# 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

* 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

* Accumulation point
* 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 log$_2$3
** irrationality of the square root of 2
* Mathematical induction
** sum identity
* Power rule
** differential of x$^n$
* 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

## Proofs using...
### topology

* Furstenberg's proof of the infinitude of primes

## Articles giving mathematical proofs within a physical model

* No-cloning theorem
* Torque