points are the doubly stochastic
Birkhoff_polytope
Topics referred to by the same term
Birkhoff decomposition refers to two different mathematical concepts: The Birkhoff factorization, introduced by George David Birkhoff at 1909, is the
Birkhoff_decomposition
Topics referred to by the same term
(relativity) Birkhoff's theorem (electromagnetism) Birkhoff's ergodic theorem It may also refer to theorems named for his son, Garrett Birkhoff: Birkhoff–von Neumann
Birkhoff's_theorem
Branch of mathematics that studies dynamical systems
to the space average. Two of the most important theorems are those of Birkhoff (1931) and von Neumann which assert the existence of a time average along
Ergodic_theory
Theoretical framework for planar Euclidean geometry
In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry in the plane, sometimes referred to as Birkhoff's axioms. These postulates
Birkhoff's_axioms
Tool for working with matrices
Birkhoff's algorithm (also called Birkhoff-von-Neumann algorithm) is an algorithm for decomposing a bistochastic matrix into a convex combination of permutation
Birkhoff_algorithm
Type of square matrix
n\times n} doubly stochastic matrices is a convex polytope known as the Birkhoff polytope B n {\displaystyle B_{n}} . Using the matrix entries as Cartesian
Doubly_stochastic_matrix
Explicitly describes the universal enveloping algebra of a Lie algebra
mathematics, more specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description
Poincaré–Birkhoff–Witt theorem
Poincaré–Birkhoff–Witt_theorem
Theorem in symplectic topology
symplectic topology and dynamical systems, Poincaré–Birkhoff theorem (also known as Poincaré–Birkhoff fixed point theorem and Poincaré's last geometric
Poincaré–Birkhoff_theorem
Statement of spherically symmetric spacetimes
In general relativity, Birkhoff–Jebsen's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically
Birkhoff's theorem (relativity)
Birkhoff's_theorem_(relativity)
Conjecture in abstract algebra about piecewise polynomial functions
In abstract algebra, the Pierce–Birkhoff conjecture asserts that any piecewise-polynomial function can be expressed as a maximum of finite minima of finite
Pierce–Birkhoff_conjecture
Classifies holomorphic vector bundles over the complex projective line
In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic
Birkhoff–Grothendieck_theorem
Matrix decomposition in mathematics
In mathematics, Birkhoff factorization or Birkhoff decomposition, introduced by George David Birkhoff (1909), is a generalization of the LU decomposition
Birkhoff_factorization
Award in applied mathematics
was known as the AMS–SIAM George David Birkhoff Prize in Applied Mathematics, in honor of George David Birkhoff. It is currently awarded every three years
Cathleen_Synge_Morawetz_Prize
Lyndsy Fonseca as Alexandra "Alex" Udinov, Aaron Stanford as Seymour Birkhoff, Ashton Holmes as Thom, Tiffany Hines as Jaden, Devon Sawa as Owen Elliot
List_of_Nikita_characters
Historic house in Massachusetts, United States
The George D. Birkhoff House is a historic house, at 22 Craigie Street, Cambridge, Massachusetts. It was designated a National Historic Landmark in 1975
George_D._Birkhoff_House
Class of algebraic structures
algebras, as do the abelian groups, the rings, the monoids etc. According to Birkhoff's theorem, a class of algebraic structures of the same signature is a variety
Variety_(universal_algebra)
In mathematics, Birkhoff interpolation is an extension of polynomial interpolation. It refers to the problem of finding a polynomial P ( x ) {\displaystyle
Birkhoff_interpolation
American actor (born 1976)
remake of The Hills Have Eyes (2006). On television, he also starred as Birkhoff in Nikita (2010–2013) and as James Cole in 12 Monkeys (2015–2018), based
Aaron_Stanford
Group that is a topological space with continuous group operations
{\displaystyle r>0} , are pre-compact. The Birkhoff–Kakutani theorem (named after mathematicians Garrett Birkhoff and Shizuo Kakutani) states that the following
Topological_group
American mathematician (1878–1932)
Theory. In 1922 with George David Birkhoff he generalized the Brouwer fixed point theorem to the theorem of Birkhoff–Kellogg. Among his doctoral students
Oliver_Dimon_Kellogg
Equivalence of distributive lattices and set families
theory. For other similarly named results, see Birkhoff's theorem (disambiguation). In mathematics, Birkhoff's representation theorem for distributive lattices
