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German software company
Until 2012, POLYAS operated as a project within the German IT company Micromata GmbH. In 2012, it was spun off as an independent entity, POLYAS GmbH. Following
Polyas
Surname list
Pólya (1876–1944), Hungarian surgeon, elder brother of George Pólya Reichel-Polya Operation, a type of partial gastrectomy developed by Eugen Pólya and
Pólya
Hungarian-American mathematician and educator (1887–1985)
George Pólya (/ˈpoʊljə/; Hungarian: Pólya György [ˈpoːjɒ ˈɟørɟ]; December 13, 1887 – September 7, 1985) was a Hungarian-American mathematician. He was
George_Pólya
Random model in mathematics
theory and statistics, a Pólya urn model (also known as a Pólya urn scheme or simply as Pólya's urn), named after George Pólya, is a family of urn models
Pólya_urn_model
Formula for number of orbits of a group action
The Pólya enumeration theorem, also known as the Redfield–Pólya theorem and Pólya counting, is a theorem in combinatorics that both follows from and ultimately
Pólya_enumeration_theorem
Disproven conjecture in number theory
function and Pólyaʼs conjecture". Journal of Number Theory. 133 (2): 545–582. arXiv:1108.1524. doi:10.1016/j.jnt.2012.08.011. Weisstein, Eric W. "Pólya Conjecture"
Pólya_conjecture
Theorem in complex analysis
Pólya's shire theorem, named after George Pólya, is a theorem in complex analysis that describes the asymptotic distribution of the zeros of successive
Pólya's_shire_theorem
Theorem on quadratic pairing functions
The Fueter–Pólya theorem, first proved by Rudolf Fueter and George Pólya, states that the only quadratic polynomial pairing functions are the Cantor polynomials
Fueter–Pólya_theorem
1945 book on problem solving by George Pólya
How to Solve It is a guide to problem solving by mathematician George Pólya. Originally published by Princeton University Press in 1945, a second edition
How_to_Solve_It
Formula for number of orbits of a group action
than its original discoverer is an example of Stigler's law of eponymy. Pólya enumeration theorem Cycle index Burnside 1897, §119 Rotman 1995, Chapter
Burnside's_lemma
Topics referred to by the same term
Pólya Prize may refer to: George Pólya Prize, awarded by the Society for Industrial and Applied Mathematics (SIAM) Pólya Prize (LMS), awarded by the London
Pólya_Prize
Mathematical conjecture about the Riemann zeta function
In mathematics, the Hilbert–Pólya conjecture states that the non-trivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint
Hilbert–Pólya_conjecture
The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among
Pólya_Prize_(LMS)
Probability distribution
expression in the original definition, we say that X has a negative binomial (or Pólya) distribution if it has a probability mass function: f ( k ; r , p ) ≡ Pr
Negative binomial distribution
Negative_binomial_distribution
Hungarian surgeon (1876–1944)
Jenő Sándor Pólya, German: Eugen Alexander Pólya, Hungarian: Pólya (Pollák) Jenő Sándor (April 30, 1876 – 1944) was a Hungarian surgeon who was a native
Eugen_Pólya
the corollaries of the Remez inequality is the Pólya inequality, which was proved by George Pólya (Pólya 1928), and states that the Lebesgue measure of
Remez_inequality
Surgical removal of the stomach
Reichel–Polya operation, this is a type of posterior gastroenterostomy which is a modification of the Billroth II operation developed by Eugen Pólya and Friedrich
Gastrectomy
Mathematical construct
N ) {\displaystyle \Sigma =O(N)} is the Pólya–Vinogradov inequality, established independently by George Pólya and I. M. Vinogradov in 1918, stating in
Character_sum
Distributions in probability theory
compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability
Dirichlet-multinomial distribution
Dirichlet-multinomial_distribution
Conjecture on zeros of the zeta function
eigenvalues of an operator, so can be thought of as an analogue of the Hilbert–Pólya conjecture for p-adic L-functions. Several mathematicians have addressed
Riemann_hypothesis
In mathematics, the Hermite or Pólya class is a set of entire functions satisfying the requirement that if E(z) is in the class, then: E(z) has no zero
