Proof

Mathematical proof

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

Several types of proofs are widely used, such as proof by contradiction and proof by induction. Proofs that rely only on certain simple forms of reasoning are sometimes called elementary proofs.

Andrew Schlafly cited the lack of a Wikipedia page on "elementary proof" as proof of bias in Wikipedia. Ironically, at that time Conservapedia did not even have a page on "proof".

Scientific proof

Unlike the theorems 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 show that a theory is false. But science can never prove that a theory is true.