Axiom. The word 'Axiom' is derived from the Greek word 'Axioma' meaning 'true without needing a proof'. A mathematical statement which we assume to be true without a proof is called an axiom. Therefore, they are statements that are standalone and indisputable in their origins.

Are axioms accepted without proof?

axiom, in mathematics and logic, general statement accepted without proof as the basis for logically deducing other statements (theorems). ... The axioms should also be consistent; i.e., it should not be possible to deduce contradictory statements from them.

Do theorems require proof?

A theorem is a statement that has been proven to be true based on axioms and other theorems. A proposition is a theorem of lesser importance, or one that is considered so elementary or immediately obvious, that it may be stated without proof.