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
• Burnside's lemma
• Cantor's theorem
• Cantor–Bernstein–Schroeder theorem
• Cayley's formula
• Cayley's theorem
• Clique problem
• Compactness theorem
• 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
• Gödel's incompleteness theorem
• * Gödel's first incompleteness theorem
• * Gödel's second incompleteness theorem
• Goodstein's theorem
• Green's theorem
• * Green's theorem when D is a simple region
• Heine–Borel theorem
• Intermediate value theorem
• Itô's lemma
• Kőnig's lemma
• Kőnig's theorem
• Kőnig's theorem
• Lagrange's theorem
• Lagrange's theorem
• Liouville's theorem
• Markov's inequality
• Mean value theorem
• Multivariate normal distribution
• 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
• Tychonoff's theorem
• 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
• Euclidean algorithm
• Kruskal's algorithm
• Gale–Shapley algorithm
• Prim's algorithm
• Shor's algorithm

  Articles where example statements are proved

• Basis
• 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
• Angle of parallelism
• Galois group
• * Fundamental theorem of Galois theory
• Gödel number
• * Gödel's incompleteness theorem
• Group
• Halting problem
• * insolubility of the halting problem
• Harmonic series
• * divergence of the 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
• 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
• Product topology
• Riemann integral
• Time hierarchy theorem
• * Deterministic time hierarchy theorem

  Articles giving mathematical proofs within a physical model

• No cloning theorem
• Torque