Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book." Content Proofs from THE BOOK contains 32 sections (45 in the sixth edition), each devoted to one theorem but often containing multiple proofs and related results. It spans a broad range of mathematical fields: number theory, geometry, analysis, combinatorics and graph theory. Erdős himself made many suggestions for the book, but died before its publication. The book is illustrated by . It has gone through six editions in English, and has been translated into Persian, French, German, Hungarian, Italian, Japanese, Chinese, Polish, Portuguese, Korean, Turkish, Russian and Spanish. In November 2017 the American Mathematical Society announced the 2018 Leroy P. Steele Prize for Mathematical Exposition to be awarded to Aigner and Ziegler for this book. The proofs include: 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 References Günter M. Ziegler's homepage, including a list of editions and translations. External links Proofs from THE BOOK (4th ed.) on the Internet Archive Mathematical proofs Mathematics books Paul Erdős 1998 non-fiction books