Mathematical proofs

rigorous demonstration that a mathematical statement follows from its premises

thumb|The Pythagorean theorem has at least 370 known proofs.

theorem that describes the result of performing the same experiment a large number of times

Q.E.D. or QED is an initialism of the Latin phrase , meaning "that which was to be demonstrated". Literally, it states "what was to be shown". Traditionally, the abbreviation is placed at the end of mathematical proofs and philosophical arguments in print publications, to indicate that the proof or the argument is complete.

study of classes of mathematical structures from the perspective of mathematical logic

proof technique in set theory

collection of maps in which all map compositions starting from the same set and ending with the same set give the same result

A proof by contradiction used to show that a statement cannot be true for all numbers. If a statement is true for one number, it will also be true for a smaller number, up to infinity, leading to a contradiction and disproving the original statement.

Way of arriving to a mathematical proof

symbol used in mathematics and typography

method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object

form of mathematical proof

scientific theory rejected by modern mainstream scientific consensus

proof by examining all individual cases

book about mathematical proofs by Martin Aigner and Günter M. Ziegler

Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as mathematical proofs which must maintain consistent answers; or socially imposed, such as the process of defining ethics and law.

mathematical proof expressed visually

technique for proving that two expressions are equal by showing that they both count the size of the same set

proof technique in combinatorics that finds a bijection between the things to be counted and some easily countable things

nonconstructive method for mathematical proofs

Mathematical proof using only basic techniques.

type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof

formal proof

result demonstrating that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general

Wiles' article