Changes

==Mathematical proof==

==Mathematical proof==

A mathematical proof is a step-by-step demonstration of the truth of a mathematical theorem. Proofs build on [[axiom | axioms]], which are statements that are assumed to be true without proof, as well as previously-proved [[theorem | theorems]].

A mathematical proof is a step-by-step demonstration of the truth of a mathematical theorem. Proofs build on [[axiom]]s, which are statements that are assumed to be true without proof, as well as previously-proved [[theorem]]s.

Several types of proofs are widely used, such as [[Reductio Ad Absurdum | proof by contradiction]]

Several types of proofs are widely used, such as [[proof by contradiction]]

and [[proof by induction | proof by induction]]. Proofs that do not rely on distant fields of maths are sometimes called [[elementary proof | elementary proofs]].  

and [[proof by induction]]. Proofs that do not rely on contested fields of maths are sometimes called [[elementary proof]]s.

==Scientific proof==

==Scientific proof==

Unlike the [[theorem | theorems]] of [[mathematics | mathematics]], [[science | science]] does not seek to prove that its [[theory | theories]] are true. Instead, the [[scientific method | scientific method]] seeks to check whether the predictions implied by a theory are observed in nature. Therefore, as philosopher of science [[Karl Popper | Karl Popper]] argued, science can only hope to show that a theory is false. But scientists recognize that science ''can never prove'' that a theory is true in the same sense that a mathematical theorem is true. Therefore scientists never claim that their theories are [[fact | facts]]. Instead, science searches for theories that are not disproved by currently-known experimental observations. Insofar as theories are consistent with nature, they may serve as a guide to improve [[technology | technology]] for example and can be considered as true in laymen's terms.

Unlike the [[theorem]]s of [[mathematics]], [[science]] does not seek to prove that its [[theories]] are true. Instead, the [[scientific method]] seeks to check whether the predictions implied by a theory are observed in nature. Therefore, as philosopher of science [[Karl Popper]] argued, science can only hope to show that a theory is false. But scientists recognize that science ''can never prove'' that a theory is true in the same sense that a mathematical theorem is true. Therefore scientists never claim that their theories are [[fact]]s. Instead, science searches for theories that are not disproved by currently-known experimental observations. Insofar as theories are consistent with nature, they may serve as a guide to improve [[technology]] for example and can be considered as true in laymen's terms.

== Legal Proof ==

== Legal Proof ==