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Equivalence between strongly orientable graphs and bridgeless graphs
In graph theory, Robbins' theorem, named after Herbert Robbins (1939), states that the graphs that have strong orientations are exactly the 2-edge-connected
Robbins'_theorem
American mathematician
The Robbins' theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The
Herbert_Robbins
Statement in probability theory
In the mathematical theory of probability, the Hsu–Robbins–Erdős theorem states that if X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} is a sequence
Hsu–Robbins–Erdős_theorem
been applied to the design of one-way road networks. According to Robbins' theorem, the graphs with strong orientations are exactly the bridgeless graphs
Strong_orientation
enumeration theorem (combinatorics) Ramsey's theorem (graph theory, combinatorics) Ringel–Youngs theorem (graph theory) Robbins' theorem (graph theory)
List_of_theorems
Partition of a graph whose components are reachable from all vertices
path sharing its two endpoints with previous subgraphs. According to Robbins' theorem, an undirected graph may be oriented in such a way that it becomes
Strongly_connected_component
Concept in graph theory
the maximum flow amount per edge, again using Robbins' theorem on totally cyclic orientations, see Theorem 2 of Kochol, Martin (2002), "Polynomials associated
Nowhere-zero_flow
Assigning directions to the edges of an undirected graph
only if it is a strong orientation of every connected component of G. Robbins' theorem states that a graph has a strong orientation if and only if it is 2-edge-connected;
Orientation_(graph_theory)
Edge whose deletion would disconnect a graph
decomposition, that each connected component is 2-edge-connected, or (by Robbins' theorem) that every connected component has a strong orientation. An important
Bridge_(graph_theory)
some other axiomatization of a Boolean algebra, as theorems of a Robbins algebra. Huntington, Robbins, Alfred Tarski, and others worked on the problem,
Robbins_algebra
Graph which remains connected when fewer than k edges are removed
or by Robbins' theorem according to which these are exactly the graphs that have a strong orientation. By a corollary of the Nash-Williams theorem, the
Edge_connectivity
Partition of graph into sequence of paths
of the given graph. Robbins introduced the ear decomposition of 2-edge-connected graphs as a tool for proving the Robbins' theorem, that these are exactly
Ear_decomposition
Fundamental theorem in probability theory and statistics
example, the following theorem is Corollary 4 of Robbins (1948). It assumes that N {\displaystyle N} is asymptotically normal (Robbins also developed other
Central_limit_theorem
Subfield of automated reasoning and mathematical logic
interesting and hard theorems, including at least one that has eluded human mathematicians for a long time, namely the Robbins conjecture. However, these
Automated_theorem_proving
1941 book
four-color map theorem and Fermat's last theorem, written by Ian Stewart. The book was based on Courant's course material. Although Robbins assisted in writing
What_Is_Mathematics?
In statistics, the Chapman–Robbins bound or Hammersley–Chapman–Robbins bound is a lower bound on the variance of estimators of a deterministic parameter
Chapman–Robbins_bound
Theorem in topology
In topology, a discipline within mathematics, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a
Jordan_curve_theorem
Mathematical problem of making a structure rigid
connectivity augmentation, and can be solved in linear time. According to Robbins' theorem, the undirected graphs that can be made strongly connected by directing
Grid_bracing
Study of rational collective decision-making
impossibility theorem is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social
Social_choice_theory
Erdős–Dushnik–Miller theorem Erdős–Fuchs theorem Erdős–Gallai theorem Erdős–Ginzburg–Ziv theorem Erdős–Kac theorem Erdős–Kaplansky theorem Erdős–Ko–Rado theorem Erdős–Nagy
List of things named after Paul Erdős
List_of_things_named_after_Paul_Erdős
Complete, full information, perfectly competitive markets are Pareto efficient
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information
Fundamental theorems of welfare economics
Fundamental_theorems_of_welfare_economics
Family of iterative methods
a_{1},a_{2},\dots } is a sequence of positive step sizes. Robbins and Monro proved, Theorem 2 that θ n {\displaystyle \theta _{n}} converges in L 2 {\displaystyle
Stochastic_approximation
Mathematical proof at least partially generated by computer
of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program.
