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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. There are several proofs that would be far longer than this if the details of the computer ...
[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics". [8] However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results.
Bertrand's postulate and a proof; Estimation of covariance matrices; 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
The equation is wrong, but it appears to be correct if entered in a calculator with 10 significant figures. [192] In the Star Trek: The Next Generation episode "The Royale", Captain Picard states that the theorem is still unproven in the 24th century. The proof was released five years after the episode originally aired. [193]
P. Oxy. 29, one of the oldest surviving fragments of Euclid's Elements, a textbook used for millennia to teach proof-writing techniques. The diagram accompanies Book II, Proposition 5. [1] A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the
A consequence of the classification of finite simple groups, completed in 2004 by the usual standards of pure mathematics. 2004: Adam Marcus and Gábor Tardos: Stanley–Wilf conjecture: permutation classes: Marcus–Tardos theorem 2004: Ualbai U. Umirbaev and Ivan P. Shestakov: Nagata's conjecture on automorphisms: polynomial rings: 2004
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. [1]
Green and Tao's proof has three main components: Szemerédi's theorem , which asserts that subsets of the integers with positive upper density have arbitrarily long arithmetic progressions. It does not a priori apply to the primes because the primes have density zero in the integers.