The editor of this volume has gathered a number of articles from well-known (The Mathematical Intelligencer, Nature, Notices of the American Mathematical Society, \dots) and not so well-known (The Montana Mathematics Enthusiast, \dots) scientific periodicals, but also from newspapers and magazines like The New York Times or The New Yorker dealing with mathematics in all its aspects. Many of the articles reprinted here have already been reviewed individually in Zentralblatt. There are six parts, entitled “Mathematics alive”, “Mathematicians and the practice of mathematics”, “Mathematics and its applications”, “Mathematics education”, “History and philosophy of mathematics”, and “Mathematics in the media”. To indicate the flavour of the collection, here is a description of some of the contributions. {\it Freeman Dyson}, in “Birds and frogs”, describes two types of personalities in science ‒ theory builders (= birds) and problem solvers (= frogs). {\it Branko Grünbaum}\/ writes on “An enduring error” occurring in the enumerative geometry of polyhedra. {\it Tim Gowers}\/ and {\it Michael Nielsen}\/ report on “Massively collaborative mathematics”, i.e., Gowers’s internet project that has led to a new proof of the density Hales-Jewett theorem. (Meanwhile, this proof has been written up in a preprint by {\it D. J. H.~Polymath}\/; see \url{arXiv:0910.3926}.) {\it Theodore P.~Hill} decribes the mathematics of optimal stopping in his piece “Knowing when to stop: How to gamble if you must”. {\it Ann Kajender}\/ and {\it Miroslav Lovric}\/ analyse flawed definitions of tangents in various textbooks in “Mathematical textbooks and their potential role in supporting misconceptions”. {\it Judith V.~Grabiner} asks “Why did Lagrange ‘prove’ the parallel postulate?” in her piece, and jazz pianist {\it Vijay Iyer} ponders on “Strength in number: On mathematics and musical rhythm”. Altogether, the choice of the articles is excellent, and the whole volume makes very good reading. Still, being a mathematician I would dispute the (unproved) title “The best writing on mathematics” ‒ but clearly the publisher’s publicity department would not have approved of “Examples of very good writing on mathematics”.

Reviewer:

Dirk Werner (Berlin)