Editing List of mathematical proofs

{{Short description|none}}
A list of articles with [[mathematical proof]]s:

==Theorems of which articles are primarily devoted to proving them==
{{See also|:Category:Article proofs}}
*[[Bertrand's postulate]] and [[Proof of Bertrand's postulate|a proof]]
*[[Estimation of covariance matrices]]
*[[Fermat's little theorem]] and [[Proofs of Fermat's little theorem|some proofs]]
*[[Gödel's completeness theorem]] and [[Original proof of Gödel's completeness theorem|its original proof]]
*[[Mathematical induction]] and [[Proof of mathematical induction|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==
{{See also|:Category:Articles containing proofs}}
*[[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]]
*[[Lindemann–Weierstrass theorem|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==
{{See also|:Category:Articles containing proofs}}
*[[Basis (linear algebra)]]
*[[Burrows–Abadi–Needham logic]]
*[[Direct proof]]
*[[Generating a vector space]]
*[[Linear independence]]
*[[Polynomial]]
*[[Mathematical proof|Proof]]
*[[Pumping lemma]]
*[[Simpson's rule]]

==Other articles containing proofs==
{{See also|:Category: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<sub>2</sub>3
**irrationality of the square root of 2
*[[Mathematical induction]]
**sum identity
*[[Power rule]]
**differential of ''x''<sup>''n''</sup>
*[[Product Rule|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]]

==See also==
* [[Gödel's ontological proof]]
* [[Invalid proof]]
* [[List of theorems]]
* [[List of incomplete proofs]]
* [[List of long proofs]]

{{Mathematical logic}}

[[Category:Mathematics-related lists|Proofs]]
[[Category:Mathematical proofs| ]]