Hermite_class
Concept in mathematical analysis
In mathematical analysis, the Pólya–Szegő inequality (or Szegő inequality) states that the Sobolev energy of a function in a Sobolev space does not increase
Pólya–Szegő_inequality
Number that is the product of factorials
In mathematics, the Jordan–Pólya numbers are the numbers that can be obtained by multiplying together one or more factorials, not required to be distinct
Jordan–Pólya_number
The Laguerre–Pólya class is the class of entire functions consisting of those functions which are locally the limit of a series of polynomials whose roots
Laguerre–Pólya_class
Problem-solving method
problems [... that have been] preserved in the wisdom of proverbs. — George Pólya, How to Solve It Gigerenzer & Gaissmaier (2011) state that sub-sets of strategy
Heuristic
Problem book in mathematical analysis
Lehrsätze aus der Analysis) is a two-volume problem book in analysis by George Pólya and Gábor Szegő. Published in 1925, the two volumes are titled (I) Series
Problems and Theorems in Analysis
Problems_and_Theorems_in_Analysis
theory and statistics, the geometric Poisson distribution (also called the Pólya–Aeppli distribution) is used for describing objects that come in clusters
Geometric Poisson distribution
Geometric_Poisson_distribution
Product of consecutive factorial numbers
first n {\displaystyle n} factorials. They are a special case of the Jordan–Pólya numbers, which are products of arbitrary collections of factorials. The
Superfactorial
prizes named after George Pólya: the George Pólya Prize for Mathematical Exposition, established in 2013; the George Pólya Prize in Applied Combinatorics
George_Pólya_Prize
English actress (born 1956)
London Saved Liz Danny Boyle Royal Court Theatre, London 1985 Philistines Polya —N/a Royal Shakespeare Company, London The Dead Monkey Dolores Roger Michell
Lesley_Manville
Dutch graphic artist (1898–1972)
had no mathematical ability, he interacted with the mathematicians George Pólya, Roger Penrose, and Donald Coxeter, and the crystallographer Friedrich Haag
M._C._Escher
Interplay between observation, experiment, and theory in science
it." —Pólya (1957), p. 114 George Pólya (1954), Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics. George Pólya (1954)
Scientific_method
American mathematician (born 1979)
The team of Marcus, Daniel Spielman and Nikhil Srivastava was awarded the Pólya Prize in 2014 for their resolution of the Kadison–Singer problem and later
Adam_Marcus_(mathematician)
Hungarian mathematician (1880–1959)
half eccentric. — George Pólya, George Pólya, "Some mathematicians I have known", Amer. Math. Monthly 76 (1969), 746–753 Pólya writes the following about
Lipót_Fejér
Classification of a two-dimensional repetitive pattern
out by Evgraf Fedorov in 1891 and then derived independently by George Pólya in 1924. The proof that the list of wallpaper groups is complete came only
Wallpaper_group
British theoretical physicist (born 1941)
Novartis/Daily Telegraph, 2002 Elected to Royal Society of Edinburgh, 2005 Pólya Prize, London Mathematical Society, 2005 Doctor of Science, honoris causa
Michael_Berry_(physicist)
Product of numbers from 1 to n
analogues to Stirling's formula and Wilson's theorem. Jordan–Pólya numbers The Jordan–Pólya numbers are the products of factorials, allowing repetitions
Factorial
Numbers obtained by adding the two previous ones
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Fibonacci_sequence
Paradox arising from an incorrect proof
that makes them incorrect. This example was originally raised by George Pólya in a 1954 book in different terms: "Are any n numbers equal?" or "Any n
All_horses_are_the_same_color
Method of deduction
Sophistic argumentation styles were equated with fallacious arguments. George Polya in his two volume book titled Mathematics and Plausible Reasoning presents
Plausible_reasoning
mathematician George Pólya describing various methods for being a good guesser of new mathematical results. In the Preface to Volume 1 of the book Pólya exhorts all
