Theorem-proving

Mathematicians, logicians, and others who prove theorems seek to establish chains of reasoning that are convincing to others.

There are many ways to prove a theorem, including:

• Reductio ad absurdum: If we can show that the assumption that our hypothesis is false leads to a contradiction, it follows that the hypothesis must be true.
• Mathematical induction

In mathematical logic, a derivation is defined as a sequence of statements, each of which is either 1) an assumption, 2) a tautology, or 3) follows from two previous statements by the rule of modus ponens - the idea is that the statements form a tree, with assumptions and tautologies at the leaves. A theorem is any statement which has a derivation.

Closely related to theorem proving is automated theorem proving.

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