Computer-assisted_proof
Mathematical model
Robbins, David P., and Rumsey, Howard Jr., Proof of the Macdonald conjecture, Inventiones Mathematicae, 66 (1982), 73–87. Mills, William H., Robbins,
Alternating_sign_matrix
Israeli mathematician
which was independently stated in 1983 by George Andrews and David P. Robbins. Zeilberger is an ultrafinitist. He is also known for crediting his computer
Doron_Zeilberger
Theorem in electrical engineering
In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a power source with internal resistance
Maximum power transfer theorem
Maximum_power_transfer_theorem
Chinese mathematician
limiting distribution of series of random variables (as in the Hsu–Robbins–Erdős theorem for which he is partially named). Another example of Hsu' work in
Pao-Lu_Hsu
In statistics, the Robbins lemma, named after Herbert Robbins, states that if X is a random variable having a Poisson distribution with parameter λ, and
Robbins_lemma
British-Lebanese mathematician (1929–2019)
3-space. Several papers were inspired by a question of Jonathan Robbins (called the Berry–Robbins problem), who asked if there is a map from the configuration
Michael_Atiyah
2023 film by Christopher Nolan
Urbaniak as Kurt Gödel, an Austrian logician and mathematician known for his theorems that revolutionized mathematics and had far-reaching implications for philosophy
Oppenheimer_(film)
Universality of construction using just a straightedge and a single circle with center
In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states
Poncelet–Steiner_theorem
Algebraic structure modeling logical operations
(4) a Robbins algebra, the question then becomes: Is every Robbins algebra a Boolean algebra? This question (which came to be known as the Robbins conjecture)
Boolean_algebra_(structure)
Branch of pure mathematics
Robbins 2006, p. 1 harvnb error: no target: CITEREFRobbins2006 (help) Duverney 2010, p. v harvnb error: no target: CITEREFDuverney2010 (help) Robbins
Number_theory
Type of construction
send the midpoint elsewhere. This is in contrast to the Mohr–Mascheroni theorem, which states that every straightedge and compass construction can be made
Straightedge-only construction
Straightedge-only_construction
Lower bound for bandit problem
The Lai–Robbins lower bound gives an asymptotic lower bound on the regret that any uniformly good algorithm must incur in the stochastic multi-armed bandit
Lai–Robbins_lower_bound
Splitting a triangle by perpendicular lines
This subdivision of a triangle is a special case of a theorem of Richard Courant and Herbert Robbins that any plane area can be subdivided into four equal
Bernoulli quadrisection problem
Bernoulli_quadrisection_problem
Two to the power of the square root of two
Theodor Schneider independently proved the more general Gelfond–Schneider theorem, which solved the part of Hilbert's seventh problem described below. The
Gelfond–Schneider_constant
Popular mathematics book from 1940
problem and the binomial theorem. Chapter VIII ("Rubber-sheet Geometry") concerns concepts in topology, such as the Jordan curve theorem, the Euler characteristics
Mathematics and the Imagination
Mathematics_and_the_Imagination
Theorem that curves of bounded curvature contain a unit disk
The Pestov–Ionin theorem in the differential geometry of plane curves states that every simple closed curve of curvature at most one encloses a unit disk
Pestov–Ionin_theorem
Approximation for factorials
Poisson distribution converges to a normal distribution by the Central Limit Theorem. Since the Poisson distribution with parameter μ {\displaystyle \mu } converges
Stirling's_approximation
Field of knowledge
and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems
Mathematics
Austrian, German, and American actor (born 1956)
named Dr. King Schultz. Waltz also starred in Carnage (2011), The Zero Theorem (2013), Big Eyes (2014), Downsizing (2017), Alita: Battle Angel (2019)
Christoph_Waltz
Points on a common circle
known as a Robbins pentagon. In all known cases, its diagonals also have rational lengths, though whether this is true for all possible Robbins pentagons
Concyclic_points
Triangle area in terms of side lengths
incenter and one excircle of the triangle, or as a special case of De Gua's theorem (for the particular case of acute triangles), or as a special case of Brahmagupta's
Heron's_formula
Smallest example which falsifies a claim
criminal, especially (but not exclusively) in the context of the four-color theorem. A proof by minimal counterexample (or by minimal/smallest/least criminal)
Minimal_counterexample
Modularity theorem (Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, 2001) Erdős–Stewart conjecture (Florian Luca, 2001) Berry–Robbins problem
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
1997 film by Gus Van Sant
physics discoveries are often made by a group, while solving a mathematical theorem can be an individual endeavour. Kleitman and mathematician Tom Bohman gave
Good_Will_Hunting
American statistician (1914–1991)
limit theorem for dependent random variables (with Herbert Robbins), 1948 "Optimum" nonparametric tests, 1951 A combinatorial central limit theorem, 1951
Wassily_Hoeffding
Triangle with at least two sides congruent
