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Mathematics question and answer website
MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions
MathOverflow
Network of Q&A sites based in New York City
"Richard Borcherds". mathoverflow.net. Archived from the original on August 7, 2020. Retrieved July 30, 2020. "Edward Witten". mathoverflow.net. Archived from
Stack_Exchange
American mathematician
MathOverflow users, by reputation score. MathOverflow announcement of Hamkins breaking 100,000 reputation score, September 17, 2014. MathOverflow announcement
Joel_David_Hamkins
Mathematical concept
org/nlab/show/pyknotic+set https://mathoverflow.net/questions/441610/properties-of-pyknotic-sets https://mathoverflow.net/questions/356618/what-is-the-
Pyknotic_set
Australian and American mathematician (born 1975)
related to Terence Tao. Terence Tao's home page Tao's research blog Tao's MathOverflow page O'Connor, John J.; Robertson, Edmund F., "Terence Tao", MacTutor
Terence_Tao
Fictitious name used for a particular purpose
mathematicians". MathOverflow. Retrieved 12 January 2020. Case & Leggett 2005, p. 39. "soft question – Pseudonyms of famous mathematicians". MathOverflow. Retrieved
Pseudonym
Theorems on the convergence of bounded monotonic sequences
(https://mathoverflow.net/users/6129/coudy), Do you know important theorems that remain unknown?, URL (version: 2018-06-05): https://mathoverflow.net/q/296540
Monotone_convergence_theorem
In mathematics, invariant of square matrices
1622. Serre, Denis (Oct 18, 2010). "Concavity of det1/n over HPDn". MathOverflow. Anton, Howard (2005), Elementary Linear Algebra (Applications Version)
Determinant
Theorem classifying finite simple groups
"Where are the second- (and third-)generation proofs of the classification of finite simple groups up to?". MathOverflow. (Last updated in February 2024)
Classification of finite simple groups
Classification_of_finite_simple_groups
Concept in differential geometry
Mathematica. 13: 21–49. https://mathoverflow.net/questions/51993/euler-characteristic-of-orbifolds https://mathoverflow.net/questions/267055/is-every-
Euler characteristic of an orbifold
Euler_characteristic_of_an_orbifold
CrypTool Logo Manim Gnumeric Google Sheets LibreOffice Calc Microsoft Excel Numbers (spreadsheet) MathOverflow MathWorld Microsoft Math Solver Wolfram Alpha
List of free educational software
List_of_free_educational_software
Wiki for mathematics, physics, and philosophy
Type Theory. Retrieved 8 August 2020. MathOverflow, 1.0 'How to ask' page. Archived on 2013-06-04. MathOverflow, Results for a search for 'nlab'. As of
NLab
inaccessible reflecting cardinal is not in general Mahlo however, see https://mathoverflow.net/q/212597. List of large cardinal properties Jech, Thomas (2003),
Reflecting_cardinal
Area of mathematics using condensed sets
"Pyknotic sets". nLab. https://mathoverflow.net/questions/441838/condensed-vs-pyknotic-vs-consequential https://mathoverflow.net/questions/tagged/condensed-mathematics
Condensed_mathematics
Result in algebraic geometry
Grothendieck-Riemann-Roch?" on MathOverflow. The thread "how does one understand GRR? (Grothendieck Riemann Roch)" on MathOverflow. The thread "Chern class
Grothendieck–Riemann–Roch theorem
Grothendieck–Riemann–Roch_theorem
Question-and-answer website for programmers
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Stack_Overflow
Branch of mathematics
numbers". mathoverflow.net. Retrieved 2017-04-16. "kt.k theory and homology - Grothendieck group for projective space over the dual numbers". MathOverflow. Retrieved
K-theory
Concept in the philosophy of mathematics
Discrete Analysis by Doron Zeilberger Discussion on formal foundations on MathOverflow History of constructivism in the 20th century by A. S. Troelstra Predicative
Ultrafinitism
A technical argument by a trusted author, which is hard to check and looks similar to arguments known to be correct, is hardly ever checked in detail.
