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As reformulated, it became the "paving conjecture" for Euclidean spaces, and then a question on random polynomials, in which latter form it was solved affirmatively. 2015: Jean Bourgain, Ciprian Demeter, and Larry Guth: Main conjecture in Vinogradov's mean-value theorem: analytic number theory: Bourgain–Demeter–Guth theorem, ⇐ decoupling ...
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 ...
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers .
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. [ 1 ] [ 2 ] It is stated in terms of three positive integers a , b {\displaystyle a,b} and c {\displaystyle c} (hence the name) that are relatively prime and satisfy a ...
The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. [1] [2] Since 1997, Beal has offered a monetary prize for a peer-reviewed proof of this conjecture or a counterexample. [3] The value of the prize has increased several times and is currently $1 ...
In mathematics, the common fixed point problem is the conjecture that, for any two continuous functions that map the unit interval into itself and commute under functional composition, there must be a point that is a fixed point of both functions.