Standard Lemma guide

theorem

noun · verb · 6 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

UK: /ˈθiː.ə.ɹəm/
British, Southern, Standard: /ˈθɪːɹ(ə)m/
British, Southern, Standard: /ˈθɪjəɹ(ə)m/
Southern-England: Recorded audio is listed in the source snapshot.
US: /ˈθiərəm/
US: /ˈθɪrəm/
rhymes with (US) -ɪəɹəm
CMU ARPABET: TH IH1 R AH0 M Digits mark lexical stress: 1 primary, 2 secondary, 0 unstressed.

noun

Meaning 1

A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called lemmas.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

noun

Meaning 2

A mathematical statement that is expected to be true.

Definition source: English Wiktionary via Wiktextract

Usage: colloquial, nonstandard

Topics: mathematics, sciences

Examples

Fermat's Last Theorem was known thus long before it was proved in the 1990s.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

noun

Meaning 3

A syntactically correct expression that is deducible from the given axioms of a deductive system.

Definition source: English Wiktionary via Wiktextract

Topics: human-sciences, logic, mathematics, philosophy, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

verb

Meaning 4

To formulate into a theorem.

Definition source: English Wiktionary via Wiktextract

Usage: transitive

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

noun

Meaning 5

an idea accepted as a demonstrable truth

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Broader terms: idea, thought

Narrower terms: Bayes' theorem

noun

Meaning 6

a proposition deducible from basic postulates

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Broader terms: proposition

Narrower terms: binomial theorem

History

Etymology

From Middle French théorème, from Late Latin theōrēma, from Ancient Greek θεώρημα (theṓrēma, “speculation, proposition to be proved”) (Euclid), from θεωρέω (theōréō, “to look at, view, consider, examine”), from θεωρός (theōrós, “spectator”), from θέα (théa, “a view”) + ὁράω (horáō, “to see, look”). See also theory, and theater.

Across languages

Translations

111 source translations are retained for this English entry.

