A mathematical proof is a deductive argument that shows a statement must be true in every possible case, because its stated assumptions logically guarantee its conclusion. It differs from empirical evidence: presenting many confirming examples is not enough for a proof, which reasons instead by exhaustive deductive logic from axioms and previously proved statements through valid steps of inference to reach a conclusion with certainty rather than reasonable expectation. This axiomatic method was formalized by Euclid in the Elements around 300 BCE, beginning from a small set of postulates and common notions and building the whole of ancient geometry from them by explicit, checkable steps, and it remains the standard by which mathematical knowledge is distinguished from mere plausibility today.
Facts
Proposed ByScoped to formal, systematic deductive proof from stated axioms as a mathematical method, established in Euclid's Elements, circa 300 BC; proof by informal or empirical demonstration is far older and has no single credited originator. Connections
Associated With
Euclid, Scientists Euclid's Elements (c. 300 BCE) systematized geometric knowledge into an axiomatic-deductive proof structure that became the template for mathematical proof.
Theorem, Concepts A theorem is a statement established as true by a mathematical proof
Studied In
Source Euclid (MacTutor)
Sources
1. Euclid (MacTutor)
MacTutor History of Mathematics, University of St AndrewsBiography sectionQuote, Biography section
These are not specific geometrical properties but rather general assumptions which allow mathematics to proceed as a deductive science.
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