Henri Poincaré was a towering figure, both in science and mathematics and in the areas melding science and philosophy. His career could serve as the definition of the “polymath”: a person that excelled in all his selected fields of study. His work in theoretical physics, one example of which was the three-body problem, led to the development of modern chaos theory. In addition to his mathematical work, he was actively involved in many of the scientific developments of his time.

This book is a collection of scholarly papers about Poincaré’s work and views on the philosophy of science. The first paper is largely historical in nature, a recapitulation of the years 1860–1873, from the time Poincaré was six until he was nineteen. The focus is on his schooling and the environment in which he grew up. Like all of the French people, he was powerfully affected by the defeat of France by the Prussian-led German coalition in 1870.

The remaining papers delve more into the man and his work. My favorite point in the book appears on page 57, after the statement of one of Newton’s laws, “force is the product of mass and the acceleration.” To Poincaré, this is a definition rather than a natural law discerned via experiment. This goes to the heart of the philosophy of science and indeed of mathematics, where fundamental principles are categorized.

The most technical of the papers is “Henri Poincaré: The Status of Mechanical Explanations and the Foundations of Statistical Mechanics” by João Príncipe. This is the only one where points are emphasized via equations; the topic is thermodynamics. Few equations appear in the other papers.

While there are many significant and occasionally critical points to be made in the area of the philosophy of science, non-philosophers will also find it intellectually stimulating to read and study. At the heart of science are our abilities to perceive and reach rational and justifiable conclusions, and reading this book will make you think. Debating whether F = ma is a law or a definition forces a level of clarity in your thinking that will make you better at math and science independent of which side you land on.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing *The Journal of Recreational Mathematics*. In his spare time, he reads about these things and helps his daughter in her lawn care business.