Paul Erdős is known for solving many problems, both simple and more complex, in extraordinary fashion. He had the idea of bringing together in a single publication the almost magical proofs given by mathematicians to solve—in the blink of an eye (or almost)—questions that were often quite standard. "You don't need to believe in God, but as a mathematician, you must believe in the Book," he went so far as to say, in 1985.
Divine proofs
It was Martin Aigner (1942–2023), an Austrian mathematician specializing in combinatorics and graph theory, and Günter M. Ziegler, born in 1963, a German mathematician working in discrete mathematics and geometry, who suggested that Erdős begin writing it. Enthused by the idea, he set to work and made numerous suggestions. The book was due to appear in March 1998, as a gift for his 85th birthday. His death in 1997 upset those plans, and although he is not listed among the authors, the work is nonetheless dedicated to him. Signed by Martin Aigner and Günter M. Ziegler, the book—whose English title is Proofs from the Book—brings together simple, elegant solutions to well-known problems.
Its first publication by Springer Verlag took place as planned in 1998, and various editions followed one another up to the latest, the sixth, in 2018. It was translated into French in 2001 under the title Raisonnements divins, and the current edition, the third, dates from 2013. Translated into seventeen other languages, it earned its two authors the Leroy P. Steele Prize in 2018, a prize awarded by the American Mathematical Society.
Erdős himself was keen to limit the mathematical background needed to understand it to the undergraduate level. Starting with the fourth English edition (carried over into the latest French edition), the proofs were organized into forty chapters (with five more in the latest English edition), each on a specific theorem, along with its consequences. The subjects are grouped under five themes: number theory, geometry, analysis, combinatorics, and graph theory. It has grown by about a hundred pages since the first English edition, and mathematical perfection in Erdős's sense is well represented in it.