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In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [ 1 ] [ 2 ] [ 3 ] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem , proven in 1995 by Andrew Wiles ), have shaped much of mathematical history as new areas of mathematics are developed in ...
Uniformity conjecture: diophantine geometry: n/a: Unique games conjecture: number theory: n/a: Vandiver's conjecture: number theory: Ernst Kummer and Harry Vandiver: Virasoro conjecture: algebraic geometry: Miguel Ángel Virasoro: Vizing's conjecture: graph theory: Vadim G. Vizing: Vojta's conjecture: number theory: ⇒abc conjecture: Paul ...
In mathematics, Thurston's geometrization conjecture (now a theorem) states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces , which states that every simply connected Riemann surface can be ...
The Poincaré conjecture was a mathematical problem in the field of geometric topology. In terms of the vocabulary of that field, it says the following: Poincaré conjecture. Every three-dimensional topological manifold which is closed, connected, and has trivial fundamental group is homeomorphic to the three-dimensional sphere.
Kawamata–Viehweg vanishing theorem (algebraic geometry) Kawasaki's theorem (mathematics of paper folding) Kelvin's circulation theorem ; Kempf–Ness theorem (algebraic geometry) Kepler conjecture (discrete geometry) Kharitonov's theorem (control theory) Khinchin's theorem (probability) Killing–Hopf theorem (Riemannian geometry)
The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.
In 2001, the proof of the local Langlands conjectures for GL n was based on the geometry of certain Shimura varieties. [27] In the 2010s, Peter Scholze developed perfectoid spaces and new cohomology theories in arithmetic geometry over p-adic fields with application to Galois representations and certain cases of the weight-monodromy conjecture ...
Keller's conjecture was shown to be true in dimensions at most six by Perron (1940a, 1940b).The disproof of Keller's conjecture, for sufficiently high dimensions, has progressed through a sequence of reductions that transform it from a problem in the geometry of tilings into a problem in group theory and, from there, into a problem in graph theory.