What does theorem mean?
A theorem is a statement that has been formally established as true, especially through mathematical or logical proof. In its dominant technical sense, a theorem follows from axioms, definitions, or previously proved results; familiar examples include the Pythagorean theorem and the fundamental theorem of calculus. The word also has a broader meaning of a principle or general truth considered reliable, as in philosophical or historical discourse, though this usage is less exact. A theorem differs from a theory: a theory is an organized body of explanations, whereas a theorem is a specific proposition within a system of reasoning. It also differs from a lemma, which commonly serves as an intermediate result in a larger proof. “Theorem” belongs mainly to formal academic language and carries an air of authority because it names something demonstrated rather than merely proposed. Recognizing the word and its technical distinction helps readers identify the status and function of claims in mathematical, philosophical, and scientific arguments.
nounIn mathematics and logic, a theorem is a proposition that has been proved to be true by means of an argument, often from axioms or previously established results.
- A proposition in mathematics or logic that has been proved from axioms or other established results.
- A principle or general statement regarded as a reliable truth.
"The fundamental theorem of calculus provides the mathematical foundation for the relationship between differentiation and integration."
"The fundamental theorem of calculus links differentiation and integration."
"The team checked the proof of the theorem line by line before accepting it."
The standard plural is theorems, with no change to the ending.
"Several important theorems were proved during the seminar."
The word theorem comes from Greek for “something to look at”—mathematics turned looking into proof.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does theorem come from?
Theorem entered English in the late 16th century from Latin theoremema, a Latinized form of Greek θεώρημα (theōrēma), meaning “something to look at” or a proposition for examination. It was ultimately associated with the Greek verb theorein, “to look at,” and with theoros, “a spectator.” The mathematical sense developed as a proposition established through proof. The same Greek foundation also underlies theory and theoretical, which likewise relate to observation, contemplation, and explanatory systems.
Related word forms
How theorem is actually used
The word is formal and is used chiefly in mathematics, logic, and scholarly writing. In technical usage, it specifically denotes a proved result, although broader senses occur in general writing.
Easily confused with theorem
A theorem is an established and proved result, whereas a lemma is usually a preliminary statement proved for use in proving a larger theorem.
A theorem is a specific proposition that has been proved, while a theory is a broader explanatory framework consisting of principles and supporting evidence.