# List of mathematical proofs

Wikipedia contains a number of articles with mathematical proofs:

## Theorems of which articles are exclusively devoted to proving them

- Bertrand's postulate and a proof
- Fermat's little theorem and some proofs
- Gödel's completeness theorem and its original proof
- Mathematical induction and a proof
- Proof that the sum of the reciprocals of the primes diverges
- Proof that e is irrational
- A simple proof that 22/7 exceeds pi

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

- Banach-Tarski paradox
- Basel problem
- Bolzano-Weierstrass theorem
- Brouwer fixed point theorem
- Buckingham Pi theorem (proof in progress)
- Burnside's lemma
- Cantor's theorem
- Cantor-Bernstein-Schroeder theorem
- Cayley's Theorem
- Clique problem (todo)
- Compactness theorem (very compact proof)
- Euler's formula
- Euler's four-square identity
- Euler's 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 (todo)
- Green's theorem when D is a simple region

- Heine-Borel theorem
- Intermediate value theorem
- Itô's lemma
- König's lemma
- König's theorem (todo)
- Lagrange's theorem
- Liouville's theorem (brief pointer to proof)
- Markov's inequality (proof of a generalization)
- Mean value theorem
- Multivariate normal distribution (todo)
- Proof that holomorphic functions are analytic
- Pythagorean theorem
- Quadratic formula
- 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 theorem
- Transcendence of
*e*and π (as corollaries of Lindemann-Weierstrass) - Tychonoff's theorem (todo)
- Ultrafilter Lemma
- Urysohn's Lemma
- Van der Waerden's theorem
- Wilson's theorem
- Zorn's lemma

## Articles devoted to algorithms of which their correctness is proven

- Bellman-Ford algorithm (todo)
- Euclidean algorithm
- Kruskal's algorithm
- Prim's algorithm
- Shor's algorithm (incomplete)

## Articles where example statements are proven

- Basis (linear algebra)
- Burrows-Abadi-Needham logic
- Generating a vector space
- Linear independence
- Naive set theory
- Polynomial
- Pumping lemma
- Simpson's rule
- Vector space example 1
- Vector space example 2
- Vector space example 3

## 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

- Calculus with polynomials
- Cantor's diagonal argument
- set is smaller than its power set
- uncountability of the real numbers

- Combinatorics
- Combinatory logic
- Co-NP
- Coset
- Countable
- countability of a subset of a countable set (todo)

- Counter
- Galois group
- Fundamental theorem of Galois theory (todo)

- 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
- 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

- irrationality of log
- Limit point
- Mathematical induction
- sum identity

- 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 (todo)
- Solvable group
- Tetris

## 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
- Product topology
- Riemann integral
- Time hierarchy theorem
- Deterministic time hierarchy theorem

- Deterministic time hierarchy theorem