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

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

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 Bell theorem refers to how entangled electrons are predicted by quantum mechanics, making them non-local — often referred to as “spooky action at a distance.”

From Salon ● Nov. 13, 2024

Every theorem in Euclidean geometry can be dualized in projective geometry, setting up a whole set of new theorems in the parallel universe of projective geometry.

From "Zero: The Biography of a Dangerous Idea" by Charles Seife

"Drawing on mathematical theorems related to incompleteness and indefinability, we demonstrate that a fully consistent and complete description of reality cannot be achieved through computation alone," explains Dr. Faizal.

From Science Daily ● Nov. 10, 2025

“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

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

One of the most commonly used books in high school geometry classes makes use of more than a hundred axioms to prove a similar number of theorems!

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

Related Words

• axiom