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

If anyone needs the axiom “Tell me who you’re with, and I’ll tell you who you are” whispered to them every morning as a reminder to do better, it’s Spencer Pratt.

From Los Angeles Times ● May 19, 2026

The old axiom is to be greedy when others are fearful.

From The Wall Street Journal ● Apr. 15, 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

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

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

Even the 2,500-year-old Greek idea of an axiomatic geometry—a few self-evident axioms being assumed, and from them the theorems being derived by logic alone—is not being effectively taught in secondary school.

From "Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen Paulos

Related Words

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