Aigner, Martin; Ziegler, Günter M. Proofs from THE BOOK. Transl. from the English. 2nd ed. (Das BUCH der Beweise.) (German) Zbl 1038.00001 Berlin: Springer (ISBN 3-540-40185-7/hbk). 271 S. (2004). The previous English, French and German editions of this wonderful and highly successful book were reviewed in 1998 (Zbl 0905.00001), 2001 (Zbl 0978.00002), 2002 (Zbl 0986.00001) and 2002 (Zbl 0988.00001). – The present second German edition largely follows the text of the second English edition (2001; Zbl 0978.00002). In addition, there are three new chapters (three proofs of Euler’s marvelous identity \[ \sum^\infty_{n=1} {1\over n^2}= {\pi^2\over 6}, \] Euler’s partition identities (the no less marvelous theorem on pentagonal numbers), and on shuffling cards), and there are of course numerous minor improvements, additions and updates, e.g. the beautiful enumeration of the positive fractions after Calkin, Wilf and Newman. Clearly writing THE BOOK is a huge world-wide project in the progress of which all mathematicians are involved. If your don’t have a (necessarily preliminary) edition yet, hurry to your bookseller, take your copy home, read it, enjoy it – and help to bring THE BOOK to eternal perfection. Reviewer: Jürgen Elstrodt (Münster) Cited in 6 ReviewsCited in 3 Documents MSC: 00A05 Mathematics in general 05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions 51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry 52-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry Keywords:zeta values; partition identities; pentagonal numbers; shuffling cards Citations:Zbl 0905.00001; Zbl 0978.00002; Zbl 0986.00001; Zbl 0988.00001 Software:HURRY PDFBibTeX XMLCite \textit{M. Aigner} and \textit{G. M. Ziegler}, Das BUCH der Beweise. 2nd ed. Berlin: Springer (2004; Zbl 1038.00001)