axiom

American  

[ak-see-uhm] / ˈæk si əm /

noun

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.

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

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

A fundamental axiom of economics is that when two individuals or countries trade, both are better off.

From The Wall Street Journal • Dec. 6, 2025

Under Lasorda’s axiom, no team wins more than two-thirds of its games.

From Los Angeles Times • Mar. 29, 2025

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

This violates a basic principle of numbers called the axiom of Archimedes, which says that if you add something to itself enough times, it will exceed any other number in magnitude.

From "Zero: The Biography of a Dangerous Idea" by Charles Seife

Related Words

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