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Surname list
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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)
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
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
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
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)
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)
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)
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)
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
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
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)
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
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
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
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
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
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
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
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
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
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.
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 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
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
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
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
bundles, is now often called the Birkhoff–Grothendieck theorem, since it is implicit in much earlier work of Birkhoff (1909) on the Riemann–Hilbert problem
Vector bundles on algebraic curves
Vector_bundles_on_algebraic_curves
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
Mathematical subject
polytopes are also considered, such as the permutohedron, associahedron and Birkhoff polytope. Topological combinatorics What is geometric combinatorics?, Ezra
Geometric_combinatorics
Ice hockey tournament group stage
Goalies Josef Kořenář Referees: Taylor Burzminski Jesse Gour Linesmen: Brian Birkhoff Anders Nyqvist 0–1 08:09 – Voženílek (Cibulka, Kempný) Hrivík (Kňažko,
2026 IIHF World Championship Group B
2026_IIHF_World_Championship_Group_B
Township in Michigan, United States
of Overijssel. Overisel is the birthplace of mathematician George David Birkhoff, best known for what is now called the ergodic theorem. Bentheim is a Dutch
Overisel_Township,_Michigan
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
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
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
Integer multiples of any irrational mod 1 are uniformly distributed on the circle
every sufficiently large odd number is the sum of three primes. George Birkhoff, in 1931, and Aleksandr Khinchin, in 1933, proved that the generalization
Equidistribution_theorem
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
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
American mathematician (1907–1989)
Coloring of Graphs, written under the supervision of George David Birkhoff. At Harvard, Birkhoff also got him a job as instructor of Mathematics for the years
Hassler_Whitney
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
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
rendering of reality. The replacement derives from the work of Garrett Birkhoff and John von Neumann on quantum logic. In their work, they showed that
Is_Logic_Empirical?
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
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
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
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
Branch of mathematical statistics
Birkhoff metrized the positive cone using Hilbert's projective metric and proved Jentsch's theorem using the contraction mapping theorem. Birkhoff's results
Algebraic_statistics
Group with a compatible partial order
topological space Glass (1999) Birkhoff (1942) M. Anderson and T. Feil, Lattice Ordered Groups: an Introduction, D. Reidel, 1988. Birkhoff, Garrett (1942). "Lattice-Ordered
Partially_ordered_group
American mathematician (1923–2017)
in 1948. His Ph.D. thesis was written under the supervision of Garrett Birkhoff. His academic appointments had been at Syracuse University from 1949 to
George_Mostow
Decomposition of an algebraic structure
composition series, but not transfinite descending composition series (Birkhoff 1934). Baumslag (2006) gives a short proof of the Jordan–Hölder theorem
Composition_series
German-American historian of mathematics (1933–2017)
history of science; it was jointly supervised by mathematician Garrett Birkhoff and historian of science I. Bernard Cohen. Merzbach joined the Smithsonian
Uta_Merzbach
American mathematician (born 1941)
Mathematics Institutions Pardee RAND Graduate School RAND Corporation Thesis Mathematical Models of Economic Growth (1969) Doctoral advisor Garrett Birkhoff
Emmett_Keeler
American mathematician (born 1952)
Differential Equations" and was written under the supervision of Garrett Birkhoff. He worked as a L.E. Dickson Instructor in Mathematics at University of
Peter_J._Olver
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
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
dissection was introduced by George (1973); the name was suggested by Garrett Birkhoff. Nested dissection consists of the following steps: Form an undirected
Nested_dissection
American mathematician (1895–1973)
Institutions Harvard University Doctoral advisor Maxime Bôcher George David Birkhoff Doctoral students Joseph Leo Doob Orin J. Farrell Maurice Heins Donald
Joseph_L._Walsh
American mathematician
a thesis on differential equations that was supervised by George David Birkhoff. Between 1925 and 1937, he taught at Harvard, Yale University, and Columbia
Marshall_H._Stone
American mathematician
theorem Harnack's inequality Awards ICM Speaker (1970, 1983) George David Birkhoff Prize (1973) Scientific career Fields Mathematician Institutions University
James_Serrin
Combinitorics of Polyhedra
the Birkhoff polytope lies, and the non-negativity constraints define facets of the Birkhoff polytope within that subspace. However, the Birkhoff polytope
Polyhedral_combinatorics
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
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
one of several ergodic theorems. It can be seen as a generalization of Birkhoff's ergodic theorem. Intuitively, the subadditive ergodic theorem is a kind
Kingman's subadditive ergodic theorem
Kingman's_subadditive_ergodic_theorem
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
Print by M. C. Escher
Patterns in Saracenic Art G. H. Hardy A Mathematician's Apology George David Birkhoff Aesthetic Measure Douglas Hofstadter Gödel, Escher, Bach Nikos Salingaros
Relativity_(M._C._Escher)
American mathematician
his PhD from Harvard University in 1927, under the direction of George Birkhoff. Boas, R. P. Jr.; Buck, R. C. (1956), "Polynomials defined by generating
Isador_M._Sheffer
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
Ice hockey game
Goalies Justus Annunen Referees: Tobias Björk André Schrader Linesmen: Brian Birkhoff Anders Nyqvist 0–1 70:42 – Helenius (Lundell, Lehtonen) 10 min Penalties
2026 IIHF World Championship final
2026_IIHF_World_Championship_final
Theory of algebraic structures in general
which encompass the isomorphism theorems of groups, rings, modules, etc. Birkhoff's HSP Theorem, which states that a class of algebras is a variety if and
Universal_algebra
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
Branch of logic
The model theory of this logic was developed into universal algebra by Birkhoff, Grätzer, and Cohn. It was later made into a branch of category theory
Equational_logic
Phenomenon in fluid dynamics
bandwidth and the vortex shedding is described by broad-band spectral content. Birkhoff, Garrett (2015). Hydrodynamics: A study in logic, fact, and similitude
Drag_crisis
Italian mathematician
Henrici (1978) Kurt O. Friedrichs (1979) Keith Stewartson (1980) Garrett Birkhoff (1981) David Slepian (1982) Joseph B. Keller (1983) Jürgen Moser (1984)
Franco_Brezzi
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
BIRKHOFF
BIRKHOFF
BIRKHOFF
BIRKHOFF
Girl/Female
American, British, English, Scottish
Crooked Nose; Bent Nose; Clan
Boy/Male
Arabic, German, Muslim
Servant of the Living
Girl/Female
Indian, Tamil
Goddess Amman
Boy/Male
Hindu
Blessings
Girl/Female
Indian, Modern
The Most Lovable
Girl/Female
Indian, Telugu
Good
Girl/Female
Tamil
Beautiful (Celebrity Name: Sanjay Kapoor)
Boy/Male
English
Boar-friend
Girl/Female
Indian
Sagacious
Boy/Male
Arabic, Muslim
Moon Light
BIRKHOFF
BIRKHOFF
BIRKHOFF
BIRKHOFF
BIRKHOFF