Albanian: teoremë — proved mathematical statement
Arabic: مُبَرْهَنَة (mubarhana) — proved mathematical statement
Arabic: نَظَرِيَّة (naẓariyya) — proved mathematical statement
Armenian: թեորեմ (tʻeorem) — proved mathematical statement
Azerbaijani: teorem — proved mathematical statement
Bashkir: теорема (teorema) — proved mathematical statement
Belarusian: тэарэ́ма (tearéma) — proved mathematical statement
Bengali: উপপাদ্য (upopaddo) — proved mathematical statement
Bulgarian: теоре́ма (teoréma) — proved mathematical statement
Catalan: teorema — proved mathematical statement
Chinese Mandarin: 定理 (dìnglǐ) — proved mathematical statement
Czech: věta — proved mathematical statement
Danish: teorem — proved mathematical statement
Danish: læresætning — proved mathematical statement
Dutch: theorema — proved mathematical statement
Dutch: stelling — proved mathematical statement
Esperanto: teoremo — proved mathematical statement
Estonian: teoreem — proved mathematical statement
Finnish: lause — proved mathematical statement
Finnish: teoreema — proved mathematical statement
French: théorème — proved mathematical statement
Galician: teorema — proved mathematical statement
Georgian: თეორემა (teorema) — proved mathematical statement
German: Theorem — proved mathematical statement
German: Satz — proved mathematical statement
German: Lehrsatz — proved mathematical statement
Greek: θεώρημα (theórima) — proved mathematical statement
Ancient Greek: θεώρημα (theṓrēma) — proved mathematical statement
Gujarati: પ્રમેય (prameya) — proved mathematical statement
Hebrew: מִשְׁפָּט (mishpát) — proved mathematical statement
Hindi: प्रमेय (pramey) — proved mathematical statement
Hungarian: tétel — proved mathematical statement
Icelandic: setning — proved mathematical statement
Icelandic: kennisetning — proved mathematical statement
Indonesian: teorema — proved mathematical statement
Irish: teoirim — proved mathematical statement
Italian: teorema — proved mathematical statement
Japanese: 定理 (teiri) — proved mathematical statement
Kazakh: теорема (teorema) — proved mathematical statement
Khmer: ទ្រឹស្ដីបទ (trɨhsdəybɑt) — proved mathematical statement
Korean: 정리 (jeongni) — proved mathematical statement
Northern Kurdish: teorem — proved mathematical statement
Kyrgyz: теорема (teorema) — proved mathematical statement
Lao: ທິດສະດີບົດ (thit sa dī bot) — proved mathematical statement
Latin: theōrēma — proved mathematical statement
Latvian: teorēma — proved mathematical statement
Lithuanian: teorema — proved mathematical statement
Macedonian: теоре́ма (teoréma) — proved mathematical statement
Malay: teorem — proved mathematical statement
Mongolian: теорем (teorem) — proved mathematical statement
Norwegian Bokmål: teorem — proved mathematical statement
Norwegian Bokmål: læresetning — proved mathematical statement
Norwegian Nynorsk: teorem — proved mathematical statement
Norwegian Nynorsk: læresetning — proved mathematical statement
Pashto: قضيه (qazya) — proved mathematical statement
Persian: قضیه (qaziye, qaziyye) — proved mathematical statement
Polish: twierdzenie — proved mathematical statement
Portuguese: teorema — proved mathematical statement
Romanian: teoremă — proved mathematical statement
Russian: теоре́ма (teoréma) — proved mathematical statement
Serbo-Croatian: теоре́ма — proved mathematical statement
Serbo-Croatian: тео̀ре̄м — proved mathematical statement
Serbo-Croatian: teoréma — proved mathematical statement
Serbo-Croatian: teòrēm — proved mathematical statement
Slovak: teorém — proved mathematical statement
Slovak: veta — proved mathematical statement
Slovene: izrek — proved mathematical statement
Slovene: teorem — proved mathematical statement
Spanish: teorema — proved mathematical statement
Swedish: teorem — proved mathematical statement
Swedish: lärosats — proved mathematical statement
Swedish: sats — proved mathematical statement
Tagalog: hunain — proved mathematical statement
Tajik: теорема (teorema) — proved mathematical statement
Tajik: қазия (qaziya) — proved mathematical statement
Thai: ทฤษฎีบท (trít-sà-dii-bòt) — proved mathematical statement
Turkish: teorem — proved mathematical statement
Turkmen: teorema — proved mathematical statement
Ukrainian: теоре́ма (teoréma) — proved mathematical statement
Urdu: قَضِیّہ (qaziyyā) — proved mathematical statement
Uyghur: تېئورېما (të'orëma) — proved mathematical statement
Uzbek: teorema — proved mathematical statement
Vietnamese: định lí — proved mathematical statement
Arabic: مُبَرْهَنَة (mubarhana) — mathematical statement that is expected to be true
Bulgarian: теорема (teorema) — mathematical statement that is expected to be true
Chinese Mandarin: 定理 (dìnglǐ) — mathematical statement that is expected to be true
Czech: teorém — mathematical statement that is expected to be true
Czech: teoréma — mathematical statement that is expected to be true
Dutch: vermoeden — mathematical statement that is expected to be true
Finnish: olettamus — mathematical statement that is expected to be true
French: théorème — mathematical statement that is expected to be true
German: Theorem — mathematical statement that is expected to be true
German: Satz — mathematical statement that is expected to be true
Greek: θεώρημα (theórima) — mathematical statement that is expected to be true
Hebrew: מִשְׁפָּט (mishpát) — mathematical statement that is expected to be true
Indonesian: teorema — mathematical statement that is expected to be true
Irish: teoirim — mathematical statement that is expected to be true
Japanese: 定理 (teiri) — mathematical statement that is expected to be true
Korean: 정리 (jeongni) — mathematical statement that is expected to be true
Malay: teorem — mathematical statement that is expected to be true
Norwegian Bokmål: teorem — mathematical statement that is expected to be true
Norwegian Bokmål: læresetning — mathematical statement that is expected to be true
Norwegian Nynorsk: teorem — mathematical statement that is expected to be true
Norwegian Nynorsk: læresetning — mathematical statement that is expected to be true
Portuguese: conjectura — mathematical statement that is expected to be true
Russian: теоре́ма (teoréma) — mathematical statement that is expected to be true
Spanish: teoría — mathematical statement that is expected to be true
Spanish: conjetura — mathematical statement that is expected to be true
Spanish: suposición — mathematical statement that is expected to be true
Spanish: especulación — mathematical statement that is expected to be true
Turkish: teorem — mathematical statement that is expected to be true