{b^{2}}{4}}}}.} This formula can also be derived from the Pythagorean theorem using the fact that the altitude bisects the base and partitions the isosceles
Isosceles_triangle
Quadrilateral whose vertices lie on a circle
this quadrilateral. Butterfly theorem Brahmagupta triangle Cyclic polygon Power of a point Ptolemy's table of chords Robbins pentagon Usiskin, Zalman; Griffin
Cyclic_quadrilateral
American mathematician and computer scientist (1903–1995)
("decision problem"), the Frege–Church ontology, and the Church–Rosser theorem. Alongside his doctoral student Alan Turing, Church is considered one of
Alonzo_Church
British physicist and popular science author (born 1964)
theoretical and particle physicist. His written works include Fermat's Last Theorem (in the United States titled Fermat's Enigma: The Epic Quest to Solve the
Simon_Singh
Strong form of uniform continuity
Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial
Lipschitz_continuity
Resource problem in machine learning
adaptive allocation rules", Lai and Robbins (following papers of Robbins and his co-workers going back to Robbins in the year 1952) constructed convergent
Multi-armed_bandit
Optimization algorithm
surely to a local minimum. This is in fact a consequence of the Robbins–Siegmund theorem. Suppose we want to fit a straight line y ^ = w 1 + w 2 x {\displaystyle
Stochastic_gradient_descent
Number constructible via compass and straightedge
Courant & Robbins (1996), pp. 120–122, Section III.1.1: Construction of fields and square root extraction. Martin (1998), pp. 38–39; Courant & Robbins (1996)
Constructible_number
In mathematics, with negligible exceptions
almost all elements of X, even if it isn't an ultrafilter. The prime number theorem shows that the number of primes less than or equal to n is asymptotically
Almost_all
1979 studio album by the Mekons
approach". The album's name and cover are an allusion to the infinite monkey theorem, that states that a monkey hitting random keys on a typewriter will eventually
The Quality of Mercy Is Not Strnen
The_Quality_of_Mercy_Is_Not_Strnen
Formula relating the area of a cyclic quadrilateral to its side lengths
quadrilateral. In a cyclic quadrilateral, pq = ac + bd according to Ptolemy's theorem, and the formula of Coolidge reduces to Brahmagupta's formula. Heron's
Brahmagupta's_formula
English actor (born 1963)
Norman Short film 2013 RED 2 The Frog The Fifth Estate Nick Davies The Zero Theorem Joby 2014 The Theory of Everything Dennis Sciama Stonehearst Asylum Mickey
David_Thewlis
Unique positive real number which when multiplied by itself gives 2
square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. The fraction
Square_root_of_2
line segment length of a unit cube is also known as Robbins constant, named after David P. Robbins. This constant has a closed form, Δ ( 3 ) = 4 + 17 2
Mean_line_segment_length
Bayesian statistical inference method
summarised by the hyperparameters η {\displaystyle \eta \;} . Using Bayes' theorem, p ( θ ∣ y ) = p ( y ∣ θ ) p ( θ ) p ( y ) = p ( y ∣ θ ) p ( y ) ∫ p (
Empirical_Bayes_method
American mathematician
of each mathematical research paper in the language of an interactive theorem prover. The goal of this project is to benefit from the increased precision
Thomas_Callister_Hales
Function that ranks states of society according to their desirability
how much better one choice is compared to another. Arrow's impossibility theorem is a key result of social welfare functions, showing an important difference
Social_welfare_function
Psychometric measurement scale
rating data is discussed at length in two papers by Robbins and Heiberger. In the first paper, Robbins and Heiberger recommend the use of what they call
Likert_scale
Enigma machine. Fermat's Last Theorem (1997) – A documentary on the mathematician Andrew Wiles proving the eponymous theorem, directed by Simon Singh. Girls
List of films about mathematicians
List_of_films_about_mathematicians
Greco-Roman astronomer and geographer (c. 100–170)
terms and its reception". (Jones, 2010). p. 68. Robbins, Frank E. (1940). "Introduction". In Robbins, F.E. (ed.). Ptolemy Tetrabiblos. J. F. Weidler (1741)
Ptolemy
Shape with five sides
sides and rational area; these are called Robbins pentagons. It has been proved that the diagonals of a Robbins pentagon must be either all rational or
Pentagon
Lower bound on variance of an estimator
2 {\displaystyle n+2} . Chapman–Robbins bound Kullback's inequality Brascamp–Lieb inequality Lehmann–Scheffé theorem Ziv–Zakai bound Cramér, Harald (1946)
Cramér–Rao_bound
Study of economics facts and values
by the 1950s some economists even asserted that Arrow's impossibility theorem proved any attempts to construct normative standards in economics were
Positive and normative economics
Positive_and_normative_economics
Arithmetic operation
Theory (generalizing the recursive base-representation used in Goodstein's theorem to use higher operations), has gained dominance. It was also popularized
Tetration
American actor (born 1969)
The Joe Rogan Experience, where he attempted to debunk the Pythagorean theorem, claimed he can kill gravity, said he does not believe in the number zero
Terrence_Howard
Discrete probability distribution
