This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.
From the citation on the occasion of the 2018 “Steele Prize for Mathematical Exposition”
“… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”
From the Reviews
“… Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. … Aigner and Ziegler… write: “… all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations.” I do. … “
Notices of the AMS, August 1999
“… This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings … It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. …”
LMS Newsletter, January 1999
“Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. …”
SIGACT News, December 2011
Peter Grogono –
“THE BOOK” is, of course, a creation by the late Hungarian mathematician Paul Erdős – a mythical “bible” containing the most elegant and insightful proofs of important theorems. You might think that only serious mathematicians would be able to understand these proofs, but it is not so. Many are quite elementary, and most are accessible to anyone with an undergraduate degree in mathematics or physics, or even people who just enjoy reading mathematics. There are many pleasant surprises: one of the first is a proof that there are an infinite number of primes – using topology! I won’t give any more spoilers. The book is not cheap but it is good value: you will get many hours of delight and amazement from it.
Ben Hsu –
I try to read a chapter a week — the ideas leave me shaking my head at how beautiful math can be
tokonoma –
Livre très intéressant mais pas si facile que cela d’accès. Il me semble qu’il faut de bonnes bases en mathématiques pour le lire.
Plane Tree –
new book as described
Nahatz –
If you know the history of “the book” (first mentioned by Paul Erdos.) you know these had to be fantastitic.
Joppe de Cuyper –
Explore the beautifull evidence to well-known theorems. Worth it for anyone interested in maths.
Gregory Connor –
The book has a number of simple, memorable and elegant proofs — it is great fun to work through Erdos’ clever proof that the infinite sum of the reciprocals of all prime numbers diverges, for example. It is a good book for dipping into and out of, but I did not read it thoroughly from cover to cover.
Archan –
Must read got anyone starting on math or general anyone wanting to prove stuff.
humberin –
Tal cual
Andrés –
Entregado en la fecha esperada y con una calidad estupenda (además de la matemática)
Marko Razpet –
Dieses Buch behandelt die elegantesten Beweise, die es in der Mathematik je gab. Ich benutze das Buch zur Ergänzung meiner mathematischen Kenntnisse und zur Unterhaltung.
Rafael W Lima –
It is a beautiful master piece about math 🙂 <3
Manuel Toribio Molinero –
Había buscado el libro por todas las librerías de Barcelona, y ni estaba ni se podía encargar. Lo cierto es que fue una entrega algo lenta, pero se puede comprender porque venía de fuera de España.
El libro es una muy buena recopilación de demostraciones elegantes en los ámbitos de teoría de números, geometría, análisis, combinatoria y teoría de grafos. Para entenderlo completamente, la exposición supone una base de primero de carrera, aproximadamente.
Miguel Angel Alcala Landeta –
Vale la pena leerlo completo como entrenamiento cerebral
El buen Davis –
Un libro bastante interesante. Llego a tiempo y sin ningún problema
Francisco Alfonso –
I loved this book
Dr Rob Baston –
For any reasonable accomplished mathematician, a fine collection of the most elegant proofs of the standard canon. Some curious proofs (e.g. topological proof of infinitude of primes) which are fun to puzzle out. But generally seeing how a given result may be proved elegantly using different techniques is a great way to get a diverse view of the subject.