List of conjectures
Encyclopedia
This is an incomplete list of mathematical conjecture
s. They are divided into four sections, according to their current status.
See also:
and, for proved results,
also
for problems not subject to conventional proof nor disproof.
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
s. They are divided into four sections, according to their current status.
See also:
- Erdős conjectureErdos conjectureThe prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects.Some of these are the following:* The Cameron–Erdős conjecture on sum-free sets of integers, proved by Ben Green....
, which lists conjectures of Paul ErdősPaul ErdosPaul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
and his collaborators - Unsolved problems in mathematicsUnsolved problems in mathematicsThis article lists some unsolved problems in mathematics. See individual articles for details and sources.- Millennium Prize Problems :Of the seven Millennium Prize Problems set by the Clay Mathematics Institute, six have yet to be solved:* P versus NP...
- List of unsolved problems
- Millennium Prize ProblemsMillennium Prize ProblemsThe Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. As of September 2011, six of the problems remain unsolved. A correct solution to any of the problems results in a US$1,000,000 prize being awarded by the institute...
and, for proved results,
also
for problems not subject to conventional proof nor disproof.
Proved (now theorems)
The theorems may not be their official names.- Adams conjecture (J-homomorphism)
- Andrews–Curtis conjectureAndrews–Curtis conjectureIn mathematics, the Andrews–Curtis conjecture states that every balanced presentation of the trivial group can be transformed into a trivial presentation by a sequence of Nielsen transformations on the relators together with conjugations of relators, named after James J. Andrews and Morton L....
- Bieberbach conjecture, 1916 (De Branges' theorem, 1984)
- Blattner's conjectureBlattner's conjectureIn mathematics, Blattner's conjecture or Blattner's formula is a description of the discrete series representations of a general semisimple group G in terms of their restricted representations to a maximal compact subgroup K . Harish-Chandra orally attributed the conjecture to Robert J Blattner,...
(Blattner formula) - Burnside conjecture (Feit–Thompson theoremFeit–Thompson theoremIn mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by - History : conjectured that every nonabelian finite simple group has even order...
) - Cameron–Erdős conjecture
- Catalan's conjecture, 1844 (Mihăilescu's theorem, 2002)
- Conway–Norton conjecture (monstrous moonshine)
- Dinitz conjectureDinitz conjectureIn combinatorics, the Dinitz conjecture is a statement about the extension of arrays to partial Latin squares, proposed in 1979 by Jeff Dinitz, and proved in 1994 by Fred Galvin....
(Galvin's theorem) - Deligne's conjecture on 1-motives
- Denjoy's conjecture
- Dodecahedral conjectureDodecahedral conjectureThe dodecahedral conjecture in geometry is intimately related to sphere packing.László Fejes Tóth, a 20th century Hungarian geometer, considered the Voronoi decomposition of any given packing of unit spheres...
(Hales–McLaughlin theorem) - Epsilon conjecture (Ribet's theorem)
- Fermat's Last TheoremFermat's Last TheoremIn number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
(Andrew WilesAndrew WilesSir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
' proof in 1994) - Frobenius conjecture (Iiyori and Yamaki)
- Gradient conjectureGradient conjectureIn mathematics, the gradient conjecture, due to René Thom, was proved in 2000 by 3 Polish mathematicians, Krzysztof Kurdyka , Tadeusz Mostowski and Adam Parusinski...
(Kurdyka–Mostowski–Parusinski theorem) - Heawood conjectureHeawood conjectureIn graph theory, the Heawood conjecture or Ringel–Youngs theorem gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus. It was proven in 1968 by Gerhard Ringel and John W. T. Youngs. One case, the non-orientable Klein bottle, proved an...
(Ringel–Youngs' theorem) - Kummer's conjecture on cubic Gauss sums (Kummer sum)
- Mahler–Manin conjecture
- Manin–Mumford conjecture (Raynaud's theorem)
- Milnor conjectureMilnor conjectureIn mathematics, the Milnor conjecture was a proposal by of a description of the Milnor K-theory of a general field F with characteristic different from 2, by means of the Galois cohomology of F with coefficients in Z/2Z. It was proved by .-Statement of the theorem:Let F be a field of...