Mathematics and Plausible Reasoning
Mathematics_and_Plausible_Reasoning
Hungarian and American mathematician and physicist (1903–1957)
car." He had an unusual ability to solve novel problems quickly. George Pólya, whose lectures at ETH Zürich von Neumann attended as a student, said, "Johnny
John_von_Neumann
Federal by-election in Quebec, Canada
LeBlanc-Courchaine 0 0.00 – Independent Lanna Palsson 0 0.00 – Independent Lajos Polya 0 0.00 – Independent Kayll Schaefer 0 0.00 – Independent Justin Steinburg
2026 Terrebonne federal by-election
2026_Terrebonne_federal_by-election
Mathematical statement of uniqueness, except for an equivalent structure
permutation, can be counted using Burnside's lemma or its generalization, Pólya enumeration theorem. Consider the seven Tetris pieces (I, J, L, O, S, T
Up_to
Red-orange chalcedony variety
(Ed. by F. Tallon), Musée du Louvre, Paris, 127–140. Insoll, T., D. A. Polya, K. Bhan, D. Irving, K. Jarvis. 2004. "Towards an understanding of the carnelian
Carnelian
Extension of the domain of an analytic function (mathematics)
substantially generalized by Eugène Fabry (see Fabry's gap theorem) and George Pólya. Let f ( z ) = ∑ k = 0 ∞ α k ( z − z 0 ) k {\displaystyle f(z)=\sum _{k=0}^{\infty
Analytic_continuation
be a particular case of the Pólya Filter (built around the famous combinatorial scheme known as the Pólya Urn). The Pólya Filter is able to adapt the
Disparity filter algorithm of weighted network
Disparity_filter_algorithm_of_weighted_network
original on 15 February 2025. Retrieved 26 March 2025. "Overhang Seat". www.polyas.com. 2021. Archived from the original on 12 December 2024. Retrieved 26
2025 Sri Lankan local elections
2025_Sri_Lankan_local_elections
Russian aristocrat (1887–1967)
which denied entrance to those in school uniforms. His brother's mistress Polya had helped him out by giving him her clothes which were a perfect fit. Dressed
Felix_Yusupov
Swiss mathematician (1894-unknown)
mathematician. The Pólya–Aeppli distribution in probability theory and statistics is named after him and his doctoral advisor George Pólya. Alfred Aeppli
Alfred_Aeppli
The George Pólya Award is presented annually by the Mathematical Association of America (MAA) for articles of expository excellence that have been published
George_Pólya_Award
English mathematician (1937–2020)
American Academy of Arts and Sciences in 1992, was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998) and received
John_Horton_Conway
Local/firm-level equivalent of a trade union
arbeiterkammer.at. Archived from the original on 2018-08-11. Retrieved 2016-11-16. "POLYAS Company". 26 June 2017. "Training and the SE Directive". Worker Participation
Works_council
Formerly proposed currency
ISBN 978-0-670-02493-3. OCLC 1039188461. MarketWatch, Lisa Twaronite, Polya Lesova, &, William L. Watts. "Dollar pares losses after Geithner clarification"
Bancor
Function uniquely mapping two numbers into a single number
that this is the only quadratic pairing function is known as the Fueter–Pólya theorem. Whether this is the only polynomial pairing function is still an
Pairing_function
Area of a right triangle with rational-numbered sides
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Congruent_number
Lény Painchaud 5; Lanna Palsson 4; Guillaume Paradis 37; Lajos Polya 12; Lorant Polya 57; Spencer Rocchi 4; Wallace Richard Rowat 2; Julian Selody 7;
Results of the 2025 Canadian federal election by riding
Results_of_the_2025_Canadian_federal_election_by_riding
Taylor Swift know him best?". The Telegraph. Retrieved 14 December 2024. Polya, Gideon (3 June 2022). "Review: "Aemilia Lanyer As Shakespeare's Co-Author":
Emilia Lanier theory of Shakespeare authorship
Emilia_Lanier_theory_of_Shakespeare_authorship
Arithmetic mean is greater than or equal to geometric mean
inequality and Cauchy–Schwarz inequality in Euclidean space Rn. George Pólya provided a proof similar to what follows. Let f(x) = ex–1 – x for all real x
AM–GM_inequality
Empirical law on the variance of species in a habitat
discrete stochastic models based on the negative binomial, Neyman type A, and Polya–Aeppli distributions that with suitable adjustment of parameters could produce