Word forms

Inflections and variants

theorems — plural
theorems — present, singular, third-person
theoreming — participle, present
theoremed — participle, past
theoremed — past

Word family

Derived and related words

Derived: antitheorem, countertheorem, metatheorem, nontheorem, theorematic, theoremhood, theoremic

Related: theoretical, theorize, theory, axiom, corollary, lemma, proof, proposition, definition, conjecture, law of nature, principle, equation, inequality, formula, mathematics, Special:Search/intitle:/ theorem/, Appendix:Roget MICRA thesaurus/Class IV § 454. Topic

Spelling and sound

Hyphenation and homophones

Hyphenation: the·o·rem

Semantic map

Other relationships

Hypernyms: statement, idea, thought, proposition

Hyponyms: Böhm-Jacopini theorem, structured program theorem, Aumann's agreement theorem, Bernoulli's theorem, binomial theorem, Carnot's theorem, central limit theorem, Ceva's theorem, Cook-Levin theorem, Cook's theorem, cosine theorem, De Morgan's theorem, double angle theorem, Dvoretzky's theorem, Eggan's theorem, Euclid's theorem, exterior angle theorem, extreme value theorem, Fermat's Last Theorem, first isomorphism theorem, Fisher-Tippett-Gnedenko theorem, Fisher-Tippett theorem, fundamental theorem, fundamental theorem of algebra, fundamental theorem of arithmetic, Gauss' theorem, Gleason's theorem, Gödel's incompleteness theorem, Gödel's theorem, Green's theorem, Haag's theorem, Hales-Jewett theorem, Hindman's theorem, Hirzebruch-Riemann-Roch theorem, inscribed angle theorem, intercept theorem, Kelvin-Stokes theorem, Knaster-Tarski theorem, Lagrange's theorem, Menelaus' theorem, Milliken-Taylor theorem, Nernst heat theorem, Paris-Harrington theorem, Parthasarathy's theorem, Pythagoras' theorem, Rado-Folkman-Sanders theorem, Rado's theorem, Schur's theorem, sine theorem, Sinkhorn's theorem, Stokes' theorem, Stone-Weierstrass theorem, Szemerédi's theorem, Thales' theorem, time hierarchy theorem, Tonelli's theorem, Turán's theorem, Van der Waerden's theorem, Abel-Ruffini theorem, Abel's impossibility theorem, Abel's irreducibility theorem, Abel's theorem, Arrow's theorem, Atiyah-Singer index theorem, Ax-Grothendieck theorem, Ax-Kochen theorem, bathtub theorem, Bayes' theorem, Bell-Kochen-Specker theorem, Bell's theorem, Belyi's theorem, Bertrand-Chebyshev theorem, Bézout's theorem, Bloch's theorem, Blum's speedup theorem, Bogoliubov-Parasyuk theorem, Bombieri-Friedlander-Iwaniec theorem, Bondareva-Shapley theorem, Borsuk-Ulam theorem, Brewer's theorem, Brouwer fixed-point theorem, Brouwer's fixed-point theorem, Bruck-Ryser-Chowla theorem, Brunn-Minkowski theorem, Brun's theorem, Budan's theorem, Cantor-Bendixson theorem, Cantor's theorem, Castigliano's first theorem, Castigliano's second theorem, Castigliano's theorem, Cayley's theorem, Chebyshev's theorem, Chen's theorem, Chinese remainder theorem, Church-Rosser theorem, Clausius theorem, Coase theorem, commutant lifting theorem, complex conjugate root theorem, consensus theorem, Darboux's theorem, de Bruijn-Erdős theorem, de Bruijn's theorem, deduction theorem, de Moivre's theorem, Desargues's theorem, Dirichlet's unit theorem, divergence theorem, Earnshaw's theorem, edge-of-the-wedge theorem, Ehrenfest theorem, Euler's rotation theorem, Fary-Milnor theorem, Feit-Thompson theorem, Fermat's little theorem, fluctuation theorem, four color theorem, free will theorem, Freiman's theorem, Frucht's theorem, Fubini's theorem, fundamental theorem of calculus, fundamental theorem of