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Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should ...
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
99 Variations on a Proof is a mathematics book by Philip Ording, in which he proves the same result in 99 different ways. Ording takes an example of a cubic equation , x 3 − 6 x 2 + 11 x − 6 = 2 x − 2 , {\displaystyle x^{3}-6x^{2}+11x-6=2x-2,} and shows that its solutions are x = 1 {\displaystyle x=1} and x = 4 {\displaystyle x=4} using a ...
It is to be regretted that this first comprehensive and thorough-going presentation of a mathematical logic and the derivation of mathematics from it [is] so greatly lacking in formal precision in the foundations (contained in 1– 21 of Principia [i.e., sections 1– 5 (propositional logic), 8–14 (predicate logic with identity/equality), 20 ...
The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something about everyday life, or when data used in an argument is numerical. It is sometimes also used to mean a "statistical proof" (below), especially when used to argue from data.
Pages which contain only proofs (of claims made in other articles) should be placed in the subcategory Category:Article proofs. Pages which contain theorems and their proofs should be placed in the subcategory Category:Articles containing proofs. Articles related to automatic theorem proving should be placed in Category:Automated theorem proving.