Taylor's_law
Property of being an even or odd number
Mathematics: A Basic Guide, John Wiley & Sons, p. 181, ISBN 9780471461630. Pólya, George; Tarjan, Robert E.; Woods, Donald R. (2009), Notes on Introductory
Parity_(mathematics)
German mathematician (1875–1941)
his daughter in Bern several times. In Zurich he met often with George Pólya, with whom he was on friendly terms since before the First World War. On
Issai_Schur
Top mathematics undergraduate at Cambridge University
knowledge, G.H. Hardy asked Pólya to sit the examinations himself, unofficially, during his stay in England in 1924–5. Pólya did so, and to Hardy's surprise
Senior_Wrangler
Romanian Swedish mathematician
only real zeros, a problem that goes back to Edmond Laguerre and to George Pólya and Issai Schur. These results were subsequently extended to several variables
Julius_Borcea
Two raised to an integer power
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Power_of_two
or asymptotically. The pioneers in this area of mathematics were George Pólya, Arthur Cayley and J. Howard Redfield. In some graphical enumeration problems
Graph_enumeration
Arithmetic function
Liouville function and Pólyaʼs conjecture". Journal of Number Theory. 133 (2): 545–582. arXiv:1108.1524. doi:10.1016/j.jnt.2012.08.011. Pólya, G. (1919). "Verschiedene
Liouville_function
British applied mathematician and physicist
Recently, his work (with Carl M. Bender and Markus Müller) on the Hilbert–Pólya conjecture received significant attention. While Bellissard gave arguments
Dorje_C._Brody
Process forming a path from many random steps
equivalent of the level-crossing problem discussed above. In 1921 George Pólya proved that the person almost surely would in a 2-dimensional random walk
Random_walk
American mathematician and researcher
can use the strategies set out in George Pólya's work How to Solve It. The strategies were based on Pólya's reflections on how he solved problems. Schoenfeld's
Alan_H._Schoenfeld
1960 article by Eugene Wigner
After coming up with this argument, Hamming found a related discussion in Pólya (1963: 83-85). Hamming's account does not reveal an awareness of the 20th-century
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
California, US-based mathematician
of California, Berkeley. In July 2014, he was named a recipient of the Pólya Prize with Adam Marcus and Daniel Spielman. Nikhil Srivastava was born New
Nikhil_Srivastava
Number divisible only by 1 and itself
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Prime_number
Requirement, and process, of a person's enrollment in order to vote in elections
laws Voter invitation card Voter registration drive "The Electoral Roll". polyas.com. 17 March 2017. Retrieved 12 June 2023. "Same Day Voter Registration"
Voter_registration
Type of composite number with an even number of digits
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Vampire_number
South African mathematician
National Academy of Sciences (elected 2009). He is a co-winner of the 1998 Pólya Prize, and was named a Guggenheim Fellow in 1999. He gave an invited address
Percy_Deift
American organization that focuses on undergraduate-level mathematics
B. Allendoerfer Award, Trevor Evans Award, Lester R. Ford Award, George Pólya Award, Merten M. Hasse Prize, Henry L. Alder Award, Euler Book Prize awards
Mathematical Association of America
Mathematical_Association_of_America
Kutsenok November 10, 1998 Socorro LINEAR · 1.7 km MPC · JPL 29646 Polya 1998 WJ Polya November 16, 1998 Prescott P. G. Comba · 1.3 km MPC · JPL 29647
List of minor planets: 29001–30000
List_of_minor_planets:_29001–30000
Integer that is a perfect square modulo some integer
consecutive values of a mimic a random variable like a coin flip. Specifically, Pólya and Vinogradov proved (independently) in 1918 that for any nonprincipal
Quadratic_residue
British mathematician
problems in percolation." In 2016, he was one of the winners of the George Pólya Prize. In 2018, he was awarded the Fulkerson Prize. Also in 2018, he was
Robert_Morris_(mathematician)
