389 problems

In mathematics, the Berry–Robbins problem asks whether there is a continuous map from configurations of n points in R3 to the flag manifold U(n)/Tn that is compatible with the acti…

In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard T…

Kato's conjecture is a mathematical problem named after mathematician Tosio Kato, of the University of California, Berkeley. Kato initially posed the problem in 1953.

In mathematics, the n! conjecture is the conjecture that the dimension of a certain bi-graded module of diagonal harmonics is n!. It was made by A. M. Garsia and M. Haiman and late…

In mathematics, the Milnor conjecture was a proposal by John Milnor of a description of the Milnor K-theory (mod 2) of a general field F with characteristic different from 2, by me…

In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscop…

Peter David Lax was a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics.

In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3-manifold with infinite fundamental group ha…

In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively elementary formulation and…

The Gaussian correlation inequality (GCI), formerly known as the Gaussian correlation conjecture (GCC), is a mathematical theorem in the fields of mathematical statistics and conve…

In mathematics, a sign sequence, or ±1–sequence or bipolar sequence, is a sequence of numbers, each of which is either 1 or −1. One example is the sequence.

Ganea's conjecture is a now disproved claim in algebraic topology. It states that

In mathematics, Nikiel's conjecture in general topology was a conjectural characterization of the continuous image of a compact total order. The conjecture was first formulated by…

In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with i…

In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere.

In geometric topology, the spherical space form conjecture states that a finite group acting on the 3-sphere is conjugate to a group of isometries of the 3-sphere.

In mathematics, the cobordism hypothesis, due to John C. Baez and James Dolan, concerns the classification of extended topological quantum field theories (TQFTs). In 2008, Jacob Lu…

In mathematics, the Atiyah conjecture is a collective term for a number of statements about restrictions on possible values of -Betti numbers.

In mathematics, the Ehrenpreis conjecture of Leon Ehrenpreis states that for any K greater than 1, any two closed Riemann surfaces of genus at least 2 have finite-degree covers whi…

In differential geometry, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S3. The conjecture was featured by the Australian…

In topology, an area of mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is…

In computational complexity, the sensitivity theorem, proved by Hao Huang in 2019, states that the sensitivity of a Boolean function $f\colon \{0,1\}^{n}\to \{0,1\}$ is at least th…

The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of al…

In mathematics, the Burr–Erdős conjecture was a problem concerning the Ramsey number of sparse graphs. The conjecture is named after Stefan Burr and Paul Erdős, and is one of many…

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers $a,b,c,n$ with $n>2$ such that…