theorem

American  

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

noun

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

• theorematic adjective
• theorematically adverb

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

A fundamental and powerful concept in probability is Bayes’s theorem, developed by the 18th-century statistician Thomas Bayes.

From The Wall Street Journal • Mar. 29, 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

He and Qin found, however, that this is not correct because the theorem does not take into account, mathematically, that photon electric fields can rotate.

From Science Daily • May 23, 2024

However, one cannot really argue with a mathematical theorem.

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

Related Words

• axiom