(Voevodsky's theorem) - Mordell conjecture (Faltings' theorem)
- Mumford conjectureMumford conjectureIn mathematics Haboush's theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-vector space V, given v ≠ 0 in V that is fixed by the action of G, there is a...
(Haboush's theorem) - Poincaré conjecturePoincaré conjectureIn mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
, 1904 (theorem about the characterization of the three-dimensional sphere) - Oppenheim conjectureOppenheim conjectureIn Diophantine approximation, the Oppenheim conjecture concerns representations of numbers by real quadratic forms in several variables. It was formulated in 1929 by Alexander Oppenheim and later the conjectured property was further strengthened by Davenport and Oppenheim...
(Margulis' theorem) - Ramanujan–Petersson conjecture (consequence of the proof of the Weil conjectures)
- Road coloring conjectureRoad coloring conjectureIn graph theory the road coloring theorem, known until recently as the road coloring conjecture, deals with synchronized instructions. The issue involves whether by using such instructions, one can reach or locate an object or destination from any other point within a network...
, 1970 (2008) - Scheinerman's conjectureScheinerman's conjectureIn mathematics, Scheinerman's conjecture, now a theorem, states that every planar graph is the intersection graph of a set of line segments in the plane. This conjecture was formulated by E. R. Scheinerman in his Ph.D. thesis , following earlier results that every planar graph could be represented...
(proved 2009) - Segal's Burnside ring conjecture (Carlsson theorem)
- Serre's conjectureQuillen–Suslin theoremThe Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra about the relationship between free modules and projective modules over polynomial rings...
(Quillen–Suslin theorem) - Seymour's conjecture
- Smith conjectureSmith conjectureIn mathematics, the Smith conjecture states that if f is a diffeomorphism of the 3-sphere, of finite order then the fixed point set of f cannot be a nontrivial knot....
(Gordon's theorem) - Stanley–Wilf conjecture (Marcus–Tardos theorem)
- Star height problemStar height problemThe star height problem in formal language theory is the question whether all regular languages can be expressed using regular expressions of limited star height, i.e. with a limited nesting depth of Kleene stars...
(Hashiguchi theorem) - Strong perfect graph conjecture (Chudnovsky–Robertson–Seymour–Thomas theorem)
- Sullivan conjectureSullivan conjectureIn mathematics, Sullivan conjecture can refer to any of several results and conjectures prompted by homotopy theory work of Dennis Sullivan. A basic theme and motivation concerns the fixed point set in group actions of a finite group G. The most elementary formulation, however, is in terms of the...
- Tameness conjectureTameness conjectureIn mathematics, the tameness theorem states that every complete hyperbolic 3-manifold with finitely generated fundamental group is topologically tame, in other words homeomorphic to the interior of a compact 3-manifold....
(Agol or Calegari–Gabai theorem) - Taniyama–Shimura conjecture (Modularity theorem)
- Thurston's geometrization conjecture (3-manifolds of the uniformization theorem for surfaces)
- Wagner's conjecture (Robertson–Seymour theorem)
- Weil conjecturesWeil conjecturesIn mathematics, the Weil conjectures were some highly-influential proposals by on the generating functions derived from counting the number of points on algebraic varieties over finite fields....
(Deligne's theorems)
Disproved (no longer conjectures)
- Atiyah conjectureAtiyah conjectureIn Mathematics, the Atiyah conjecture is a collective term for a number of statements about restrictions on possible values of l^2-Betti numbers.-History:...
(not a conjecture to start with) - Borsuk's conjectureBorsuk's conjectureThe Borsuk problem in geometry, for historical reasons incorrectly called a Borsuk conjecture, is a question in discrete geometry.-Problem:...
