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, ˌθɪərəˈmætɪk, ˌθɪəˈrɛmɪk /

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

A mistaken theorem can work its way into flawed financial, medical or engineering systems.

From The Wall Street Journal ● Jun. 14, 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

Known as the "infinite monkey theorem", the mathematical thought-experiment has long been used to explain the principles of probability and randomness.

From BBC ● Oct. 31, 2024

As Hobbes remarked of his friend, ‘Roberval has this peculiarity: whenever people publish any remarkable theorem they have discovered, he immediately announces, in papers which he distributes, that he discovered it first.’

From "The Invention of Science" by David Wootton

“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

As a result, mathematicians tended to keep their discoveries to themselves, deploying their theorems, corollaries and lemmas only to win intellectual battles.

From Scientific American ● Apr. 24, 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

According to the singularity theorems of classical general relativity, there would still have been a big bang singularity.

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

Related Words

• axiom