Proofs from THE BOOK

Content

• 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
• Sylvester–Gallai theorem and De Bruijn–Erdős theorem
• Cauchy's theorem
• Borsuk's conjecture
• Schr%C3%B6der%E2%80%93Bernstein theorem
• Wetzel's problem on families of analytic functions with few distinct values
• The fundamental theorem of algebra
• Monsky's theorem
• 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