List_of_incomplete_proofs
Theorem in complex analysis
Étale Cohomology Riemann's existence theorem (Mathoverflow) Finite Covers of Complex Varieties (Mathoverflow) Riemann's existence theorem (nLab) v t e
Riemann's_existence_theorem
Algebraic structure with addition, multiplication, and division
Chapter V, §14, No. 2, Theorem 1 Artin (1991), §13.9 Banaschewski (1992). Mathoverflow post Ribenboim (1999), p. 186, §7.1 Bourbaki (1988), Chapter VI, §2.3
Field_(mathematics)
manuscript: Notes on categorical probability, July 13, 2009. https://mathoverflow.net/questions/463712/hopf-monads-in-categorical-probability-theory https://golem
Categorical_probability
Counterexample to the converse of the intermediate value theorem
2025-06-28. Stein, Noah. "Is Conway's base-13 function measurable?". mathoverflow. Retrieved 6 August 2023. Oman, Greg (2014). "The Converse of the Intermediate
Conway's_base_13_function
Method of mathematical integration
(https://mathoverflow.net/users/113756/daniele-tampieri), Do you know important theorems that remain unknown?, URL (version: 2021-12-31): https://mathoverflow
Lebesgue_integral
Matrix decomposition method
(1985, p. 407). "matrices - Diagonalizing a Complex Symmetric Matrix". MathOverflow. Retrieved 2020-01-25. Schabauer, Hannes; Pacher, Christoph; Sunderland
Cholesky_decomposition
American mathematician (1940–2025)
he lived in Berkeley, California and was an occasional participant on MathOverflow. Near the end of his life, he endowed a prize for "Excellence in Mathematical
I._Martin_Isaacs
Decomposition of periodic functions
"Characterizations of a linear subspace associated with Fourier series". MathOverflow. 2010-11-19. Retrieved 2014-08-08. Edwards 1982, p. 67. Katznelson 2004
Fourier_series
Type of catenary curve
accessdate: April 13, 2017 MathOverflow: classical mechanics - Catenary curve under non-uniform gravitational field - MathOverflow, accessdate: April 13,
Weighted_catenary
Formula computing the inverse of the sum of a matrix and the outer product of two vectors
Propagator#Spin 1 "Perturbative quantum field theory". "MathOverflow discussion". MathOverflow. Weisstein, Eric W. "Sherman–Morrison formula". MathWorld
Sherman–Morrison_formula
Australian mathematician
Emerton on Aug14Thu, retrieved 11 February 2020 "User Emerton - MathOverflow". Mathoverflow.net. Retrieved 13 March 2016. "Too Much Ain't Enough Langlands"
Matthew_Emerton
Set theory concept
(2022-12-24). "Does anyone still seriously doubt the consistency of ZFC?". MathOverflow. nLab authors (2025-06-27). "Large Cardinal". nLab. Retrieved 2025-09-13
Large_cardinal
Mathematical model of the time dependence of a point in space
generalized into real, complex or discrete n-dimensional vector spaces https://mathoverflow.net/questions/105071/dynamical-systems-with-multidimensional-complex
Dynamical_system
Algebraic variety with a group structure
14005. Borel 1991, p. 16. Borel 1991, p. 47. "Non-linear Lie group". MathOverflow. Retrieved May 13, 2022. Chevalley, Claude, ed. (1958), Séminaire C.
Algebraic_group
Mathematical technique used in proof theory
(2010). "Proof-Theoretic Ordinal of ZFC or Consistent ZFC Extensions?". MathOverflow. Retrieved 2026-01-23. Arai, Toshiyasu (2023). "Lectures on Ordinal Analysis"
Ordinal_analysis
Theorem in mathematics
(https://mathoverflow.net/users/4042/dan-ramras), On a proof of the existence of tubular neighborhoods., URL (version: 2017-04-13): https://mathoverflow.net/q/58124
Inverse_function_theorem
Mathematical group formed from the automorphisms of an object
Graduate Texts in Mathematics. Vol. 66. Springer Verlag. ISBN 9781461262176. https://mathoverflow.net/questions/55042/automorphism-group-of-a-scheme
Automorphism_group
British-Lebanese mathematician (1929–2019)
structures on the 6-sphere? (MathOverflow), retrieved 24 September 2018 Atiyah's May 2018 paper on the 6-sphere (MathOverflow), retrieved 24 September 2018
Michael_Atiyah
System to format mathematics on the web
including arXiv, Elsevier's ScienceDirect, MathSciNet, n-category cafe, MathOverflow, Wikipedia (formerly, on the backend), Scholarpedia, Project Euclid journals
MathJax
Algebraic field extension
Math., 38 (4): 383–385, doi:10.1002/malq.19920380136, Zbl 0739.03027 Mathoverflow discussion Brawley, Joel V.; Schnibben, George E. (1989), "2.2 The Algebraic