Birkhoff's representation theorem
Birkhoff's_representation_theorem
Concept in mathematics
construction of the enveloping algebra. Indeed, it follows from the Poincaré–Birkhoff–Witt theorem (discussed § below) that the elements 1 , e , e 2 , e 3 ,
Universal_enveloping_algebra
Algebraic structure
is the only proper partial operation effect algebras There is a "Meta Birkhoff Theorem" by Andreka, Nemeti and Sain (1982). Operations and partial operations
Partial_algebra
Crater on the Moon
Birkhoff is a giant lunar walled plain that is located on the far side of the Moon, in the northern hemisphere. This class of formation is known as a peak
Birkhoff_(crater)
In physics, in the context of electromagnetism, Birkhoff's theorem concerns spherically symmetric static solutions of Maxwell's field equations of electromagnetism
Birkhoff's theorem (electromagnetism)
Birkhoff's_theorem_(electromagnetism)
Theorem in equational logic
In logic, Birkhoff's theorem in equational logic states that an equality t = u is a semantic consequence of a set of equalities E, if and only if t = u
Birkhoff's theorem (equational logic)
Birkhoff's_theorem_(equational_logic)
Norwegian physicist (1888–1922)
he became known after his early death for what many now call the Jebsen-Birkhoff theorem for the metric tensor outside a general, spherical mass distribution
Jørg_Tofte_Jebsen
Hungarian and American mathematician and physicist (1903–1957)
paper by von Neumann and Garrett Birkhoff, the first to introduce quantum logics, wherein von Neumann and Birkhoff first proved that quantum mechanics
John_von_Neumann
Banach space with a compatible structure of a lattice
StackOverflow. Schaefer & Wolff 1999, pp. 234–242. Birkhoff 1948, p. 251. Birkhoff 1948, pp. 250, 254. Birkhoff 1948, pp. 269–271. Abramovich, Yuri A.; Aliprantis
Banach_lattice
Number in {..., –2, –1, 0, 1, 2, ...}
of N is denoted by Z; its elements are called the rational integers.] Birkhoff, Garrett (1948). Lattice Theory (Revised ed.). American Mathematical Society
Integer
American mathematician
conferred the Bachelor of Science degree from Haverford. According to Garrett Birkhoff, Whitman was an undergraduate Harvard student in 1937, and an outstanding
Philip_M._Whitman
Basis for Euclidean geometry
axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff. Hilbert's axiom system is constructed with six primitive notions: three
Hilbert's_axioms
Branch of mathematics
60 Rowen 2006, p. 12 Pratt 2022, § 3.3 Birkhoff's Theorem Grätzer 2008, p. 34 Pratt 2022, § 3.3 Birkhoff's Theorem Rowen 2006, p. 12 Gowers, Barrow-Green
Algebra
2010 American action thriller drama television series
Michael manage to expose or kill most of Oversight, with the help of Seymour Birkhoff, a former Division head technician, who left the organization after Percy
Nikita_(TV_series)
bornological A bornological space. Birkhoff orthogonality Two vectors x and y in a normed linear space are said to be Birkhoff orthogonal if ‖ x + λ y ‖ ≥ ‖
Glossary of functional analysis
Glossary_of_functional_analysis
American mathematician
Marquette University in 1959. Formally under the guidance of Professor Garrett Birkhoff, Rockafellar completed his Doctor of Philosophy degree in mathematics from
R._Tyrrell_Rockafellar
of the things (and topics) listed below. Birkhoff–von Neumann algorithm Birkhoff–von Neumann theorem Birkhoff–von Neumann decomposition Dirac–von Neumann
List of things named after John von Neumann
List_of_things_named_after_John_von_Neumann
Set whose pairs have minima and maxima
p. 52. Birkhoff 1948, p. 18. "since a = a ∨ ( a ∧ ( a ∨ a ) ) = a ∨ a {\displaystyle a=a\vee (a\wedge (a\vee a))=a\vee a} and dually". Birkhoff attributes
Lattice_(order)
Mathematical model of the physical space
and to make clear the ramifications of the parallel postulate. Birkhoff's axioms: Birkhoff proposed four postulates for Euclidean geometry that can be confirmed
Euclidean_geometry
Study of geometries as axiomatic systems
century. In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoff's axioms. These postulates
Foundations_of_geometry
Ring with a compatible partial order
{\displaystyle |x\cdot y|\leq |x|\cdot |y|} holds. An f-ring, or Pierce–Birkhoff ring, is a lattice-ordered ring ( A , ≤ ) {\displaystyle (A,\leq )} in
Partially_ordered_ring
Season of television series
Bishop Lyndsy Fonseca as Alexandra "Alex" Udinov Aaron Stanford as Seymour Birkhoff Noah Bean as Ryan Fletcher Dillon Casey as Sean Pierce Devon Sawa as Owen
