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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
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 ...
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.
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 ...
Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic) Cramér’s decomposition theorem ; Cramér's theorem (large deviations) (probability) Cramer's theorem (algebraic curves) (analytic geometry) Cramér–Wold theorem (measure theory) Critical line theorem (number theory) Crooks fluctuation theorem
Many mathematicians then attempted to construct elementary proofs of the theorem, without success. G. H. Hardy expressed strong reservations; he considered that the essential "depth" of the result ruled out elementary proofs: No elementary proof of the prime number theorem is known, and one may ask whether it is reasonable to expect one.
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.
Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. [2] Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.