The authors have done an excellent job choosing topics and proofs that Erdos would have appreciated. We will loosely follow Aigner and Ziegler’s book by the same title, going through the beautiful proofs they present and putting them into a broader mathematical context.. Some of the proofs are classics, but … It is unusual for a reviewer to have the opportunity to review the first three editions of a book - the first edition was published in 1998, the second in 2001 and the third in 2004. … Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems … that would undoubtedly be in the Book of Erdős. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". "The newest edition contains three completely new chapters. Over 10 million scientific documents at your fingertipsThis service is more advanced with JavaScript availableThis revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. (Gerry Leversha, The Mathematical Gazette, March, 2005)Every finite division ring is a fieldThree famous theorems on finite sets“This book is the fourth edition of Aigner and Ziegler’s attempt to find proofs that Erdos would find appealing.
Moreover, the exposition makes them transparent. It is unusual for a reviewer to have the opportunity to review the first three editions of a book - the first edition was published in 1998, the second in 2001 and the third in 2004. Indeed I have recommended the book to talented undergraduates and to mathematically literate friends. ..." From the reviews of the third edition:Every large point set has an obtuse angle From the Reviews...Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, wh This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. Moreover, the exposition makes them transparent. … this is a very nice book.” (Donald L. Vestal, The Mathematical Association of America, May, 2010)“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 Erdős. (Gerry Leversha, The Mathematical Gazette, March, 2005)Every finite division ring is a fieldThree famous theorems on finite sets“This book is the fourth edition of Aigner and Ziegler’s attempt to find proofs that Erdos would find appealing.
It shows that the sequence of primes does not end. The theorems are so fundamental … that every mathematician, regardless of speciality, can benefit from reading this book.” (Miklós Bóna, SIGACT News, Vol.
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