An axiom is a statement or proposition that is accepted as being self-evidently true without the need for proof. Axioms serve as the foundational truths or starting points from which a mathematical or logical system is developed.

Axioms should not be confused with theorems, which are statements that require a proof, typically derived from the axioms of the system. In other words, axioms are the starting points, while theorems are the end points.

A postulate, also known as an axiom, is a statement that is assumed to be true without proof. Postulates are the foundational assumptions upon which a mathematical or logical system is built. They serve as the starting points from which other truths can be logically deduced.

A theorem is a statement that has been proven to be true within the framework of a mathematical system, based on the system's axioms and previously established theorems. Theorems are central to mathematics because they establish truths that we can rely on for solving problems and understanding the structure of mathematical systems.