calculus for line integrals, Futurama theorem, Gauss-Bonnet theorem, Gauss-Lucas theorem, Geiringer-Laman theorem, Gelfond-Schneider theorem, Gibbard-Satterthwaite theorem, Gibbard's theorem, Ginsberg's theorem, Goddard-Thorn theorem, Gomory's theorem, Goodstein's theorem, Gottesman-Knill theorem, Gougu theorem, Green-Tao theorem, Grothendieck-Riemann-Roch theorem, Grötzsch's theorem, Hadwiger's theorem, hairy ball theorem, ham sandwich theorem, Harnack's curve theorem, Heine-Borel theorem, Helly-Bray theorem, Helly's selection theorem, Helly's theorem, Herbrand-Ribet theorem, Herbrand's theorem, Herglotz-Noether theorem, Hilbert's basis theorem, Hjelmslev's theorem, Holevo's theorem, Hurewicz theorem, infinite monkey theorem, intermediate value theorem, Japanese theorem, Jordan curve theorem, Kazhdan-Margulis theorem, Kleene fixed-point theorem, Kleene's fixed-point theorem, Kleene's recursion theorem, Kleene's theorem, Kochen-Specker theorem, Kodaira vanishing theorem, Kolmogorov-Arnold-Moser theorem, Koopmans' theorem, Kramers' theorem, Krein-Milman theorem, Kruskal's tree theorem, KS theorem, Kummer's theorem, Kuratowski-Ulam theorem, Kutta-Joukowski theorem, Lefschetz fixed-point theorem, Lickorish-Wallace theorem, Lindelöf covering theorem, Lindemann-Weierstrass theorem, Liouville-Arnold theorem, Löb's theorem, Löwenheim-Skolem theorem, Maharam's theorem, Matiyasevich's theorem, Mayer-Norton theorem, mean value theorem, Menger's theorem, midline theorem, midpoint theorem, Miquel's theorem, Mittag-Leffler's theorem, monotone convergence theorem, Monsky's theorem, Mordell-Weil theorem, Morley's trisector theorem, MRDP theorem, Nachbin's theorem, Neukirch-Uchida theorem, no-communication theorem, Noether's theorem, no free lunch theorem, no-ghost theorem, no-go theorem, no-hair theorem, Norton's theorem, orbit-stabilizer theorem, Ore's theorem, pancake theorem, Pappus's hexagon theorem, parallel axis theorem, Parseval's theorem, Pasch's theorem, perpendicular axis theorem, Petersen-Morley theorem, Petersen's theorem, Picard-Lindelöf theorem, Poincaré-Birkhoff-Witt theorem, Poynting's theorem, Price's theorem, prime number theorem, Ptolemy's theorem, Pythagorean theorem, Radon's theorem, Ramsey's theorem, rank-nullity theorem, rational root theorem, Rice's theorem, Richardson's theorem, Riemann-Roch theorem, Robertson-Seymour theorem, Rolle's theorem, Romanov's theorem, Roth's theorem, Runge's theorem, Savitch's theorem, scallop theorem, Schiffler's theorem, Sharkovskii's theorem, Siegel-Walfisz theorem, Slutsky's theorem, Solèr's theorem, spectral theorem, Sperner's theorem, Sprague-Grundy theorem, squeeze theorem, Stark-Heegner theorem, Stone's representation theorem, Størmer's theorem, Sturm's theorem, Sumihiro's theorem, Sylow theorem, Sylvester-Gallai theorem, Tarski-Seidenberg theorem, Tarski's fixed-point theorem, Tauberian theorem, Thales's theorem, theorem of Pythagoras, Thévenin's theorem, Thue's theorem, Titchmarsh convolution theorem, Torricelli's theorem, Varignon's theorem, Veblen's theorem, Vinogradov's theorem, virial theorem, Vitali-Carathéodory theorem, Wallace-Bolyai-Gerwien theorem, Weierstrass-Lindemann theorem, Whitney's theorem, Wick's theorem, Wigner-Eckart theorem, Wilks's theorem, Zeckendorf's theorem, Zermelo's theorem

Holonyms: theory

Sources

Where this information comes from

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Real reading context

Meaning relationships

Examples

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