see mainly proofs
- Six proofs of the infinitude of the primes, including Euclid's and Furstenberg's
- Proof of Bertrand's postulate
- Fermat's theorem on sums of two squares
- Two proofs of the Law of quadratic reciprocity
- Proof of Wedderburn's little theorem asserting that every finite division ring is a field
- Four proofs of the Basel problem
- Proof that e is irrational (also showing the irrationality of certain related numbers)
- Hilbert's third problem
- Sylvester–Gallai theorem and De Bruijn–Erdős theorem
- Cauchy's theorem
- Borsuk's conjecture
- Schröder–Bernstein theorem
- Wetzel's problem on families of analytic functions with few distinct values
- The fundamental theorem of algebra
- Monsky's theorem (4th edition)
- Van der Waerden's conjecture
- Littlewood–Offord lemma
- Buffon's needle problem
- Sperner's theorem, Erdős–Ko–Rado theorem and Hall's theorem
- Lindström–Gessel–Viennot lemma and the Cauchy–Binet formula
- Four proofs of Cayley's formula
- Kakeya sets in vector spaces over finite fields
- Bregman–Minc inequality
- Dinitz problem
- Steve Fisk's proof of the art gallery theorem
- Five proofs of Turán's theorem
- Shannon capacity and Lovász number
- Chromatic number of Kneser graphs
- Friendship theorem
- Some proofs using the Probabilistic method