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

Once that axiom is treated as constitutional common sense, public safety appears already on the side of the enforcement vehicle.

From Slate ● Jul. 27, 2026

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

From Salon ● Jul. 14, 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

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

This was an axiom in videogames, and would be until humans invented true artificial intelligence.

From "Ready Player One: A Novel" by Ernest Cline

Pathway has identified what Stamirowska calls equations of reasoning, fundamental mathematical axioms that explain how intelligence emerges from smaller, local interactions in the brain, she said.

From The Wall Street Journal ● Dec. 1, 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

However, I believe there may not be any single formulation of the fundamental theory any more than, as Godel showed, one could formulate arithmetic in terms of a single set of axioms.

From "A Brief History of Time: And Other Essays" by Stephen Hawking

Related Words

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