Overview
- Revised and enlarged sixth edition
- New chapter on Van der Waerden’s permanent conjecture
- New sections on the asymptotics for the number of Latin squares
- New proof for the Basel problem
- Geometric explanation for the involution proof for Fermat's two squares theorem
- Presents some recent jewels and surprises
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Table of contents (45 chapters)
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Front Matter
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Number Theory
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Front Matter
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Keywords
About this book
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
Authors and Affiliations
About the authors
Martin Aigner received his Ph.D. from the University of Vienna and has been professor of mathematics at the Freie Universität Berlin since 1974. He has published in various fields of combinatorics and graph theory and is the author of several monographs on discrete mathematics, among them the Springer books Combinatorial Theory and A Course on Enumeration. Martin Aigner is a recipient of the 1996 Lester R. Ford Award for mathematical exposition of the Mathematical Association of America MAA.
Günter M. Ziegler received his Ph.D. from M.I.T. and has been professor of mathematics in Berlin – first at TU Berlin, now at Freie Universität – since 1995. He has published in discrete mathematics, geometry, topology, and optimization, including the Lectures on Polytopes with Springer, as well as „Do I Count? Stories from Mathematics“. Günter M. Ziegler is a recipient of the 2006 Chauvenet Prize of the MAA for his expository writing and the 2008 Communicator award ofthe German Science Foundation.
Martin Aigner and Günter M. Ziegler have started their work on Proofs from THE BOOK in 1995 together with Paul Erdös. The first edition of this book appeared in 1998 – it has since been translated into 13 languages: Brazilian, Chinese, German, Farsi, French, Hungarian, Italian, Japanese, Korean, Polish, Russian, Spanish, and Turkish.
Bibliographic Information
Book Title: Proofs from THE BOOK
Authors: Martin Aigner, Günter M. Ziegler
DOI: https://doi.org/10.1007/978-3-662-57265-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2018
Hardcover ISBN: 978-3-662-57264-1Published: 06 July 2018
eBook ISBN: 978-3-662-57265-8Published: 14 June 2018
Edition Number: 6
Number of Pages: VIII, 326
Topics: Number Theory, Geometry, Analysis, Combinatorics, Graph Theory, Mathematics of Computing