# theorem

/ˈθɪɹəm/ (US) · /θˈiəɹəm/ (UK)

Source: https://englishreference.com/word/theorem
Updated: 2026-06-20

## Senses

### 1. proven math statement

noun · CEFR B2

a mathematical rule or statement that has been proven to be true using facts and logic.

For teachers: a mathematical proposition of significant importance that has been demonstrated to be true through a formal proof.

- In school, we learned how to use Pythagoras' theorem to find the length of a triangle's side.
- The mathematician spent decades attempting to provide a definitive proof for the theorem, which had remained a conjecture since the seventeenth century.

### 2. logical deduction

noun · CEFR C1 · Technical · Academic

a statement in logic that follows correctly from a set of starting rules.

For teachers: a formula or statement within a formal system that is derived from the axioms of that system by applying its rules of inference.

- The computer program checked if the new statement was a valid theorem of the system.
- In formal logic, a theorem is distinguished from an axiom by the fact that it must be derived through a sequence of valid transformations.

### 3. to make into a theorem

verb · CEFR C2 · Technical · Formal

to turn a mathematical idea or rule into a formal theorem.

For teachers: to formulate a proposition or set of observations into a formal mathematical theorem.

- The researcher attempted to theorem the observed patterns in the data.
- The author sought to theorem the preliminary findings, though the complexity of the variables made a formal proof exceptionally difficult to construct.

Usage: This verb is rare and almost exclusively found in academic or historical mathematical texts.

## Examples

- The teacher explained the Pythagorean theorem in class today.
- After years of research, the mathematician finally published a complete proof for the new theorem.
- While a conjecture is merely a hypothesis that appears likely to be true, a theorem requires a formal demonstration of its validity within a specific logical framework.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.