# 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

*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

*Banach fixed point theorem
*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)
*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
*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

*Basis (linear algebra)
*Generating a vector space
*Linear independence
*Polynomial
*Proof
*Pumping lemma
*Simpson's rule

Other articles containing proofs

** 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 (to do)
*Counter
*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
*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

Articles giving mathematical proofs within a physical model

*No cloning theorem
*Torque

Other related articles

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

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• List of mathematical jargon — The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in… …   Wikipedia

• Mathematical proof — In mathematics, a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true.[1][2] Proofs are obtained from deductive reasoning, rather than from inductive or empirical… …   Wikipedia

• List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

• List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …   Wikipedia

• List of mathematics reference tables — See also: List of reference tables Mathematics *List of mathematical topics *List of statistical topics *List of mathematical functions *List of mathematical theorems *List of mathematical proofs *List of matrices *List of numbers *List of… …   Wikipedia

• Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …   Wikipedia

• Mathematical fallacy — In mathematics, certain kinds of mistakes in proof, calculation, or derivation are often exhibited, and sometimes collected, as illustrations of the concept of mathematical fallacy. The specimens of the greatest interest can be seen as… …   Wikipedia

• List of basic discrete mathematics topics — Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally , in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite… …   Wikipedia

• List of computability and complexity topics — This is a list of computability and complexity topics, by Wikipedia page. Computability theory is the part of the theory of computation that deals with what can be computed, in principle. Computational complexity theory deals with how hard… …   Wikipedia

• Mathematical induction — can be informally illustrated by reference to the sequential effect of falling dominoes. Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers (positive… …   Wikipedia