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The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. 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 ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Kong posted the puzzle following a debate with his wife, and he incorrectly thought it to be part of a mathematics question for a primary school examination, aimed at 10- to 11-year-old students, [5] although it was actually part of the 2015 Singapore and Asian Schools Math Olympiad meant for 14-year-old students, a fact later acknowledged by ...
This problem concerns the issue of whether questions that are easy to verify (a class of queries called NP) also have solutions that are easy to find (a class called P). Hosch, William L (11 August 2009). "P versus NP problem mathematics". Encyclopædia Britannica "P vs NP Problem". www.claymath.org (Cook, Levin)
The American Invitational Mathematics Examination (AIME) is a selective 15-question, 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics examination (formerly known as the AHSME), and starting in 2010, those who rank in the top 2.5% on the AMC 10. Two different versions of the test are administered ...
Problems 1, 2, 5, 6, [a] 9, 11, 12, 15, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis), 13 and 16 [b] unresolved. Problems 4 and 23 are considered as too vague to ever be described as solved; the withdrawn 24 would also be in ...
The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler , in 1736, [ 1 ] laid the foundations of graph theory and prefigured the idea of topology .
An example of the second case is the decidability of the first-order theory of the real numbers, a problem of pure mathematics that was proved true by Alfred Tarski, with an algorithm that is impossible to implement because of a computational complexity that is much too high. [122]
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