List of mathematical proofs

A list of articles with mathematical proofs:

Theorems of which articles are primarily devoted to proving them

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 (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
Itō's lemma
König's lemma
König's theorem (set theory)
König'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
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

Articles where example statements are proved

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 (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
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 (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

See also

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