Algebraic_closure
Geometric construction used in Ancient Greek mathematics
Theorem 5.1. Ramshaw, Lyle (Mar 14, 2014). "Neusis constructions". MathOverflow. Retrieved May 4, 2025. This article incorporates text from this source
Neusis_construction
ISSN 0163-5700. Archived from the original (PDF) on 2022-07-05. What are some reasonable-sounding statements that are independent of ZFC?, mathoverflow.net
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Continuous function on an interval takes on every value between its values at the ends
23638/LMCS-16(3:5)2020. Keith Devlin (2007) How to stabilize a wobbly table https://mathoverflow.net/questions/253059/approximate-intermediate-value-theorem-in-pure-
Intermediate_value_theorem
Operation in algebra and mathematics
Turi, Daniele (1996–2001), Category Theory Lecture Notes (PDF) https://mathoverflow.net/questions/55182/what-is-known-about-the-category-of-monads-on-set
Monad_(category_theory)
Conjecture in number theory
Barry Mazur Philosophy behind Mochizuki's work on the ABC conjecture on MathOverflow ABC Conjecture Polymath project wiki page linking to various sources
Abc_conjecture
Theorem of matrix ranks
considerations when using the Woodbury matrix identity numerically?". MathOverflow. Henderson, H. V.; Searle, S. R. (1981). "On deriving the inverse of
Woodbury_matrix_identity
Property of large sets
would most like to see solved, Combinatorica, 1(1981), 28. doi:10.1007/BF02579174 The Erdős–Turán conjecture or the Erdős conjecture? on MathOverflow
Erdős conjecture on arithmetic progressions
Erdős_conjecture_on_arithmetic_progressions
Variation of chess
2010 onwards, infinite chess was popularized among mathematicians on MathOverflow, where concepts such as the decidability of checkmate on the unbounded
Infinite_chess
Conjecture in algebraic geometry
vol. 242, Cambridge University Press, pp. 49–58, ISBN 978-0-521-59642-8, MR 1483108 "Why is the section conjecture important?". mathoverflow.net. v t e
Section_conjecture
Property of measure-preserving dynamical systems
a measure-preserving system with dense orbits that is not ergodic". MathOverflow. September 1, 2011. Retrieved May 16, 2020. Walters 1982, Section 1.7
Ergodicity
Used to compare mixed characteristic situations with purely finite characteristic ones
the AMS. Retrieved 2 January 2020. "What are "perfectoid spaces"?". MathOverflow. Foundations of Perfectoid Spaces by Matthew Morrow Lean perfectoid spaces
Perfectoid_space
Algebra used in certain conformal field theories
Press, Cambridge, MA, pp. 357–422, arXiv:hep-th/9312104, Bibcode:1993hep.th...12104W, MR 1358625 MathOverflow discussion with a number of references.
Verlinde_algebra
Planar maps require at most four colors
Notices of the American Mathematical Society. 73 (3): 216–228. doi:10.1090/noti3305. List of generalizations of the four color theorem on MathOverflow
Four_color_theorem
Differential map between manifolds whose differential is everywhere surjective
Mineola, New York: Dover Publications. ISBN 978-0-486-47855-5. https://mathoverflow.net/questions/376129/what-are-the-sufficient-and-necessary-condition
Submersion_(mathematics)
Algebraic structure used in topology
36; Remarks. "Are spectra really the same as cohomology theories?". MathOverflow. Switzer 1975, 7.68. Dieudonné, Jean (1989), History of Algebraic and
Cohomology
Seminal math text
Mathoverflow.net Cat as a closed model category Is there a high-concept explanation for why “simplicial” leads to “homotopy-theoretic”?, Mathoverflow
Pursuing_Stacks
2020-04-07. Formally smooth with smooth fibers, but not smooth https://mathoverflow.net/q/333596 Formally smooth but not smooth https://mathoverflow.net/q/195
Formally_smooth_map
French mathematician (1906–2000)
Quarterly, 22: 218–228. A Tribute to Eugène Ehrhart, Philippe Clauss, University of Strasbourg. Mathematicians who were late learners?-list – MathOverflow
Eugène_Ehrhart
Smallest convex set containing a given set
See also Douglas Zare, answer to "the perimeter of a non-convex set", MathOverflow, May 16, 2014. Oberman (2007). Knuth (1992). Rockafellar (1970), p. 12;
Convex_hull
Mathematical parametrization of vector spaces by another space
Mathematics, EMS Press, 2001 [1994] Why is it useful to study vector bundles ? on MathOverflow Why is it useful to classify the vector bundles of a space ?
