It has been stated many times that mathematics is a surprising descriptor of the way the universe behaves. I agree with that statement, but only to a point. For the extremely organized structures that we call life to exist, the laws of the universe would have to be stable and consistent to a very high degree. This would be especially true when intelligent life exists, for it requires an efficient long-term memory and that requires highly proficient reproducibility. Therefore, extremely stable laws of the universe are an essential precondition for life — and mathematical models can then describe those laws.

As can be seen from this book and others, a great deal of mathematics evolved to describe what the universe was observed to be doing. Therefore, it should be no surprise that mathematics describes the universe, for one directly follows from the other. The authors do an excellent job in explaining how some of the greatest mathematicians observed nature and then created the mathematics that could be used to model the natural actions.

The chapter headings and the topics are:

- The Beginnings of Mechanics — Archimedes, Galileo and Stevin develop the laws of the level and inclined plane.
- Growth functions — Gauss and Maxwell develop the mathematics of error computation and Malthus and others develop the equations of population expansion and contraction.
- Mathematics and Optics — Euclid, Archimedes, Kepler and Newton develop the laws of how light waves behave.
- Matrices — transformations — this chapter provides the mathematical foundation for the subsequent chapters.
- What is Time? Einstein’s Transformation Problem — the mathematics of space-time transformations in relativity.
- Relativistic Addition of Velocities — how to add velocities near those of light.
- Energy — the mathematics of two bodies impacting that was completely developed by Newton as well as the role of energy in the theory of relativity.

The universe existed before human consciousness could contemplate it, mathematics was developed so that it could be understood. Some of the greatest achievements in the development of mathematics were the creation of equations that modeled how the universe works and a few of those are brilliantly described in this book.

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.