Nikita_season_3
Israeli mathematician
Schock Prize for Mathematics. In 2024 he was awarded the George David Birkhoff Prize. Birth Place Ronald Coifman at the Mathematics Genealogy Project
Ronald_Coifman
American mathematician
received his PhD in 1971 from Harvard University under supervision of Garrett Birkhoff and worked from 1970 to 1972 at the Fluid Mechanics Research Institute
Jerry_L._Bona
In functional analysis, the Birkhoff–Kellogg invariant-direction theorem, named after G. D. Birkhoff and O. D. Kellogg, is a generalization of the Brouwer
Birkhoff–Kellogg invariant-direction theorem
Birkhoff–Kellogg_invariant-direction_theorem
Season of television series
Udinov Melinda Clarke as Helen "Amanda" Collins Aaron Stanford as Seymour Birkhoff/Lionel Peller Noah Bean as Ryan Fletcher Devon Sawa as Owen Elliot/Sam
Nikita_season_4
Mathematical function defined piecewise by polynomials
at Citroën, Pierre Bézier at Renault, and Birkhoff, Garabedian, and de Boor at General Motors (see Birkhoff and de Boor, 1965), all for work occurring
Spline_(mathematics)
Square of numbers with equal row, column and diagonal totals
Thus, such matrices constitute a subset of doubly stochastic matrix. The Birkhoff–von Neumann theorem states that for any doubly stochastic matrix A {\displaystyle
Magic_square
Function in algebraic graph theory
function of the number of colors and was originally defined by George David Birkhoff to study the four color problem. It was generalised to the Tutte polynomial
Chromatic_polynomial
Season of television series
Bishop Lyndsy Fonseca as Alexandra "Alex" Udinov Aaron Stanford as Seymour Birkhoff Ashton Holmes as Thom Tiffany Hines as Jaden Melinda Clarke as Helen "Amanda"
Nikita_season_1
German-American mathematician (1910–1994)
nonlinear waves. He received many awards during his career including the Birkhoff Prize in Applied Mathematics in 1973 and the Steele Prize in 1982. On 5
Fritz_John
Visual depiction of a partially ordered set
diagrams are named after Helmut Hasse (1898–1979); according to Garrett Birkhoff, they are so called because of the effective use Hasse made of them. However
Hasse_diagram
Sequence acceleration method in numerical analysis
algorithm for solving ordinary differential equations. In the words of Birkhoff and Rota, "its usefulness for practical computations can hardly be overestimated
Richardson_extrapolation
Canadian mathematician and writer (1926–2022)
Toronto Thesis Lattices and Modal Operators (1950) Doctoral advisor Garrett Birkhoff Doctoral students John Benedetto Mehdi Radjabalipour [fa] Man-Duen Choi [de]
Chandler_Davis
American mathematician
University Harvard University Known for Finite Element Method Phase-field model Scientific career Fields Mathematics Doctoral advisor Garrett Birkhoff
George_Fix
Awarded every year by the American Mathematical Society
a bequest of Leroy P. Steele and were set up in honor of George David Birkhoff, William Fogg Osgood and William Caspar Graustein. The way the prizes are
Leroy_P._Steele_Prize
Theory of logic to account for observations from quantum theory
The formal system takes as its starting point an observation of Garrett Birkhoff and John von Neumann, that the structure of experimental tests in classical
Quantum_logic
semimodular if it satisfies the following condition due to Garrett Birkhoff: Birkhoff's condition If a ∧ b <: a and a ∧ b <: b, then a <: a ∨ b
Semimodular_lattice
American mathematician (born 1941)
Mathematics Workplaces Pardee RAND Graduate School RAND Corporation Thesis Mathematical Models of Economic Growth (1969) Doctoral advisor Garrett Birkhoff
Emmett_Keeler
Season of television series
Bishop Lyndsy Fonseca as Alexandra "Alex" Udinov Aaron Stanford as Seymour Birkhoff Dillon Casey as Sean Pierce Melinda Clarke as Helen "Amanda" Collins Xander
Nikita_season_2
Method of deriving an ontology
mathematical theory of lattices and ordered sets that was developed by Garrett Birkhoff and others in the 1930s. Formal concept analysis finds practical application
Formal_concept_analysis
American mathematician (1892–1977)
of a Surface of Negative Curvature, under the direction of George David Birkhoff. Morse was married on June 20, 1922 to Celeste Phelps and they had two
Marston_Morse
American mathematician
and a Ph.D in 1950, working under the supervision of Professor Garrett Birkhoff. Young began his academic career at the University of Maryland, College
David_M._Young_Jr.
