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]"

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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
Pólya enumeration theorem	combinatorial theorem
Hirzebruch signature theorem	—
Gagliardo–Nirenberg interpolation inequalities	mathematical inequality
Rice's theorem	theorem in computability theory
no-cloning theorem	theorem in quantum mechanics
Page theorem	theorem
Wick’s theorem	theorem in quantum field theory
Gell-Mann–Low theorem	theorem in quantum field theory
Doob–Meyer decomposition	theorem
martingale representation theorem surface form: Martingale representation theorem	theorem in stochastic calculus
Itô’s lemma	—
Cameron–Martin theorem	—
Kleene surface form: Kleene’s recursion theorem	theorem in recursion theory
Kleene’s normal form theorem	—
positive mass theorem	—
Kleene’s recursion theorem	theorem in computability theory
Hausdorff maximal principle	—
Shapley–Gale theorem	theorem
Gale’s theorem on flows with convex costs	—
Gale’s theorem on linear inequalities	—
Gale–Nikaidō–Debreu theorem	—
Bochner surface form: Bochner–Martinelli formula	theorem
Bochner theorem on characteristic functions	—
Donaldson–Uhlenbeck–Yau theorem	—
Brockett’s condition for smooth feedback stabilization	—
Cauchy's theorem in group theory	theorem in group theory
Sylow theorems	theorem in group theory
orbit-stabilizer theorem	theorem
Legendre's three-square theorem	theorem
Kac's lemma	theorem
Liouville's theorem in Hamiltonian mechanics	theorem
Bendixson–Dulac criterion	—
Verdier duality	theorem in algebraic topology
Alexander duality	theorem in algebraic topology
Sobolev inequality	mathematical inequality
Korn inequality	mathematical inequality
Rellich–Kondrachov compactness theorem	—
Green's theorem	theorem
rank–nullity theorem	theorem in linear algebra
Cayley–Hamilton theorem	theorem
Jordan normal form theorem	—
Riesz representation theorem	—
Lasker–Noether theorem on primary decomposition	—
Krull’s principal ideal theorem	theorem in commutative algebra
Schreier refinement theorem	theorem
Yoneda lemma	theorem
Freyd–Mitchell embedding theorem	—
Freyd adjoint functor theorem	—
Alon–Boppana bound	theorem
Combinatorial Nullstellensatz	theorem