List of mathematical proofs

A list of articles with mathematical proofs:

Theorems of which articles are primarily devoted to proving them

Bertrand's postulate and a proof
Estimation of covariance matrices
Fermat's little theorem and some proofs
Gödel's completeness theorem and its original proof
Mathematical induction and a proof
Proof that 0.999... equals 1
Proof that 22/7 exceeds π
Proof that e is irrational
Proof that π is irrational
Proof that the sum of the reciprocals of the primes diverges

Articles devoted to theorems of which a (sketch of a) proof is given

Banach fixed-point theorem
Banach–Tarski paradox
Basel problem
Bolzano–Weierstrass theorem
Brouwer fixed-point theorem
Buckingham π theorem (proof in progress)
Burnside's lemma
Cantor's theorem
Cantor–Bernstein–Schroeder theorem
Cayley's formula
Cayley's theorem
Clique problem (to do)
Compactness theorem (very compact proof)
Erdős–Ko–Rado theorem
Euler's formula
Euler's four-square identity
Euler's theorem
Five color theorem
Five lemma
Fundamental theorem of arithmetic
Gauss–Markov theorem (brief pointer to proof)
Gödel's incompleteness theorem
- Gödel's first incompleteness theorem
- Gödel's second incompleteness theorem
Goodstein's theorem
Green's theorem (to do)
- Green's theorem when D is a simple region
Heine–Borel theorem
Intermediate value theorem
Itô's lemma
Kőnig's lemma
Kőnig's theorem (set theory)
Kőnig's theorem (graph theory)
Lagrange's theorem (group theory)
Lagrange's theorem (number theory)
Liouville's theorem (complex analysis)
Markov's inequality (proof of a generalization)
Mean value theorem
Multivariate normal distribution (to do)
Holomorphic functions are analytic
Pythagorean theorem
Quadratic equation
Quotient rule
Ramsey's theorem
Rao–Blackwell theorem
Rice's theorem
Rolle's theorem
Splitting lemma
squeeze theorem
Sum rule in differentiation
Sum rule in integration
Sylow theorems
Transcendence of e and π (as corollaries of Lindemann–Weierstrass)
Tychonoff's theorem (to do)
Ultrafilter lemma
Ultraparallel theorem
Urysohn's lemma
Van der Waerden's theorem
Wilson's theorem
Zorn's lemma

Articles devoted to algorithms in which their correctness is proved

Articles where example statements are proved

Articles which mention dependencies of theorems

Cauchy's integral formula
Cauchy integral theorem
Computational geometry
Fundamental theorem of algebra
Lambda calculus
Invariance of domain
Minkowski inequality
Nash embedding theorem
Open mapping theorem (functional analysis)
Product topology
Riemann integral
Time hierarchy theorem
- Deterministic time hierarchy theorem

Proofs using...

topology

Furstenberg's proof of the infinitude of primes

Articles giving mathematical proofs within a physical model

Traditional	Classical logic Logical truth Tautology Proposition Inference Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram
Propositional	Boolean algebra Boolean functions Logical connectives Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞
Predicate	First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus

Set theory

Set hereditary Class (Ur-)Element Ordinal number Extensionality Forcing Relation equivalence partition Set operations: intersection union complement Cartesian product power set identities
Types of sets	Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe constructible Grothendieck Von Neumann
Maps and cardinality	Function/Map domain codomain image In/Sur/Bi-jection Schröder–Bernstein theorem Isomorphism Gödel numbering Enumeration Large cardinal inaccessible Aleph number Operation binary
Set theories	Zermelo–Fraenkel axiom of choice continuum hypothesis General Kripke–Platek Morse–Kelley Naive New Foundations Tarski–Grothendieck Von Neumann–Bernays–Gödel Ackermann Constructive

Formal systems (list),
language and syntax

Alphabet Arity Automata Axiom schema Expression ground Extension by definition conservative Relation Formation rule Grammar Formula atomic closed ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃ ! ∀ rank Sentence atomic spectrum Signature String Substitution Symbol function logical/constant non-logical variable Term Theory list
Example axiomatic systems (list)	of arithmetic: Peano second-order elementary function primitive recursive Robinson Skolem of the real numbers Tarski's axiomatization of Boolean algebras canonical minimal axioms of geometry: Euclidean: Elements Hilbert's Tarski's non-Euclidean Principia Mathematica