American mathematician (1927 to 1992)
Research Fellow. There he became acquainted with Garrett Birkhoff. Together they made the Pierce-Birkhoff conjecture, which concerned a minimax approximation
Richard_S._Pierce
Matrix with exactly one 1 per row and column
stochastic matrices is called the Birkhoff polytope, and the permutation matrices play a special role in that polytope. The Birkhoff–von Neumann theorem says that
Permutation_matrix
First article on transfinite set theory
the bibliography of Birkhoff and Mac Lane's book and in the bibliography of Spivak's book. (Hardy & Wright 1938, p. 400; Birkhoff & Mac Lane 1941, p. 441;
Cantor's first set theory article
Cantor's_first_set_theory_article
Mathematical concept for comparing objects
of Analytical Geometry of Sig. Bellavitis, link from HathiTrust Garrett Birkhoff and Saunders Mac Lane, 1999 (1967). Algebra, 3rd ed. p. 35, Th. 19. Chelsea
Equivalence_relation
Hungarian mathematician
Gyula Kőnig, Rudolf Ortvay [hu], on chairs: József Kürschák, George David Birkhoff, O.D. Kellog, Leopold Fejér, sitting on the floor: Tibor Radó, István Lipka [hu]
Alfréd_Haar
Scottish mathematician
with the all-male Harvard College. There she studied under George David Birkhoff. Her thesis was titled 'Expansion Theorems for Solution of a Fredholm's
Eleanor_Pairman
Ice hockey tournament group stage
David Kickert Referees: Christoffer Holm Lukas Kohlmüller Linesmen: Brian Birkhoff Njaal Søstumoen 0–1 02:50 – Nissner (Zwerger, Wolf) 0–2 06:00 – Schneider
2026 IIHF World Championship Group A
2026_IIHF_World_Championship_Group_A
Exercise in general relativity
spherically symmetric and static. The static assumption is unneeded, as Birkhoff's theorem states that any spherically symmetric vacuum solution of Einstein's
Derivation of the Schwarzschild solution
Derivation_of_the_Schwarzschild_solution
Paradox by d'Alembert on fluid dynamics
331–337. Garrett Birkhoff, Hydrodynamics: a study in logic, fact, and similitude, Princeton University Press, 1950 Birkhoff (1950) p. 4. Birkhoff (1950) p. 21
D'Alembert's_paradox
Irish actor (born 1959)
Heffernan 2018 Black '47 Brown 2020 Adventures of a Mathematician G. D. Birkhoff The World We Knew Carpenter 2022 York Witches' Society Matthias 2023 Unwelcome
Finbar_Lynch
Order whose elements are all comparable
a < a {\displaystyle a<a} by asymmetry. References Halmos 1968, Ch.14. Birkhoff 1967, p. 2. Schmidt & Ströhlein 1993, p. 32. Fuchs 1963, p. 2. Davey &
Total_order
2026 edition of the Men's Ice Hockey World Championship
Holm Cedric Borga Michael Tscherrig Nolan Bloyer Sean MacFarlane Brian Birkhoff Mitchell Gibbs Jiří Ondráček Lukáš Rampir Onni Hautamäki Tommi Niittylä
2026_IIHF_World_Championship
American mathematician
theorem Harnack's inequality Awards ICM Speaker (1970, 1983) George David Birkhoff Prize (1973) Scientific career Fields Mathematician Workplaces University
James_Serrin
Geologic period, 4533 to 3920 million years ago
Lorentz 360 6 Amundsen-Ganswindt 355 7 Schiller-Zucchius 325 Planck 325 Birkhoff 330 Freundlich-Sharonov 600 8 Grimaldi 430 9 Apollo 505 For basins with
Pre-Nectarian
Equations of motion for viscous fluids
to Navier Stokes Equation and Oceanography, Springer ISBN 3-540-35743-2 Birkhoff, Garrett (1960), Hydrodynamics, Princeton University Press Campos, D. (editor)
Navier–Stokes_equations
In mathematics, a concept that formalizes a certain idea of movement and mixing
system. The notion of wandering sets in phase space was introduced by Birkhoff in 1927.[citation needed] A common, discrete-time definition of wandering
