List of 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

Itō's lemma

König's lemma

König's theorem (set theory)

König'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

Bellman–Ford algorithm (to do)

Euclidean algorithm

Kruskal's algorithm

Gale–Shapley algorithm

Prim's algorithm

Shor's algorithm (incomplete)

Articles where example statements are proved

Basis (linear algebra)

Burrows–Abadi–Needham logic

Direct proof

Generating a vector space

Linear independence

Polynomial

Proof

Pumping lemma

Simpson's rule

Other articles containing proofs

Addition in N

associativity of addition in N

commutativity of addition in N

uniqueness of addition in N

Algorithmic information theory

Boolean ring

commutativity of a boolean ring

Boolean satisfiability problem

NP-completeness of the Boolean satisfiability problem

Cantor's diagonal argument

set is smaller than its power set

uncountability of the real numbers

Cantor's first uncountability proof

uncountability of the real numbers

Combinatorics

Combinatory logic

Co-NP

Coset

Countable

countability of a subset of a countable set (to do)

Angle of parallelism

Galois group

Fundamental theorem of Galois theory (to do)

Gödel number

Gödel's incompleteness theorem

Group (mathematics)

Halting problem

insolubility of the halting problem

Harmonic series (mathematics)

divergence of the (standard) harmonic series

Highly composite number

Area of hyperbolic sector, basis of hyperbolic angle

Infinite series

convergence of the geometric series with first term 1 and ratio 1/2

Integer partition

Irrational number

irrationality of log₂3

irrationality of the square root of 2

Limit point

Mathematical induction

sum identity

Power rule

differential of xⁿ

Product and Quotient Rules

Derivation of Product and Quotient rules for differentiating.

Prime number

Infinitude of the prime numbers

Primitive recursive function

Principle of bivalence

no propositions are neither true nor false in intuitionistic logic

Recursion

Relational algebra (to do)

Solvable group

Square root of 2

Tetris

Algebra of sets

idempotent laws for set union and intersection

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

Articles giving mathematical proofs within a physical model

No cloning theorem

Torque