Difference Between Axiom and Theorem

The terms “axiom” and “theorem” are often used in fields of study such as mathematics, physics and logic. Both have a certain relationship, however it is important to understand that they are not synonymous words; therefore, they do not describe the same thing. Difference Between Axiom and Theorem

To clarify a bit the confusion you may have around this topic, below we explain what the difference between axiom and theorem is.

AXIOM  Difference Between Axiom and Theorem

An axiom is a statement that is accepted as true without needing to be proved. It does not require any proof and is universally accepted, since its non-acceptance would contradict all logic.

The axioms have no contradiction and are obvious to anyone without the need for any deep analysis of things. Some examples of axioms are as follows:

  • The whole is greater than any of its parts.
  • A proposition cannot be true and false at the same time.
  • Two straight lines cannot enclose a space.


Examples of axioms can be 3+3=6, 2*2=6 etc. We have a similar statement that a line can extend to infinity, in geometry. This is an Axiom because you do not need a proof to state its truth as it is evident in itself.


On the other hand, theorems are theoretical proposals that require verification. Unlike axioms, they are not automatically accepted, but are subjected to tests from which the results that support the theory are extracted.

The theorems are made up of two parts: hypotheses and conclusions. Among the examples of theorems, one of the best known is the Pythagorean Theorem.

In this article I have tried to discuss and explain the proper definition of axiom, theorem and also highlight their main differences I hope you all will get it better.

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