This book is the byproduct of a singular event that occurred in 2013. Starting as what Kaper and Rousseau describe as a “grass roots movement”, an extraordinary international collaboration of more than 150 universities, mathematical institutes, and scientific societies came together during that year in a mammoth partnership known as *Mathematics of Planet Earth 2013 *(the website can be found at mpe2013.org), the goal of which was research and education on a variety of issues dealing with the mathematics of planet earth, a phrase that should be interpreted, the editors tell us, “in the broadest possible terms”.

Some hint of the broadness of this phrase is obtained by considering the variety of topics that are discussed in this book, but before doing that I should make clear just what these discussions are and how they came to be. The MPE2013 partnership resulted in the formation of two blogs, one in English and the other in French; the book now under review contains over a hundred of the entries in the English-language blog, edited where necessary. Reflecting the range of the partnership, the affiliations listed by the authors include many universities from a number of different countries, the mathematical society SIAM, a newspaper (the *San Diego Union-Tribune*) and mathematical institutes both foreign (Consiglio Nazionale delle Richerche, Mitacs, INRIA, Insituto per le Applicazioni del Calcolo) and domestic (American Institute of Mathematics).

These pieces are, consistent with their origin, quite short; the smallest is (excluding references) one paragraph long and very few exceed three pages, including drawings, graphs, diagrams, photos, and, on one occasion, a cartoon. A blurb on the back cover of the book states that these entries are “accessible to a general audience with a basic scientific background”; this is true in general, though a small handful of the pieces contained enough mathematical formalism (partial derivatives, integrals, Greek letters, etc.) to scare away anybody without prior mathematical training.

As for the topics covered: this book is divided into four parts, corresponding to the four parts of the MPE program. I cannot improve upon the succinct description offered in the Preface by the editors:

- A PLANET TO DISCOVER: planet Earth, Earth’s climate system, weather and climate, beyond planet Earth;
- A PLANET SUPPORTING LIFE: biosphere; ecology; evolution
- A PLANET ORGANIZED BY HUMANS: communication and representation, energy, human behavior, economics and finance;
- A PLANET AT RISK: climate change, invasive species, infectious diseases, natural disasters

As the breadth of these topics indicate, the mathematics discussed in these short articles is quite varied: we see mentioned, for example, fractals and self-similarity, chaos, game theory, differential and integral equations, least squares and data assimilation, optimal control theory, statistics and graph theory.

Given the short length of each piece, and the fact that these all appeared originally as blog entries, it is not surprising that the mathematics involved is generally not developed in depth; the articles are mostly expository. However, reading them does convey some sense of the applicability of mathematics (and other sciences) to the issues addressed in this book. Some articles don’t even discuss mathematics much at all, and perform other functions such as directing the reader’s attention to a recently published article elsewhere, or pointing out the limitations of mathematics in a particular problem. References follow almost all of the entries, so that somebody interested in pursuing a topic in more depth will know where to go.

A number of the topics discussed here (e.g., global warming) have obvious political dimensions, but this book is not a political tract. First and foremost, the idea is to discuss things from a rational, logical and scientific perspective, not an emotional one. The various chapters in the book are, of course, all the more persuasive for doing so. While some of the chapters may convey a sense of urgency, this is an educated reaction rather than a political one.

To conclude: this book is an unusual one, and a fitting memorialization of an important partnership. It makes interesting reading both for professionals and educated laypeople.

Mark Hunacek ([email protected]) teaches mathematics at Iowa State University.