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.

Try in SPARQL

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
Noether's theorem	theorem
Noether normalization lemma	—
Noether's isomorphism theorems	family of theorems
Gauss’s lemma in number theory surface form: Gauss’s lemma (number theory)	lemma in number theory
Gauss–Bonnet theorem (early form)	—
Euler’s theorem	theorem in number theory
Mertens’ theorems	theorem in analytic number theory
Poisson summation formula	theorem in harmonic analysis
Andrew C. Berry surface form: Berry–Esseen theorem	theorem in probability theory
Urdi lemma	geometric theorem
CLT	statistical theorem
Kolmogorov–Arnold–Moser theory	theorem in Hamiltonian dynamics
Kolmogorov zero–one law	probability theorem
Kolmogorov extension theorem	theorem in probability theory
Kolmogorov continuity theorem	—
Ky Fan’s lemma	—
Berry–Esseen theorem	probability theorem
Picard theorem	—
Richard H. Cameron surface form: Cameron–Martin theorem	—
Hadamard inequality	mathematical inequality
Hadamard three-circle theorem	theorem in complex analysis
Itô isometry	—
Löb's theorem	—
Tarski–Mostowski–Robinson theorem	theorem in mathematical logic
Tarski’s theorem on the completeness of elementary algebra and geometry	—
Tarski’s fixed point theorem	—
Bernstein inequalities	mathematical inequality
MIP equals NEXP surface form: MIP = NEXP	theorem in computational complexity theory
Kakutani fixed-point theorem	—
implicit function theorem	—
Janet–Cartan theorem	—
Khinchin surface form: Khinchin's law of the iterated logarithm	theorem
Khinchin's law of the iterated logarithm	probability theorem
Khinchin–Kolmogorov theorem	probability theorem
Khinchin's representation theorem	—
Riesz–Fischer theorem	—
Böhm–Jacopini theorem	theorem
Erdős–Szekeres theorem	—
Szekeres–Lindström theorem	—
Painlevé–Kruskal theorem	—
families index theorem	—
equivariant index theorem	—
Banach–Steinhaus theorem	theorem in functional analysis
Steinhaus theorem	theorem
Steinhaus chessboard theorem	—
Kuhn’s theorem	theorem in game theory
Smale’s paradox	—
Tychonoff theorem for products of compact spaces	theorem in topology
Banach–Tarski paradox	—
Thales’ theorem	geometric theorem