• 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

• 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
• 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

• Bellman–Ford algorithm (to do)
• Euclidean algorithm
• Kruskal's algorithm
• Gale–Shapley algorithm
• Prim's algorithm
• Shor's algorithm (incomplete)

• Basis (linear algebra)
• Burrows–Abadi–Needham logic
• Direct proof
• Generating a vector space
• Linear independence
• Polynomial
• Proof
• Pumping lemma
• Simpson's rule

• 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 log₂3
  • irrationality of the square root of 2
• 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

• 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

topology edit

• Furstenberg's proof of the infinitude of primes

• No-cloning theorem
• Torque

• Gödel's ontological proof
• Invalid proof
• List of theorems
• List of incomplete proofs
• List of long proofs