- Euler's sum of powers conjecture
- Ganea conjectureGanea conjectureGanea's conjecture is a claim in algebraic topology, now disproved. It states thatwhere cat is the Lusternik–Schnirelmann category of a topological space X, and Sn is the n dimensional sphere....
- Generalized Smith conjecture
- HauptvermutungHauptvermutungThe Hauptvermutung of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them. It was originally formulated in 1908, by Steinitz and Tietze.This conjecture is now known to be false...
- Intersection graph conjecture
- Kouchnirenko's conjecture
- Mertens conjectureMertens conjectureIn mathematics, the Mertens conjecture is the incorrect statement that the Mertens function M is bounded by √n, which implies the Riemann hypothesis...
- Pólya conjecturePólya conjectureIn number theory, the Pólya conjecture stated that 'most' of the natural numbers less than any given number have an odd number of prime factors. The conjecture was posited by the Hungarian mathematician George Pólya in 1919, and proved false in 1958...
, 1919 (1958) - Ragsdale conjectureRagsdale conjectureThe Ragsdale conjecture is a mathematical conjecture that concerns the possible arrangements of real algebraic curves embedded in the projective plane...
- Tait's conjectureTait's conjectureIn mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle through all its vertices". It was proposed by and disproved by , who constructed a counterexample with 25 faces, 69 edges and 46 vertices...
- Von Neumann conjectureVon Neumann conjectureIn mathematics, the von Neumann conjecture stated that a topological group G is not amenable if and only if G contains a subgroup that is a free group on two generators. The conjecture was disproved in 1980....
- Weyl–Berry conjecture
- Chinese Conjecture
Recent work
- Bloch–Kato conjecture
- Erdős–Straus conjectureErdos–Straus conjectureIn number theory, the Erdős–Straus conjecture states that for all integers n ≥ 2, the rational number 4/n can be expressed as the sum of three unit fractions. Paul Erdős and Ernst G...
- Guralnick–Thompson conjecture (Riemann surfaces)
- Herzog–Schönheim conjecture
- Kepler conjectureKepler conjectureThe Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic...
- Nagata conjecture on automorphisms
- quantum unique ergodicity conjecture, (2004, Elon LindenstraussElon LindenstraussElon Lindenstrauss is an Israeli mathematician, and a winner of the 2010 Fields Medal.Since 2004, he has been a professor at Princeton University...
, for arithmetic hyperbolic surfaces, 2008, Kannan SoundararajanKannan SoundararajanKannan Soundararajan is an Indian mathematician. He currently is a professor of mathematics at Stanford University. Before moving to Stanford in 2006, he was a faculty at University of Michigan where he pursued his undergraduate studies...
& Roman Holowinsky, for holomorphic forms of increasing weight for Hecke eigenforms on noncompact arithmetic surfaceArithmetic surfaceIn mathematics, an arithmetic surface over a Dedekind domain R with fraction field K is a geometric object having one conventional dimension, and one other dimension provided by the infinitude of the primes. When R is the ring of integers Z, this intuition depends on the prime ideal spectrum Spec...
s ) - Sato–Tate conjecture
Open problems
- The 1/3 − 2/3 conjecture
- abc conjectureAbc conjectureThe abc conjecture is a conjecture in number theory, first proposed by Joseph Oesterlé and David Masser in 1985. The conjecture is stated in terms of three positive integers, a, b and c , which have no common factor and satisfy a + b = c...
- Andrews–Curtis conjectureAndrews–Curtis conjectureIn mathematics, the Andrews–Curtis conjecture states that every balanced presentation of the trivial group can be transformed into a trivial presentation by a sequence of Nielsen transformations on the relators together with conjugations of relators, named after James J. Andrews and Morton L....
- Angel problemAngel problemThe angel problem is a question in game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard...
