Proof
A proof is a chain of reasoning showing that a statement follows with certainty from things already accepted. Every step has to be justified by a definition, an axiom, or a result already proved, so that anyone who grants the starting points is forced to grant the conclusion. This is what separates mathematics from evidence gathering. Checking a claim for the first billion numbers is not a proof, and one valid argument settles it for all numbers at once.
Why it matters
Proof is the standard every mathematical claim is held to, so knowing what one is tells you what a mathematical text is trying to do on each of its pages.
Also written: proofs, mathematical proof
Where it comes up
Sources
- Mathematical proof WikipediaCovers the standard proof methods, direct, contradiction, and induction, with examples.
- Philosophy of Mathematics Stanford Encyclopedia of PhilosophyExplains why the demand for proof took the shape it did, and what is still argued about it.
