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 key foundation for understanding why time seems to move in one direction is Boltzmann's H theorem, a central principle in statistical mechanics tied to the second law of thermodynamics.

From Science Daily • May 3, 2026

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

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

From BBC • Oct. 9, 2025

When she looked, he pointed to a page with the Pythagorean theorem.

From "Out of Darkness" by Ashley Hope Pérez

Related Words

• axiom