Vector_bundle
twice would "cancel out". "Characterization of cocompact group actione". MathOverflow. Retrieved 2026-04-25. Daverman, Robert J.; Sher, R. B. (2002). Handbook
Cocompact_group_action
platform Markdown editors – CoCalc, TiddlyWiki, Gollum, and Wiki.js. MathOverflow – mathematics Q&A website MDN Web Docs – documentation repository and
List of online educational resources
List_of_online_educational_resources
Website and series of mathematical challenges
of computer science awards List of things named after Leonhard Euler MathOverflow — mathematics Q&A website Suri, Manil (12 October 2015). "The importance
Project_Euler
Matrix defined using smaller matrices called blocks
matrix block inverse in terms of the entire matrix inverse known?". MathOverflow. Escalante-B., Alberto N.; Wiskott, Laurenz (2016). "Improved graph-based
Block_matrix
Concept in mathematics
commutative algebra – Existence of a minimal generating set of a module – MathOverflow". mathoverflow.net. Dummit, David; Foote, Richard. Abstract Algebra.
Generating_set_of_a_module
Result in combinatorics and graph theory
combinatorics - Fractional Matching version of Hall's Marriage theorem". MathOverflow. Retrieved 2020-06-29. Oxley, James (1992). Matroid Theory. Oxford, UK:
Hall's_marriage_theorem
Algebra in algebraic topology
algebraic topology – (Co)homology of the Eilenberg–MacLane spaces K(G,n)". MathOverflow. Retrieved 2021-01-15. Adams (1974), p. 277. Adams (1974), p. 279. Adams
Steenrod_algebra
Dorais, Back to Cantor?, a blog post structural set theory in nLab https://mathoverflow.net/questions/90820/set-theories-without-junk-theorems v t e
Structural_set_theory
Computation process in mathematical algorithms
'butterfly' Cipra, Barry A. (2012-06-04). "FFT and Butterfly Diagram". mathoverflow.net. Retrieved 2015-02-10. Press, William H.; Teukolsky, Saul A.; Vetterling
Butterfly_diagram
Category of mathematics papers in ArXiv
system Outline of mathematics Quantum logic "What is quantum algebra?". mathoverflow.net. Retrieved 2018-01-22. "Quantum Algebra". arxiv.org. Retrieved 2025-10-27
Quantum_algebra
Method for evaluating indefinite integrals
Does there exist a complete implementation of the Risch algorithm?". MathOverflow. October 15, 2020. Retrieved February 10, 2023. "Mathematica 7 Documentation:
Risch_algorithm
Software used in mathematical applications
software and tools List of open-source software for mathematics Mathlete MathOverflow Plot (graphics) Time complexity See, e.g., the editorial charter of the
Mathematical_software
Mathematical group of the homotopy classes of loops in a topological space
Animations to introduce fundamental group by Nicolas Delanoue Sets of base points and fundamental groupoids: mathoverflow discussion Groupoids in Mathematics
Fundamental_group
Condition under which an odd prime is a sum of two squares
"windmill" figures, given by Alexander Spivak in 2006 and described in this MathOverflow post by Moritz Firsching and this YouTube video by Mathologer. In 2016
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Equation in mathematical physics
Veerman, Frits (March 8, 2016). "What is the L2 gradient flow?". MathOverflow. Bartels, Sören (2015). Numerical Methods for Nonlinear Partial Differential
Allen–Cahn_equation
Mathematical property
Introduction, Graduate Texts in Mathematics, vol. 222 (2nd ed.), Springer MathOverflow:Are abelian non-degenerate tensor categories semisimple? Semisimple category
Semi-simplicity
Branch of mathematics
noncommutative geometry in the nLab Theories of Noncommutative Geometry at MathOverflow Noncommutative geometry on arXiv Noncommutative geometry and particle
Noncommutative_geometry
Whether a decision problem has an effective method to derive the answer
doi:10.1017/S0022481200051513. S2CID 798307. Retrieved 11 September 2026. Mathoverflow.net/Decidability-of-chess-on-an-infinite-board Decidability-of-chess
Decidability_(logic)
Typically linear operator defined in terms of differentiation of functions
Fourier. 52 (3): 899–982. doi:10.5802/aif.1906. ISSN 1777-5310. https://mathoverflow.net/questions/451110/reference-request-inverse-of-differential-operators
Differential_operator
Group with an addition as its operation
Rings", Algebra I: Chapters 1–3, Springer, p. 97, ISBN 978-3-540-64243-5 "MathOverflow: The Origin(s) of Modular and Moduli". Retrieved 8 March 2024.
