# The Best Writing on Mathematics 2016

This is the seventh volume in the series for which Mircea Pitici selects every year a set of papers that discuss popular mathematics-related topics. This genre, if it can be called so, has gained an increasing interest, and the number of pages in each volume seems to be a nondecreasing sequence. Pitici's task may become more difficult every year in making some selection within the scope of the book taking into account the limitations of space and copyright restrictions. On the other hand, with a larger supply to choose from, the quality of the eventual selection is easily kept as high as in previous years.

In the first four volumes some *big shot* wrote an introduction, but since the 2014 volume, the series has established a reputation of its own and Pitici writes his own introduction with a long list of books that fall into the same class as the papers in the collection. As usual, there is also a long enumeration at the end of the book with other publications that were not included but that are still highly interesting. That list also has references to notable book reviews, interviews, and special issues of journals. Pitici stresses in his introduction that each volume is an integral part of the whole series. He announces the compilation of an index over all volumes to be produced in the near future. That would indeed be a nice tool to browse through the whole series more easily.

There are 30 papers selected for this book, all published in 2015. The numbering is indeed a bit misleading, yet reasonable and correct if you think of it practically. This collection is published in 2017, with the title *Best writing on Mathematics 2016*, since 2016 is the year in which the papers of 2015 are harvested and the book is being prepared. It takes indeed some time to deal with copyright and to typeset the papers in a uniform format.

What exactly should be understood by fitting under the umbrella of *popular mathematics*? The last contribution by Ian Stewart, who is a prolific writer of this kind of books, gives a possible answer. Besides children's books, topics treated can be philosophy, history and biography, fun and games, big problems, pure versus applied, or links with arts and culture. He also gives a lot of good advice for anyone who feels the urge to write a book in this class. We find papers in this collection that represent most of the topics that Stewart enumerates, to which we should probably add education and teaching. Not exactly a "popular" topic, but it certainly addresses a public much broader than just mathematicians. Therefore also this topic has in the collections of this series found a settled place.

Remarkable in the current collection are the three contributions that debunk or at least place in proper perspective what has been a firm folk belief: Wigner's "the unreasonable effectiveness of mathematics in physics" and Hardy's "defense of pure mathematics" and Leibniz's formulation of "the fundamental theorem of calculus". The authors if these papers show that these statements seem not to be as accurate as generally accepted. Another historical contribution is about the most illustrious constant in mathematics. The constant *π*

is often defined as the ratio of the circumference of a circle over its diameter, but if we consider this as a theorem, then its origin is surprisingly very fuzzy. One more generally accepted expression is to say that a theorem is "deep". It is used lightly by many, but difficult to define. What exactly does it mean when a theorem is called deep? You can find some answers to all these puzzling issues in this book.

Of course the other topics mentioned are also represented: games and recreation (design of a card deck for Spot It!, stacking wine bottles, billiards), art (mathematics in the collection of the Metropolitan Museum of Arts in NY), and the big problems (The monster group, and Mochizuli's "proof" of the abc conjecture). And there is much more of course. Each paper is selected among the best papers that were published. Not only are the subjects teasing, but the stories are told with vivacity that just gets you hooked after reading the first paragraph. If you do not know where to start, you can find a 3 page survey of all contributions in Pitici's introduction. It is clear that each paper can be read independently, but there is some loose logical ordering. For example the five papers with a statistical flavor are placed together.

Once again a highly recommended collection that saves you the time to search for the papers yourself and finding out whether it is top quality or not. You do not need to be a mathematician. Mathematical technicalities are totally avoided. These are papers *on* mathematics, not mathematical papers. It also aims at politicians, managers, philosophers, and whoever has a broader interest in science or society. It presents mathematics in its broadest cultural and social context.

For reviews of previous volumes see 2012, 2013, 2014, and 2015.

**Submitted by Adhemar Bultheel |

**10 / Apr / 2017