This is a list of mathematical

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 19 ...

Open problems

The following conjectures remain open. The (incomplete) column "cites" lists the number of results for a

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search for the term, in double quotes .

Conjectures now proved (theorems)

The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic names. * Deligne's conjecture on 1-motives *

Goldbach's weak conjecture In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that : Every odd number greater than 5 can be expressed as the sum of three primes. (A prime ma ...

(proved in 2013) *

Sensitivity conjecture In computational complexity the decision tree model is the model of computation in which an algorithm is considered to be basically a decision tree, i.e., a sequence of ''queries'' or ''tests'' that are done adaptively, so the outcome of the previ ...

(proved in 2019)

Disproved (no longer conjectures)

Atiyah conjecture In mathematics, the Atiyah conjecture is a collective term for a number of statements about restrictions on possible values of l^2-Betti numbers. History In 1976, Michael Atiyah introduced l^2-cohomology of manifolds with a free co-compact actio ...

(not a conjecture to start with) *

Borsuk's conjecture The Borsuk problem in geometry, for historical reasons incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk. Problem In 1932, Karol Borsuk showed that an ordinary 3-dimensional ball in Eucl ...

* Chinese hypothesis (not a conjecture to start with) *

Doomsday conjecture In algebraic topology, the doomsday conjecture was a conjecture about Ext groups over the Steenrod algebra made by Joel Cohen, named by Michael Barratt, published by and disproved by . stated a modified version called the new doomsday conjecture. ...

Euler's sum of powers conjecture Euler's conjecture is a disproved conjecture in mathematics related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that for all integers and greater than 1, if the sum of many th powers of positive integers is ...

Ganea conjecture Ganea's conjecture is a claim in algebraic topology, now disproved. It states that : \operatorname(X \times S^n)=\operatorname(X) +1 for all n>0, where \operatorname(X) is the Lusternik–Schnirelmann category of a topological space ''X'', and ' ...

Generalized Smith conjecture A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common character ...

Hauptvermutung The ''Hauptvermutung'' of geometric topology is a now refuted conjecture asking whether any two Triangulation (topology), triangulations of a triangulable space have subdivisions that are combinatorially equivalent, i.e. the subdivided triangulati ...

Hedetniemi's conjecture In graph theory, Hedetniemi's conjecture, formulated by Stephen T. Hedetniemi in 1966, concerns the connection between graph coloring and the tensor product of graphs. This conjecture states that : \chi (G \times H ) = \min\. Here \chi(G) denotes ...

, counterexample announced 2019 * Hirsch conjecture (disproved in 2010) * Intersection graph conjecture * Kelvin's conjecture * Kouchnirenko's conjecture *

Mertens conjecture In mathematics, the Mertens conjecture is the statement that the Mertens function M(n) is bounded by \pm\sqrt. Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 ...

Pólya conjecture In number theory, the Pólya conjecture (or Pólya's conjecture) stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an ''odd'' number of prime factors. The conjecture was set forth by the Hungarian mat ...

, 1919 (1958) * Ragsdale conjecture * Schoenflies conjecture (disproved 1910) *

Tait's conjecture In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices". It was proposed by and disproved by , who constructed a counterexample with 25 faces, 69 ed ...

Von Neumann conjecture In mathematics, the von Neumann conjecture stated that a group (mathematics), group ''G'' is non-Amenable group, amenable if and only if ''G'' contains a subgroup that is a free group on two Generating set of a group, generators. The conjecture was ...

Weyl–Berry conjecture To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory. "Can One Hear the Shape of a Drum?" is the title of a 1966 article ...

* Williamson conjecture

References

{{reflist

External links

Open Problem Garden

Conjectures In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 19 ...

Open problems

Conjectures now proved (theorems)

Disproved (no longer conjectures)

See also

References

External links