- Agoh–Giuga conjecture
- Andrica's conjecture
- Artin conjectureArtin conjectureIn mathematics, there are several conjectures made by Emil Artin:* Artin conjecture * Artin's conjecture on primitive roots* The conjecture that finite fields are quasi-algebraically closed; see Chevalley–Warning theorem....
s - Bateman–Horn conjecture
- Baum–Connes conjectureBaum–Connes conjectureIn mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the K-theory of the C*-algebra of a group and the K-homology of the corresponding classifying space of proper actions of that group....
- Beal's conjectureBeal's conjectureBeal's conjecture is a conjecture in number theory proposed by Andrew Beal in about 1993; a similar conjecture was suggested independently at about the same time by Andrew Granville....
- Beilinson conjecture
- Berry–Tabor conjecture
- Birch and Swinnerton-Dyer conjectureBirch and Swinnerton-Dyer conjectureIn mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. Its status as one of the most challenging mathematical questions has become widely recognized; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay...
- Birch–Tate conjectureBirch–Tate conjectureThe Birch–Tate conjecture is based on algebraic K-theory proposed by both Bryan John Birch and John Tate. It relates the value of a Dedekind zeta function at s = −1 to the order of K2 of the ring of integers, for a number field F....
- Birkhoff conjecture
- Bloch–Beilinson conjectures
- Borel conjectureBorel conjectureIn mathematics, specifically geometric topology, the Borel conjecture asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism...
- Bost conjecture
- Brocard's conjecture
- Brumer–Stark conjectureBrumer–Stark conjectureThe Brumer–Stark conjecture is a conjecture in algebraic number theory giving a rough generalization of both the analytic class number formula for Dedekind zeta functions, and also of Stickelberger's theorem about the factorization of Gauss sums...
- Bunyakovsky conjectureBunyakovsky conjectureThe Bunyakovsky conjecture stated in 1857 by the Russian mathematician Viktor Bunyakovsky, claims that an irreducible polynomial of degree two or higher with integer coefficients generates for natural arguments either an infinite set of numbers with greatest common divisor exceeding unity, or...
- Catalan–Dickson conjecture on aliquot sequencesAliquot sequenceIn mathematics, an aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term. The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ1 in the following way:For example, the...
- Carathéodory conjectureCarathéodory conjectureThe Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a session of the Berlin Mathematical Society in 1924, [1]. Other early references are the Invited Lecture [3] of Stefan Cohn-Vossen at the International Congress of...
- Carmichael totient conjecture
- Catalan's Mersenne conjecture
- Cherlin–Zilber conjecture
- Collatz conjectureCollatz conjectureThe Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture , Kakutani's problem , the Thwaites conjecture , Hasse's algorithm The Collatz conjecture is a...
- Cramér's conjecture
- Conway's thrackle conjectureConway's thrackle conjectureA thrackle is an embedding of a graph, such that each edge is a Jordan arcand every pair of edges meet once. Edges may either meet at a common endpoint, or, if they have no endpoints in common, at a point in their interiors. In the latter case, the crossing must be transverse.John H...
- Deligne conjectureDeligne conjectureIn mathematics, there are a number of so-called Deligne conjectures, provided by Pierre Deligne. These are independent conjectures in various fields of mathematics....
disambiguation - Eilenberg−Ganea conjecture
- Elliott–Halberstam conjecture
- Erdős–Burr conjectureErdos–Burr conjectureIn mathematics, the Erdős–Burr conjecture is an unsolved problem concerning the Ramsey number of sparse graphs. The conjecture is named after Paul Erdős and Stefan Burr, and is one of many conjectures named after Erdős; it states that the Ramsey number of graphs in any sparse family of graphs...
- Erdős–Faber–Lovász conjectureErdos–Faber–Lovász conjectureIn graph theory, the Erdős–Faber–Lovász conjecture is an unsolved problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972...
- Erdős–Gyárfás conjectureErdos–Gyárfás conjectureIn graph theory, the unproven Erdős–Gyárfás conjecture, made in 1995 by the prolific mathematician Paul Erdős and his collaborator András Gyárfás, states that any graph with minimum degree 3 contains a simple cycle whose length is a power of two...
