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This is a list of unusually long mathematical proofs.Such proofs often use computational proof methods and may be considered non-surveyable.. As of 2011, the longest mathematical proof, measured by number of published journal pages, is the classification of finite simple groups with well over 10000 pages.
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 ...
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.
Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges
The proof is based on the distribution of parity vectors and uses the central limit theorem. In 2019, Terence Tao improved this result by showing, using logarithmic density , that almost all (in the sense of logarithmic density) Collatz orbits are descending below any given function of the starting point, provided that this function diverges to ...
His rather complicated proof was simplified in 1840 by Lebesgue, [109] and still simpler proofs [110] were published by Angelo Genocchi in 1864, 1874 and 1876. [111] Alternative proofs were developed by Théophile Pépin (1876) [112] and Edmond Maillet (1897). [113] Fermat's Last Theorem was also proved for the exponents n = 6, 10, and 14.
The proof is an extension of ... The Green–Tao paper states 'At the time of writing the longest known arithmetic progression of ... Clay Mathematics Proceeding. ...
List of mathematical functions; List of mathematical identities; List of mathematical proofs; List of misnamed theorems; List of scientific laws; List of theories; Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.