theorem

American  

[thee-er-uhm, theer-uhm] / ˈθi ər əm, ˈθɪər əm /

noun

• theorems
  plural

1. Mathematics. a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas.

2. a rule or law, especially one expressed by an equation or formula.

3. Logic. a proposition that can be deduced from the premises or assumptions of a system.

4. an idea, belief, method, or statement generally accepted as true or worthwhile without proof.

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theorem British  

/ ˈθɪərəm /

noun

1. maths logic a statement or formula that can be deduced from the axioms of a formal system by means of its rules of inference

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theorem Scientific  

/ thē′ər-əm,thîr′əm /

1. A mathematical statement whose truth can be proved on the basis of a given set of axioms or assumptions.

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theorem Cultural  

1. A statement in mathematics that is not a basic assumption, such as an axiom, but is deduced (see deduction) from basic assumptions.

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Other Word Forms

Derived Forms

• theorematic
  adjective
• theorematically
  adverb

Inflected Forms

Nouns

• theorems
  plural

Etymology

Origin of theorem

1545–55; < Late Latin theōrēma < Greek theṓrēma spectacle, hence, subject for contemplation, thesis (to be proved), equivalent to theōrē-, variant stem of theōreîn to view + -ma noun suffix

Explanation

A theorem is a proposition or statement that can be proven to be true every time. In mathematics, if you plug in the numbers, you can show a theorem is true. Just as a theory is an idea that can be supported or disproved, a theorem is also an idea, but it's one that has been proven and can be demonstrated again and again if used properly. In math class, you might have learned some theorems. One example is the Pythagorean theorem, which can be represented as A squared plus B squared equals C squared. Although it’s usually used in math, theorems can be laws, rules, formulas, or even logical deductions.

Example Sentences

See Examples For:

theorem theorems

In Bayes’ theorem, “priors” are initial predictions about an event, which we update as new information becomes available.

From The Wall Street Journal ● May 16, 2026

However, the H theorem itself is time-symmetric, meaning it does not prefer one direction of time over another.

From Science Daily ● May 3, 2026

AI can’t sit with a student after class and talk through a complex theorem until the child finally gets it.

From MarketWatch ● Mar. 9, 2026

The meaning of life, the laws of general relativity, quantum mechanics, Fermat's last theorem.

From BBC ● Oct. 9, 2025

The “no hair” theorem is of great practical importance, because it so greatly restricts the possible types of black holes.

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

“He was a war hero and a Renaissance man that did math theorems while he was in Congress and who could recite Homer from memory,” he says.

From Los Angeles Times ● Nov. 6, 2025

Participants worked through undergraduate-level mathematical theorems with the assistance of an LLM and were asked to rate each individual LLM response for correctness and helpfulness.

From Science Daily ● Jun. 4, 2024

The halting problem is a direct application of mathematician Kurt Gödel’s incompleteness theorems, which state that not all mathematical statements can be proved.

From Scientific American ● May 23, 2023

Rambling conversations on aliens and math theorems, time travel and TED talks, contribute to an atmosphere in which everything feels unstable, not least the men’s sanity.

From New York Times ● Nov. 3, 2022

I started to think a lot about infinity, and what it was like there, and how all the postulates and theorems and principles were true across all the universe.

From "October Sky" by Homer Hickam

Related Words

• axiom