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."
Proofs from THE BOOK contains 32 sections (44 in the fifth 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 Karl Heinrich Hofmann. It has gone through five 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:
- Proof of Bertrand's postulate
- Proof that e is irrational (also showing the irrationality of certain related numbers)
- Six proofs of the infinitude of the primes, including Euclid's and Furstenberg's
- Monsky's theorem (4th edition)
- Wetzel's problem on families of analytic functions with few distinct values
- Steve Fisk's proof of the art gallery theorem
- Proofs from THE BOOK, Springer, Berlin 1998, ISBN 3-540-63698-6
- Günter M. Ziegler's homepage, including a list of editions and translations.
- Shepard, Mary (1999). "Read This! Review of Proofs from THE BOOK". Mathematical Association of America..
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