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.
# Response Format
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
Hermite–Minkowski theorem	—
Schur–Weyl duality	—
Peter–Weyl theorem	theorem
speedup theorem	theorem in computational complexity theory
Borel–Weil theorem	—
Helly’s theorem	—
Radon’s theorem	theorem
Krein–Milman theorem	theorem
Minkowski’s theorem on convex sets	—
Darboux theorem	—
Liouville–Arnold theorem	—
Cook–Levin theorem	theorem in computational complexity theory
Thurston’s classification of surface diffeomorphisms	—
Faltings' theorem	—
Knaster–Kuratowski–Mazurkiewicz lemma	—
open mapping theorem	theorem in functional analysis
Baire category theorem	—
Lindelöf theorem in complex analysis	theorem in complex analysis
Wilson's theorem	theorem in number theory
Chinese remainder theorem	theorem
second fundamental theorem of welfare economics	theorem in economics
Fefferman–Phong inequality	mathematical inequality
Artin reciprocity law	theorem in number theory
Artin–Wedderburn theorem	theorem
Whitney approximation theorem	—
Bourgain–Tzafriri restricted invertibility principle	—
Carathéodory existence theorem	—
May–Wigner stability theorem	—
Eliassen–Palm theorem	theorem
Hard Lefschetz theorem	theorem
Hodge–Riemann bilinear relations	—
Hodge decomposition	theorem
Erdős–Kac theorem	theorem in number theory
Erdős–Ko–Rado theorem	theorem
Erdős–Gallai theorem	graph theory theorem
Erdős–Stone theorem	theorem
Erdős–Rényi law of large numbers	probability theorem
convolution theorem	—
Chevalley–Warning theorem	theorem
Chevalley’s theorem in algebraic geometry	theorem in algebraic geometry
Slutsky surface form: Slutsky theorem	theorem in probability theory
Sylvester’s law of inertia	theorem
Sylvester–Gallai theorem	theorem
Sylvester’s theorem on partitions	—
Bombieri–Vinogradov theorem	theorem in analytic number theory
Coleman theorem on symmetry breaking in two dimensions	theorem in quantum field theory
LLN	probability theorem
ergodic theorem	—
Leibniz rule	—
Lipton–Tarjan separator theorem	theorem in graph theory