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.

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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]"

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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
Kronecker–Weber theorem	theorem in algebraic number theory
Kronecker’s lemma	mathematical lemma
completeness theorem for first-order logic	—
Gödel's ontological proof	formal proof
Robbins theorem	theorem
Low’s theorem	theorem
Hume’s Principle (derivable, not postulated)	theorem
Kantorovich duality	duality theorem
Penrose singularity theorem	theorem in general relativity
Lévy–Itô decomposition	theorem in probability theory
Lévy’s continuity theorem	theorem in probability theory
Malgrange preparation theorem	—
Malgrange–Ehrenpreis theorem	—
Borel–Cantelli lemmas	mathematical lemma
Bell's theorem linked to: Bell’s theorem	theorem in quantum mechanics
Weierstrass approximation theorem	theorem in real analysis
Weierstrass factorization theorem	—
Weierstrass M-test	theorem in real analysis
Weierstrass preparation theorem	—
Lindemann–Weierstrass theorem precursor	—
Arrow’s impossibility theorem	theorem
Feynman–Hellmann theorem	quantum mechanics theorem
Weyl character formula	—
Weyl law	—
Carathéodory’s extension theorem	—
Carathéodory’s theorem in convex geometry	theorem in convex geometry
Carathéodory–Jacobi–Lie theorem	—
Carathéodory–Fejér interpolation	theorem in complex analysis
Hardy–Littlewood conjectures	result in analytic number theory
Håstad’s switching lemma	—
Schauder fixed-point theorem	—
Sperner's lemma	mathematical lemma
Pythagorean theorem	—
Banach inverse mapping theorem	theorem in functional analysis
Hardy–Ramanujan asymptotic formula	theorem in analytic number theory
Cartan decomposition	structure theorem
Banach fixed-point theorem	—
Peano existence theorem	—
Bayes’ theorem	probability theorem
law of large numbers	probability theorem
Frisch–Waugh–Lovell theorem	theorem
Fermat's Last Theorem	—
Fermat's little theorem	theorem
Fermat's theorem on sums of two squares	theorem in number theory
Fermat polygonal number theorem	theorem
Minkowski inequality	mathematical inequality
Stokes' theorem	theorem in vector calculus
Lagrange's theorem in group theory	theorem in group theory
Lagrange's four-square theorem	theorem in number theory
Poincaré recurrence theorem	—