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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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
Poincaré–Bendixson theorem	—
Poincaré–Hopf theorem	—
Poincaré lemma	—
Poincaré duality	theorem in algebraic topology
Gauss’s remarkable theorem	theorem
Jordan–Hölder theorem	theorem
Poincaré–Birkhoff fixed-point theorem	—
Wiener–Khinchin theorem	—
Brownian motion	Markov process
Einstein field equations	tensor equation
Cantor–Bernstein–Schröder theorem	theorem
Sprague–Grundy theorem	—
Louis Mordell surface form: Mordell–Weil theorem	—
spin–statistics theorem	theorem
Kakutani’s random ergodic theorem	—
Cauchy–Kovalevskaya theorem	—
quadratic reciprocity law	theorem in number theory
Swan constructed counterexamples over the rational numbers	mathematical result
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED	theoretical physics result
Alexandrov–Hausdorff theorem	—
Lindeberg–Feller central limit theorem	probability theorem
Lyapunov inequality	mathematical inequality
Jacobi’s four-square theorem	theorem in number theory
Noether’s theorem in algebraic geometry (Noether’s AF+BG theorem) surface form: Noether’s AF+BG theorem	—
small-gain theorem	theorem
Fisher separation theorem	theorem in financial economics
Hotelling surface form: Hotelling's lemma	theorem
Menger surface form: Menger theorem in graph theory	theorem
Feynman–Kac formula	theorem in probability theory
Deuring reduction theorem	—
Deuring–Heilbronn phenomenon	result in analytic number theory
Hasse bound for elliptic curves	theorem in number theory
Hasse–Arf theorem	—
complete class theorem in decision theory	theorem in decision theory
Hasse norm theorem	theorem
Amdahl's law	theorem in parallel computing
Chebotarev density theorem	theorem in algebraic number theory
Auslander–Buchsbaum formula	theorem in commutative algebra
Brouwer fixed-point theorem	topological theorem
inverse function theorem	—
local existence and uniqueness theorem	—
Maurice Janet surface form: Janet–Cartan theorem	—
Glicksberg fixed-point theorem	fixed-point theorem
Herbrand's theorem	—
de Bruijn–Erdős theorem	—
de Bruijn–van Aardenne–Ehrenfest theorem	—
Cauchy integral theorem	theorem in complex analysis
Cauchy–Schwarz inequality	mathematical inequality
Cauchy–Hadamard theorem	—
Cauchy condensation test	theorem in real analysis