- Farrell–Jones conjectureFarrell–Jones conjectureIn mathematics, the Farrell–Jones conjecture, named after F. Thomas Farrell and Lowell Edwin Jones states that certain assembly maps are isomorphisms...
- Filling area conjectureFilling area conjectureIn mathematics, in Riemannian geometry, Mikhail Gromov's filling area conjecture asserts that among all possible fillings of the Riemannian circle of length 2π by a surface with the strongly isometric property, the round hemisphere has the least area...
- Frankl conjecture
- Gauss circle problemGauss circle problemIn mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centred at the origin and with radius r. The first progress on a solution was made by Carl Friedrich Gauss, hence its name....
- Gilbreath conjecture
- Giuga's conjecture
- Goldbach's conjectureGoldbach's conjectureGoldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:A Goldbach number is a number that can be expressed as the sum of two odd primes...
- Goldbach's weak conjectureGoldbach's weak conjectureIn number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that:...
- Gold partition conjecture
- Goormaghtigh conjectureGoormaghtigh conjectureIn mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh. The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equation...
- Green's conjecture
- Grimm's conjectureGrimm's conjectureIn mathematics, and in particular number theory, Grimm's conjecture states that to each element of a set of consecutive composite numbers one can assign a distinct prime that divides it...
- Grothendieck–Katz p-curvature conjectureGrothendieck–Katz p-curvature conjectureIn mathematics, the Grothendieck–Katz p-curvature conjecture is a problem on linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case...
- Hadamard conjecture
- Hanna Neumann conjectureHanna Neumann conjectureIn the mathematical subject of group theory, the Hanna Neumann conjecture is a statement about the rank of the intersection of two finitely generated subgroups of a free group. The conjecture was posed by Hanna Neumann in 1957...
- Happy Ending Conjecture
- Hedetniemi's conjectureHedetniemi's conjectureIn graph theory, Hedetniemi's conjecture, named after Stephen T. Hedetniemi, concerns the connection between graph coloring and the tensor product of graphs...
- Hilbert–Smith conjecture
- Hirsch conjectureHirsch conjectureIn mathematical programming and polyhedral combinatorics, Hirsch's conjecture states that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n − d. That is, any two vertices of the polytope must be connected to each other by a...
- Hopf conjectureHopf conjectureIn mathematics, Hopf conjecture may refer to one of several conjectural statements from differential geometry and topology attributed to Heinz Hopf.- Positively curved Riemannian manifolds :...
- Hodge conjectureHodge conjectureThe Hodge conjecture is a major unsolved problem in algebraic geometry which relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de Rham cohomology classes are algebraic, that is, they...
- Homological conjectures in commutative algebraHomological conjectures in commutative algebraIn mathematics, the homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated conjectures relating various homological properties of a commutative ring to its internal ring structure, particularly its Krull...
- Jacobian conjectureJacobian conjectureIn mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott-Heinrich Keller...
- Kaplansky conjectureKaplansky conjectureThe mathematician Irving Kaplansky is notable for proposing numerous conjectures in several branches of mathematics, including a list of ten conjectures on Hopf algebras...
- Keating–Snaith conjecture
- Lawson's conjecture
- Lenstra–Pomerance–Wagstaff conjecture
- Lichtenbaum conjecture
- List coloring conjecture
- Littlewood conjecture
- Lovász conjectureLovász conjectureIn graph theory, the Lovász conjecture is a classical problem on Hamiltonian paths in graphs. It says:The original article of Lovász stated the result in the opposite, butthis version became standard...
- Marshall Hall's conjectureMarshall Hall's conjectureIn mathematics, Marshall Hall's conjecture is an open question, , on the differences between perfect squares and perfect cubes. Aside from the case of a perfect sixth power, it asserts that a perfect square m2 and a perfect cube n3 must lie a substantial distance apart...
