List of mathematical proofs

List of mathematical proofs

A list of articles with mathematical proofs:

Theorems of which articles are primarily devoted to proving them

:"See also: "
*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 the sum of the reciprocals of the primes diverges

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

:"See also: "
*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
*König's lemma
*König's theorem (to do)
*Lagrange's theorem
*Liouville's theorem (brief pointer to proof)
*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 proven

*Bellman-Ford algorithm (to do)
*Euclidean algorithm
*Kruskal's algorithm
*Prim's algorithm
*Shor's algorithm (incomplete)

Articles where example statements are proven

:"See also: "
*Basis (linear algebra)
*Burrows-Abadi-Needham logic
*Generating a vector space
*Linear independence
*Pumping lemma
*Simpson's rule

Other articles containing proofs

:"See also: "
*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
*Combinatory logic
** 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
*Prime number
** Infinitude of the prime numbers
*Primitive recursive function
*Principle of bivalence
** no propositions are neither true nor false in intuitionistic logic
*Relational algebra (to do)
*Solvable group
*Square root of 2
*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

Other related articles

*Gödel's ontological proof
*Invalid proof
*List of theorems

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