In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism...

problems in mathematics The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple...

In the mathematical field of geometric topology, the Poincaré conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about...

for the section conjecture", Lecture Notes in mathematics 2054, Springer 2013 (Habilitation thesis) "The Brauer–Manin obstruction for sections of the fundamental...

analysis of Ricci flow, and proved the Poincaré conjecture and Thurston's geometrization conjecture, the former of which had been a famous open problem...

2000, six remain unsolved to date: Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis...

contain at least m primes. Moreover (see also the next section) assuming the Elliott–Halberstam conjecture and its generalized form, the Polymath Project wiki...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b,...

William Thurston's elliptization conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of...

statement was known as the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture, or the modularity conjecture for elliptic curves. The theorem states...

Galois groups of number fields and mixed-characteristic local fields. Section conjecture Class field theory Fiber functor Neukirch–Uchida theorem Belyi's theorem...

problems in mathematics In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even...

principal Scheme (mathematics) Section conjecture Semistable abelian variety Sheaf cohomology Stack (mathematics) Standard conjectures on algebraic cycles Sketch...

Andrica's conjecture (named after Romanian mathematician Dorin Andrica (es)) is a conjecture regarding the gaps between prime numbers. The conjecture states...

the zero section. More unsolved problems in mathematics In mathematics, more specifically symplectic topology, the nearby Lagrangian conjecture, is an open...

Unique Games Conjecture true? More unsolved problems in computer science In computational complexity theory, the unique games conjecture (often referred...

field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee...

. {\displaystyle 2k.} Andrica's conjecture, Brocard's conjecture, Legendre's conjecture, and Oppermann's conjecture all suggest that the largest gaps...

In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them...

also commonly written as ln(x) or loge(x). In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an...

In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology...

This was conjectured in 1922 by Louis Mordell, and known as the Mordell conjecture until its 1983 proof by Gerd Faltings. The conjecture was later generalized...

problems in mathematics The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer n {\displaystyle...

field extensions). Anabelian geometry, for example Grothendieck's section conjecture, seeks to identify classes of varieties which are determined by their...

a high asymptotic density of them, although there is a well-supported conjecture as to what that asymptotic density should be. In 1932, 31 years prior...

SYZ conjecture is an attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics. The original conjecture was...

Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime...

In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential...

Rota's excluded minors conjecture is one of a number of conjectures made by the mathematician Gian-Carlo Rota. It is considered an important problem by...

In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that...