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
Cauchy interlacing theorem	theorem
Cauchy residue theorem	theorem
Cauchy integral formula	theorem in complex analysis
Selberg trace formula	—
Harish-Chandra isomorphism	—
Harish-Chandra character formula	—
Plancherel theorem for real reductive groups	—
Serre duality	theorem in algebraic geometry
Grothendieck–Riemann–Roch theorem	theorem in algebraic geometry
Grothendieck inequality	mathematical inequality
OU process surface form: Ornstein–Uhlenbeck process	Markov process
Hamilton’s compactness theorem	—
Atiyah–Bott fixed-point theorem	—
prime number theorem	—
Fundamental Theorem of Calculus	—
uniformization theorem	—
Schwarz lemma	—
Koebe quarter theorem	theorem in complex analysis
Montel theorem surface form: Montel's theorem	theorem in complex analysis
Hirzebruch–Riemann–Roch theorem	—
Fourier inversion theorem	—
Dynkin formula	theorem in probability theory
Voronin universality theorem	—
Hurwitz bound on automorphism groups of curves	—
Lefschetz fixed-point theorem	—
Grothendieck–Ogg–Shafarevich formula	—
Dehn lemma	theorem in topology
h-cobordism theorem	—
Milnor–Wood inequality	—
Conway circle theorem	geometric theorem
multinomial theorem	—
Gelfand representation of commutative C*-algebras	theorem in functional analysis
Gelfand–Naimark theorem	—
generalized binomial theorem	—
Fitting lemma	—
Fitting decomposition	group theory theorem
Isserlis’ theorem in probability theory surface form: Isserlis’ theorem	theorem in probability theory
monotone convergence theorem	theorem
dominated convergence theorem	theorem in measure theory
Fatou's lemma	lemma in measure theory
Fubini's theorem	theorem in measure theory
Tonelli's theorem	theorem in measure theory
Clark–Ocone formula	result in stochastic calculus
Green–Tao theorem	—
Ben Green surface form: Green–Tao theorem	—
Connes–Moscovici index theorem	—
Jordan curve theorem	—
virial theorem	theorem
Theorema Egregium	—
Gauss–Markov theorem	statistical theorem