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
Bézout’s theorem	theorem in algebraic geometry
Tarski's undefinability theorem	—
Furtwängler’s theorem in class field theory	theorem in algebraic number theory
Gödel's incompleteness theorems	—
passivity theorem	theorem in control theory
Menger theorem in graph theory surface form: Menger's theorem (graph theory)	theorem in graph theory
Ehrenfest surface form: Ehrenfest theorem	theorem in quantum mechanics
Ehrenfest theorem	quantum mechanics theorem
PCP theorem	theorem in computational complexity theory
Riesz surface form: Riesz representation theorem	—
Riesz lemma	—
Riesz–Thorin interpolation theorem	—
Slutsky substitution matrix is negative semidefinite	theorem in consumer theory
Riesz rearrangement inequality	mathematical inequality
Siegel’s theorem on zeros of L-functions	theorem in analytic number theory
Linnik’s theorem on the least prime in an arithmetic progression	theorem in analytic number theory
Graham–Rothschild theorem	—
Graham–Pollak theorem	theorem
Turán's theorem	theorem
Turán–Kubilius inequality	mathematical inequality
Positivstellensatz	theorem
admissibility theorem	theorem
Scarf’s lemma	mathematical lemma
van der Corput lemma	mathematical lemma
van der Corput inequality	mathematical inequality
Cantor’s theorem	—
Siegel's theorem on integral points	theorem
Calderón reproducing formula	—
Calderón transference principle	—
Calderón interpolation theorem	—
BEST theorem	theorem
matrix-tree theorem	theorem
Koksma–Hlawka inequality	mathematical inequality
Cauchy’s integral test	—
Cauchy’s mean value theorem	theorem in real analysis
Morera's theorem	theorem in complex analysis
Bolzano–Weierstrass theorem	—
Bessel inequality	—
Cauchy–Binet formula	—
Courant–Fischer min–max theorem	theorem
Poincaré separation theorem	—
Rouché's theorem	theorem in complex analysis
Zassenhaus lemma	—
Tucker’s lemma	combinatorial lemma
Bayes surface form: Bayes' theorem	theorem
Davis–Putnam–Robinson–Matiyasevich theorem	—
Kesten’s theorem on random walks on groups	—
Kesten’s theorem	—
Kesten–Stigum theorem	—
Atiyah–Singer index theorem	—