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

When she dropped out to start Axiom Math, she raised $64 million, poached a handful of Meta’s AI researchers—and hired her mentor.

From The Wall Street Journal • Dec. 4, 2025

Additionally, Lonestar Data Holdings said in March that it had successfully tested a small data center on the moon, while Axiom Space launched an orbital-data-center prototype to the International Space Station in August.

From MarketWatch • Nov. 20, 2025

But Vast faces fierce competition from other contenders, including Axiom Space, Voyager Space in partnership with Airbus, and Amazon founder Jeff Bezos's Blue Origin.

From Barron's • Nov. 13, 2025

The crew were seen floating in the spacecraft on Thursday in a video shared by private firm Axiom Space.

From BBC • Jun. 26, 2025

In Axiom 1 this operation is addition, in Axiom 2 it is subtraction, and so on.

From The Teaching of Geometry by Smith, David Eugene

Related Words

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