{Pois} \left(\sum _{i=1}^{n}\lambda _{i}\right).} A converse is Raikov's theorem, which says that if the sum of two independent random variables is Poisson-distributed
Poisson_distribution
American computer scientist and logician
automated reasoning systems, and the automated proof of the Robbins conjecture using the EQP theorem prover. In 2000, McCune received the Herbrand Award for
William_McCune
Totality of psychological phenomena
Reason Deutsch 2013, p. 354 Schweizer 1993, p. 848 Robbins 2017, § 1. What Is a Mental Module? Robbins 2017, Lead Section, § 1. What Is a Mental Module
Mind
Triangle with circular arc edges
shrinks towards the Fermat point of the given three points. Circle packing theorem, for which the gaps between circles are often circular triangles Hart circle
Circular_triangle
Equations of motion for viscous fluids
body force. This result follows from the Helmholtz theorem (also known as the fundamental theorem of vector calculus). The first equation is a pressureless
Navier–Stokes_equations
2018 film by J. A. Bayona
earlier films, is no longer inhabited. The website was designed by Chaos Theorem, a creative digital storytelling company founded by Jack Anthony Ewins
Jurassic World: Fallen Kingdom
Jurassic_World:_Fallen_Kingdom
2010–2018) Henry O. Pollak, 98, Austrian-born mathematician (Graham–Pollak theorem, Gilbert–Pollak conjecture) Phil Regan, 89, baseball player (Los Angeles
2026 deaths in the United States
2026_deaths_in_the_United_States
Number
Kaplan 2000, p. 68–75. Roy, Rahul (January 2003). "Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of
0
Mathematical problem involving optimal stopping theory
be:2013/182735. Bruss, F. Thomas (October 2003). "A note on bounds for the odds theorem of optimal stopping". The Annals of Probability. 31 (4): 1859–1961. doi:10
Secretary_problem
Number, approximately 1.618
golden ratio with the Pythagorean theorem. Kepler said of these: Geometry has two great treasures: one is the theorem of Pythagoras, the other the division
Golden_ratio
Size of a two-dimensional surface
and b is the number of boundary points. This result is known as Pick's theorem. The area between a positive-valued curve and the horizontal axis, measured
Area
Central limit theorem Central limit theorem (illustration) – redirects to Illustration of the central limit theorem Central limit theorem for directional
List_of_statistics_articles
Plane figure bounded by line segments
equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior
Polygon
British author and scholar (1832–1898)
in linear algebra (e.g., the first printed proof of the Rouché–Capelli theorem), probability, and the study of elections (e.g., Dodgson's method) and
Lewis_Carroll
Social science studying goods and services
Robbins: "Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses". Robbins'
Economics
"lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures
List_of_lemmas
Sum of an (infinite) geometric progression
convergence of 1. This could be seen as a consequence of the Cauchy–Hadamard theorem and the fact that lim n → ∞ a n = 1 {\displaystyle \lim _{n\rightarrow
Geometric_series
Predator at the top of a food chain
Archived (PDF) from the original on 12 July 2010. Retrieved 25 January 2010. Robbins, Jim (May–June 1998). "Weaving a new web: wolves change an ecosystem".
Apex_predator
American theoretical physicist (1918–1988)
to have it published. Its main result is known as the Hellmann–Feynman theorem. In 1939, Feynman received a bachelor's degree and was named a Putnam Fellow
Richard_Feynman
American mathematician
carrying a pad under his arm. It is entirely possible that he proved a theorem or two during the ceremony." Publication list from Winkler's home page
Peter_Winkler
American mathematician
this work, she began research on a generalization of Pascal's theorem. Pascal's theorem concerns six points on a conic curve, and her work considered
Sophia_Foster_Richardson
2015 American television series
Schuchman, Matthew (September 19, 2014). "Terry Gilliam Talks The Zero Theorem, Television, And Radiohead". Den of Geek. Retrieved July 2, 2018. Sloma
12_Monkeys_(TV_series)
Model of humans as rational, self-interested agents
assumptions. In the 20th century, the rational choice theory of Lionel Robbins came to dominate mainstream economics. The term "economic man" then took
Homo_economicus
Mathematical assumptions
eventually proved in 1996 with the aid of theorem-proving software. This proof established that the Robbins axiom, together with associativity and commutativity
Minimal axioms for Boolean algebra
Minimal_axioms_for_Boolean_algebra
German-American mathematician (1888–1972)
general public for the book What is Mathematics?, co-written with Herbert Robbins. His research focused on the areas of real analysis, mathematical physics
Richard_Courant
Chaotic model of atmospheric convection
on the Lyapunov dimension Lorenz 96 model List of chaotic maps Takens' theorem Lorenz (1963) Lorenz (1960) Sparrow (1982) Haken (1975) Knobloch (1981)
Lorenz_system
Brothers Grimm (2005), The Imaginarium of Doctor Parnassus (2009), The Zero Theorem (2013) John Gilling Sid James Escape by Night (1953), Interpol (1957),
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
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