mathematical theorem

C716

concept

A mathematical theorem is a rigorously proven statement derived from axioms and previously established results, expressing a fundamental truth within a formal mathematical system.

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All labels observed (115)

Label	Occurrences
mathematical theorem canonical	255
theorem	80
theorem in complex analysis	26
mathematical inequality	25
theorem in number theory	20
theorem in functional analysis	19
theorem in probability theory	15
theorem in algebraic geometry	14
theorem in analytic number theory	13
probability theorem	11
result in analytic number theory	10
result in algebraic geometry	8
result in mathematical logic	8
fixed-point theorem	7
mathematical lemma	7
theorem in algebraic topology	6
theorem in quantum mechanics	6
geometric theorem	5
theorem in harmonic analysis	5
theorem in measure theory	5
theorem in real analysis	5
index theorem	4
result in stochastic calculus	4
theorem in algebraic number theory	4
theorem in commutative algebra	4
theorem in computational complexity theory	4
theorem in differential topology	4
theorem in general relativity	4
theorem in graph theory	4
theorem in group theory	4
theorem in quantum field theory	4
theorem in topology	4
Markov process	3
approximation theorem	3
combinatorial theorem	3
duality theorem	3
statistical theorem	3
theorem in analysis	3
theorem in model theory	3
combinatorics theorem	2
convergence theorem	2
lemma	2
lemma in number theory	2
quantum mechanics theorem	2
result in abstract algebra	2
result in commutative algebra	2
result in elementary number theory	2
theorem in algebra	2
theorem in calculus	2
theorem in computability theory	2
theorem in control theory	2
theorem in differential geometry	2
theorem in linear algebra	2
theorem in mathematical logic	2
axiomatization of entropy	1
class of mathematical theorems	1
combinatorial lemma	1
enumeration theorem	1
equivalence theorem	1
existence theorem	1
family of theorems	1
formal proof	1
graph theory theorem	1
group theory theorem	1
interpolation theorem	1
lemma in measure theory	1
mathematical result	1
mean value theorem	1
metalogical theorem	1
metamathematical theorem	1
no-hair theorem	1
number theory result	1
result in linear regression theory	1
result in mathematics	1
result in stochastic analysis	1
set theory theorem	1
structure theorem	1
tensor equation	1
theorem about curvature	1
theorem in Hamiltonian dynamics	1
theorem in Riemannian geometry	1
theorem in analytic geometry	1
theorem in category theory	1
theorem in combinatorial geometry	1
theorem in combinatorics	1
theorem in consumer theory	1
theorem in convex geometry	1
theorem in decision theory	1
theorem in descriptive set theory	1
theorem in differential equations	1
theorem in economics	1
theorem in financial economics	1
theorem in game theory	1
theorem in homological algebra	1
theorem in information theory	1
theorem in mathematical analysis	1
theorem in mathematical economics	1
theorem in mechanics	1
theorem in numerical analysis	1
theorem in ordinary differential equations	1
theorem in parallel computing	1
theorem in physics	1
theorem in recursion theory	1
theorem in ring theory	1
theorem in set theory	1
theorem in sheaf theory	1
theorem in signal processing	1
theorem in statistics	1
theorem in stochastic calculus	1
theorem in symplectic geometry	1
theorem in topological group theory	1
theorem in vector calculus	1
theorem of calculus	1
theoretical physics result	1
topological theorem	1

Description generation (CDg)

The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.

Instruction

generate a one-sentence description for a given conceptual class.
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Return only the sentence: "Description: [one-sentence description of the conceptional class]"

Input

Class: mathematical theorem

Generated description

A mathematical theorem is a rigorously proven statement derived from axioms and previously established results, expressing a fundamental truth within a formal mathematical system.

Instances (537)

Instance	Via concept surface
area theorem	theorem in general relativity
Denjoy–Young–Saks theorem	—
Blaschke selection theorem	—
Liouville's theorem surface form: Liouville's theorem (complex analysis)	theorem in complex analysis
Cauchy–Pompeiu formula	theorem in complex analysis
Busemann–Feller theorem	—
Künneth formula	—
Stone–von Neumann theorem	—
Siegel’s lemma	lemma in number theory
Siegel mass formula	—
Siegel–Walfisz theorem	theorem in analytic number theory
Beilinson–Bernstein localization theorem	—
Harish-Chandra regularity theorem	—
Plancherel theorem for locally compact abelian groups	theorem in harmonic analysis
Hölder inequality	mathematical inequality
Jensen inequality surface form: Jensen's inequality	mathematical inequality
Dini's theorem	—
Dini test for convergence of Fourier series	theorem in harmonic analysis
Lax equivalence theorem	—
Paley–Wiener theorem for real reductive groups	—
Serre vanishing theorem	theorem in algebraic geometry
GAGA	equivalence theorem
GAGA principle	theorem in algebraic geometry
GAGA theorems	result in algebraic geometry
Serre’s theorem on projective embeddings via ample line bundles	theorem in algebraic geometry
Poitou–Tate duality	duality theorem
Pisier’s factorization theorems	—
Gabriel–Popescu theorem	—
Bose–Nair theorem	—
Brown representability theorem	—
Bott periodicity	—
Segal conjecture	theorem in algebraic topology
Cheeger–Gromov compactness theorem	—
Hamilton’s compactness theorem for Ricci flow	—
Longuet-Higgins theorem in molecular symmetry	theorem
John–Nirenberg inequality	mathematical inequality
Lax–Milgram theorem	theorem in functional analysis
Pósa’s theorem in graph theory surface form: Pósa’s theorem	theorem in graph theory
Duistermaat–Heckman formula	—
Chebyshev’s estimates for π(x)	—
FTC surface form: Fundamental Theorem of Calculus	—
Mostow rigidity theorem	—
Ahlfors finiteness theorem	—
Thurston hyperbolization theorem	—
Bloch theorem	theorem in complex analysis
Bieberbach conjecture	—
distortion theorem	theorem in complex analysis
Arzelà–Ascoli theorem	theorem in mathematical analysis
Vitali convergence theorem	theorem in measure theory
Noether’s formula	theorem in algebraic geometry