Model in probability theory
pt]&=q(q/p)^{X_{n}}+p(q/p)^{X_{n}}=(q/p)^{X_{n}}=Y_{n}.\end{aligned}}} Pólya's urn contains a number of different-coloured marbles; at each iteration
Martingale (probability theory)
Martingale_(probability_theory)
Fourier transform of the probability density function
Mathias’s, or Cramér’s, although their application is just as difficult. Pólya’s theorem, on the other hand, provides a very simple convexity condition
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Canadian politician
Donovan Eckstrom 3 0.01 Independent Ryan Huard 2 0.01 Independent Lorant Polya 2 0.01 Independent Benjamin Teichman 2 0.01 Independent Gavin Vanderwater
Ben_Carr_(politician)
Scale-free network generation algorithm
1923 in the celebrated urn model of the Hungarian mathematician György Pólya in 1923. The master equation method, which yields a more transparent derivation
Barabási–Albert_model
Infinite integer series where the next number is the sum of the two preceding it
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Lucas_number
Natural number with a decimal representation made of repeated instances of the same digit
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Repdigit
American mathematician
section in 1994, the Beckenbach Book Prize in 1999, and he was a George Pólya Lecturer from 2002 to 2004. Bressoud was elected president of the Mathematical
David_Bressoud
Emigration of well-trained individuals
Kármán, John von Neumann, Paul Halmos, Eugene Wigner, Edward Teller, George Pólya, John G. Kemeny and Paul Erdős. Several were from Budapest, and were instrumental
Human_capital_flight
American mathematics and science writer (1914–2010)
awards Leroy P. Steele Prize for Mathematical Exposition (1987) George Pólya Award (1999) Allendoerfer Award (1990) Trevor Evans Award (1998) Spouse
Martin_Gardner
nonintersecting chords joining n (labeled) points on a circle. A001006 Jordan–Pólya numbers 1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, ... Numbers that are
List_of_integer_sequences
Function that is holomorphic on the whole complex plane
this limit is an entire function. Such entire functions form the Laguerre–Pólya class, which can also be characterized in terms of the Hadamard product
Entire_function
British logician
University in 1986. Zilber received the Senior Berwick Prize (2004) and the Pólya Prize (2015) from the London Mathematical Society. He also gave the Tarski
Boris_Zilber
Court. May 31, 2012. Retrieved September 11, 2020. "Write-in Candidate". Polyas. March 18, 2017. Retrieved September 12, 2020. "2013 New Jersey Revised
2020 United States Senate elections
2020_United_States_Senate_elections
Numbers k where x - phi(x) = k has many solutions
Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet
Highly_cototient_number
Certain type of mistaken proof
{4}{8}}={\frac {1}{2}}\end{aligned}}} Hypotenuse–leg congruence George Pólya's original "proof" was that any n girls have the same colour eyes. Maxwell
Mathematical_fallacy
Mathematical concept
F does not satisfy the smoothness condition.) According to the Hilbert–Pólya conjecture, the complex zeroes ρ should be the eigenvalues of some linear
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
1831 novel by Victor Hugo
Alabama during the Great Depression. In 2019, an adaptation by Benjamin Polya was staged by Iris Theatre at St Paul's Church, Covent Garden, London. Artists
The_Hunchback_of_Notre-Dame
British mathematician
Cardiff under the supervision of Rosa M. Morris. In 1996, he was awarded the Pólya Prize of the London Mathematical Society. In 2011, he was elected a Fellow
David_Edmunds
Topics referred to by the same term
electron transfer, a process of electron transfer under action of light Pólya enumeration theorem, a mathematical theorem in enumerative combinatorics
Pet_(disambiguation)
Public school in Devon, England
1925–1932 C. Brian Haselgrove mathematician best known for disproving the Pólya conjecture in 1958 Thomas Hayter, bishop of Norwich 1749–61, bishop of London
Blundell's_School
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