axiom

American  

[ak-see-uhm] / ˈæk si əm /

noun

axioms plural

1. a self-evident truth that requires no proof.

2. a universally accepted principle or rule.

3. Logic, Mathematics. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.

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axiom British  

/ ˈæksɪəm /

noun

1. a generally accepted proposition or principle, sanctioned by experience; maxim

2. a universally established principle or law that is not a necessary truth

   the axioms of politics

3. a self-evident statement

4. logic maths a statement or formula that is stipulated to be true for the purpose of a chain of reasoning: the foundation of a formal deductive system Compare assumption

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axiom Scientific  

/ ăk′sē-əm /

1. A principle that is accepted as true without proof. The statement “For every two points P and Q there is a unique line that contains both P and Q” is an axiom because no other information is given about points or lines, and therefore it cannot be proven.

2. Also called postulate

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axiom Cultural  

1. In mathematics, a statement that is unproved but accepted as a basis for other statements, usually because it seems so obvious.

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Discover More

The term axiomatic is used generally to refer to a statement so obvious that it needs no proof.

Other Word Forms

Noun Inflected Forms

• axioms
  plural

Etymology

Origin of axiom

First recorded in 1475–85; from Latin axiōma, from Greek: “something worthy,” equivalent to axiō-, variant stem of axioûn “to reckon worthy” + -ma, noun suffix

Explanation

An axiom is a statement that everyone believes is true, such as "the only constant is change." Mathematicians use the word axiom to refer to an established proof. The word axiom comes from a Greek word meaning “worthy.” An axiom is a worthy, established fact. For philosophers, an axiom is a statement like “something can’t be true and not be true at the same time.” An example of a mathematical axiom is “a number is equal to itself.” In everyday usage, an axiom is just a common saying, but it’s one that pretty much everyone agrees on.

Example Sentences

See Examples For:

axiom axioms

There is an old military axiom: The enemy gets a vote too.

From Salon ● Jul. 14, 2026

It is a well-established baseball axiom that after 1,000 plate appearances, you are what your statistics say you are.

From The Wall Street Journal ● Jul. 1, 2026

For a decade, the global luxury industry operated on a simple axiom: As China goes, so goes the bottom line.

From MarketWatch ● Jan. 27, 2026

If Ben Franklin were alive today, he might add a third certainty to his now-familiar axiom: death, taxes, and the late-summer creep of Spirit Halloween filling in vacant retail storefronts across the country.

From Slate ● Oct. 10, 2024

With the feeling that he was speaking to O’Brien, and also that he was setting forth an important axiom, he wrote: Freedom is the freedom to say that two plus two make four.

From "1984" by George Orwell

But the math professor who’s now working for a math startup did share one of his own axioms.

From The Wall Street Journal ● Dec. 4, 2025

Their mathematics and geometry, built on logical proofs from axioms, remain eternal.

From Slate ● Sep. 26, 2025

One of the key axioms of politics in our, and any other, era is that nothing lasts forever.

From Salon ● Jun. 2, 2025

“One of the axioms of the system of international relations is that such a system is intrinsically anarchic.”

From Seattle Times ● Sep. 20, 2023

The new science often presented itself as a system of axioms and demonstrations, in Galileo’s Two New Sciences for example, or Newton’s Principia, but it was always grounded in facts and, less surely, in analogies.

From "The Invention of Science" by David Wootton

Related Words

• adage
• aphorism
• dictum
• maxim
• precept
• proverb
• theorem