Additive_group
Geometric graph with unit edge lengths
arXiv:2605.20579 [math.CO]. "What is the unit distance exponent?". MathOverflow. Retrieved 2026-10-17. Naslund, Eric (2026-10-02). "An Exponent of 1
Unit_distance_graph
Type of infinite number in set theory
2022). "Does anyone still seriously doubt the consistency of ZFC?". MathOverflow. A. Enayat, "Analogues of the MacDowell-Specker_theorem for set theory"
Inaccessible_cardinal
Set of functions from a topological space to [0,1] which sum to 1 for any input
Tobias. "Pairwise orthogonality for partitions of unity in a *-algebra". Mathoverflow. Retrieved 7 February 2024. Murphy, Gerard J. (1990). C*-Algebras and
Partition_of_unity
Mapping from p forms to p-1 forms
Steenrod algebra. Is "Cartan's magic formula" due to Élie or Henri?, MathOverflow, 2010-09-21, retrieved 2018-06-25 Elementary Proof of the Cartan Magic
Interior_product
Condition for a linear operator to be open
2020). "Can the inverse operator in Bartle-Graves theorem be linear?". MathOverflow. Borwein, J. M.; Dontchev, A. L. (2003). "On the Bartle–Graves theorem"
Open mapping theorem (functional analysis)
Open_mapping_theorem_(functional_analysis)
Formula in number theory
Weston, 2004. "Did Gauss know Dirichlet's class number formula in 1801?". MathOverflow. October 10, 2012. Davenport, Harold (2000). Montgomery, Hugh L. (ed
Class_number_formula
Mathematical set with some added structure
not generated by a topology. A proof can be found in this answer on MathOverflow. Carlson, Kevin (August 2, 2012). "Difference between 'space' and 'mathematical
Space_(mathematics)
Concept in topology
Mathematics Stack Exchange. "Classic applications of Baire category theorem". MathOverflow. Engelking 1989, Historical notes, p. 199. Bourbaki 1989, p. 192. Baire
Baire_space
Groups. Springer Science & Business Media. ISBN 9781468401288. https://mathoverflow.net/questions/286393/how-do-i-know-if-an-irreducible-representation-
Permutation_representation
Physics question-and-answer website
Forums is ranked 8th on "Aelieve's List of 20 Best Physics Websites". MathOverflow Stack Exchange nLab PhysicsOverflow Main, Douglas (2015-09-14). "Bubble
Physics_Forums
1957 mathematics paper by Alexander Grothendieck
Vol. 38. Cambridge University Press. ISBN 0-521-43500-5. "Grothendieck's Tohoku Paper and Combinatorial Topology". MathOverflow. Retrieved 23 July 2026.
Grothendieck's_Tôhoku_paper
Partial differential equations whose solutions are instantons
Yang–Mills–Higgs equations For a proof of this fact, see the post https://mathoverflow.net/a/265399. Uhlenbeck, Karen K.; Freed, Daniel S. (1984). Instantons
Yang–Mills_equations
Mathematical proof of Hilbert's Nullstellensatz
(Юлий Лазаревич Рабинович). For a detailed discussion, see: https://mathoverflow.net/questions/416577/identity-of-j-l-rabinowitsch-of-rabinowitsch-trick
Rabinowitsch_trick
algebraic geometry - Is there any rational curve on an Abelian variety?". MathOverflow. Retrieved 2020-02-28. Maulik, Davesh. "Lectures on Donaldson-Thomas
Convexity (algebraic geometry)
Convexity_(algebraic_geometry)
"Example of a triangulable topological manifold which does not admit a PL structure (answer on Mathoverflow)". Kirby-Siebenmann invariant on nLab v t e
Kirby–Siebenmann_class
Type of mathematical function
Does there exist a complete implementation of the Risch algorithm?". MathOverflow. Oct 15, 2020. Retrieved 2023-02-10. Morris Tenenbaum (1985). Ordinary
Elementary_function
Person who competes in mathematics
programming Computer-based mathematics education Mathematical software MathOverflow Project Euler — computational mathematics and computer programming problem
Mathlete
Matrix normal form
ISBN 0201182432. OCLC 19456124. "Computation time of Smith normal form in Maple". MathOverflow. Retrieved 2024-04-05. Wolfram Research (2015). "SmithDecomposition"
Smith_normal_form
and Example 7 on p. 232. "Simply-connected rational homology spheres". MathOverflow. Retrieved 2025-07-08. Barden 1965, Lemma 1.1.(v) and Lemma 1.2. Barden
Wu_manifold
identities for perfect complexes". MathOverflow. "An alternative definition of pseudo-coherent complex". MathOverflow. "15.74 Perfect complexes". The Stacks
Perfect_complex
Relation between genus, degree, and dimension of function spaces over surfaces
Gray, The Riemann–Roch theorem and Geometry, 1854–1914. Is there a Riemann–Roch for smooth projective curves over an arbitrary field? on MathOverflow
Riemann–Roch_theorem
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