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 (40 in the 4th 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 four editions in English, and has been translated into Persian, French, German, Hungarian, Italian, Japanese, Chinese, Polish, Portuguese, Korean, Turkish, Russian and Spanish.
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)
Famous quotes containing the words proofs and/or book:
“I do not think that a Physician should be admitted into the College till he could bring proofs of his having cured, in his own person, at least four incurable distempers.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Every book is a quotation; and every house is a quotation out of all forests, and mines, and stone quarries; and every man is a quotation from all his ancestors.”
—Ralph Waldo Emerson (1803–1882)