Wandering_set
number theory Bryan John Birch and John Tate 149 Birkhoff conjecture integrable systems George David Birkhoff 345 Bloch–Beilinson conjectures number theory
List_of_conjectures
necessarily being the whole direct product. The notion was introduced by Birkhoff in 1944, generalizing Emmy Noether's special case of the idea (and decomposition
Subdirect_product
American mathematician
American mathematician. His Ph.D. advisor at Harvard was George David Birkhoff. Brink entered Kansas State College at age 14 and by age 19 had two bachelor's
Raymond_Woodard_Brink
United States historic place
Buckman Tavern Christ Church Converse Memorial Library Elmwood George D. Birkhoff House Gore Place Gropius House Hancock–Clarke House Lexington Battle Green
Thomas_Crane_Public_Library
Mathematical concept
Numbers, W. W. Norton & Company, p. 128, ISBN 9780393040029 Mac Lane and Birkhoff (1999) define "linear", "quadratic", "cubic", "quartic", and "quintic"
Degree_of_a_polynomial
American mathematician (1942–2017)
Academy of Sciences in 1978 (for pure mathematics) and the George David Birkhoff Prize in applied mathematics in 2003. He also received the Brazilian Order
John_N._Mather
United States historic place
Buckman Tavern Christ Church Converse Memorial Library Elmwood George D. Birkhoff House Gore Place Gropius House Hancock–Clarke House Lexington Battle Green
Peabody_Museum_of_Salem
American mathematician (1919–2000)
works of Leonhard Euler. Bingham Medal of the Society of Rheology, 1963; Birkhoff Prize of the American Mathematical Society and Society for Industrial and
Clifford_Truesdell
Ice hockey results
Magnus Hellberg Referees: Riku Brander Mikko Kaukokari Linesmen: Brian Birkhoff Mitchell Gibbs 0–1 06:21 – Karlsson (Heineman, Ekman-Larsson) Josi (Malgin)
2026 IIHF World Championship playoff round
2026_IIHF_World_Championship_playoff_round
Hungarian mathematician
Dénes Kőnig, Rudolf Ortvay [hu], on chairs: József Kürschák, George David Birkhoff, O.D. Kellog, Lipót Fejér, sitting on the floor: Tibor Radó, István Lipka [hu]
József_Kürschák
princely state of Gondal, doctor, writer Bhagavadgomandal George David Birkhoff United States 21 March 1884 12 November 1944 Mathematician, discoverer
2015_in_public_domain
American physician, geologist and paleontologist
Thorndike (1934) Karl Taylor Compton (1935) Edwin Conklin (1936) George David Birkhoff (1937) Wesley Clair Mitchell (1938) Walter Bradford Cannon (1939) Albert
John_Strong_Newberry
Distance from zero to a number
Resource". Bartle (2011), p. 163. Curnier (1999), p. 31–32. Mac Lane & Birkhoff (1999), p. 264. Shechter (1997), p. 260. Shechter (1997), pp. 260–261.
Absolute_value
Special type of lattice
citing Birkhoff, G. "Subdirect unions in universal algebra", Bulletin of the American Mathematical Society SO (1944), 764-768. See Birkhoff's representation
Distributive_lattice
Soviet mathematician (1899–1981)
as it is called now, is based on the previous work by Poincaré, David Birkhoff, and Marston Morse. It has led to numerous advances in differential geometry
Lazar_Lyusternik
Bound lattice in which every element has a complement
axiomisation of the Hilbert space formulation of quantum mechanics. Garrett Birkhoff and John von Neumann observed that the propositional calculus in quantum
Complemented_lattice
American mathematician (1879–1967)
was done under the guidance of the noted American mathematician G. David Birkhoff, and it is considered to be the first significant American contribution
Robert_Daniel_Carmichael
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