- Mazur's conjectures
- Deligne conjectureDeligne conjectureIn mathematics, there are a number of so-called Deligne conjectures, provided by Pierre Deligne. These are independent conjectures in various fields of mathematics....
in monodromyMonodromyIn mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology and algebraic and differential geometry behave as they 'run round' a singularity. As the name implies, the fundamental meaning of monodromy comes from 'running round singly'... - New Mersenne conjecture
- Novikov conjectureNovikov conjectureThe Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965....
- Oppermann's conjecture
- Petersen coloring conjecture
- Pierce–Birkhoff conjecturePierce–Birkhoff conjectureIn abstract algebra, the Pierce–Birkhoff conjecture asserts that any piecewise-polynomial function can be expressed as a maximum of finite minima of finite collections of polynomials. It was first stated, albeit in non-rigorous and vague wording, in the 1956 paper of Garrett Birkhoff and Richard S....
- Pillai's conjecture
- De Polignac's conjecture
- Quillen–Lichtenbaum conjectureQuillen–Lichtenbaum conjectureIn mathematics, the Quillen–Lichtenbaum conjecture is a conjecture relating étale cohomology to algebraic K-theory introduced by , who was inspired by earlier conjectures of . and proved the Quillen–Lichtenbaum conjecture at the prime 2 for some number fields...
- Reconstruction conjectureReconstruction conjectureInformally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to Kelly and Ulam.-Formal statements:...
- Riemann Hypotheses: see also Weil conjectures, above
- Riemann hypothesisRiemann hypothesisIn mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
- Generalized Riemann hypothesisGeneralized Riemann hypothesisThe Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function...
- Grand Riemann hypothesisGrand Riemann hypothesisIn mathematics, the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and Generalized Riemann hypothesis. It states that the nontrivial zeros of all automorphic L-functions lie on the critical line...
- Generalized Riemann hypothesis
- Density hypothesis
- Lindelöf hypothesis
- Hilbert–Pólya conjecture on the Riemann hypothesis
- Riemann hypothesis
- Ringel-Kotzig conjecture
- Schanuel's conjectureSchanuel's conjectureIn mathematics, specifically transcendence theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence degree of certain field extensions of the rational numbers.-Statement:The conjecture is as follows:...
- Schinzel's hypothesis HSchinzel's hypothesis HIn mathematics, Schinzel's hypothesis H is a very broad generalisation of conjectures such as the twin prime conjecture. It aims to define the possible scope of a conjecture of the nature that several sequences of the type...
- Scholz conjectureScholz conjectureIn mathematics, the Scholz conjecture sometimes called the Scholz–Brauer conjecture or the Brauer–Scholz conjecture In mathematics, the Scholz conjecture sometimes called the Scholz–Brauer conjecture or the Brauer–Scholz conjecture In mathematics, the Scholz conjecture sometimes called the...
- Second Hardy–Littlewood conjecture
- Selfridge's conjecture
- Serre conjecture (number theory)Serre conjecture (number theory)In mathematics, Jean-Pierre Serre conjectured the following result regarding two-dimensional Galois representations. This was a significant step in number theory, though this was not realised for at least a decade.-Formulation:...
- Serre's multiplicity conjecturesSerre's multiplicity conjecturesIn mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry...
- Singmaster's conjecture
- Tate conjectureTate conjectureIn mathematics, the Tate conjecture is a 1963 conjecture of John Tate linking algebraic geometry, and more specifically the identification of algebraic cycles, with Galois modules coming from étale cohomology...
- Twin prime conjectureTwin primeA twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
- Vandiver's conjecture
- Waring's conjecture
- Weight-monodromy conjecture
- Weinstein conjectureWeinstein conjectureIn mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the current understanding is that a regular compact contact type level set of a Hamiltonian on a symplectic manifold should carry at least one...
- Whitehead conjectureWhitehead conjectureThe Whitehead conjecture is a claim in algebraic topology. It was formulated by J. H. C. Whitehead in 1941. It states that every connected subcomplex of a two-dimensional aspherical CW complex is aspherical....
- Zhou conjecture