The philosopher Teilhard De Chardin once made the statement “all is one,” referring to the fact that there is no field of study that is totally disjoint from another field. Pythagoras studied the properties of music, which interact with mathematics, philosophy, and science; Rimsky-Korsakov was a brilliant composer despite his duties as a naval officer; and for hundreds of years, a person in Europe could not be awarded a doctorate in philosophy without an advanced degree in mathematics. And finally, when Einstein was at a point of difficulty in developing the equations for his theory, he would play Mozart, saying that it helped him understand the “harmony of the spheres.”

The lion’s share of research in this field is a result of conferences held in Mexico under the aegis of the Society for Mathematics and Computation in Music (SMCM). This is a book of contributions from several authors joining in the International Congress of Music and Mathematics (ICMM) held in Puerto Vallarta, Mexico, November 26 to 29, 2014. There are 33 individual papers touching on a variety of mathematical-musical studies.

The book is definitely not for the casual reader who is a music lover. It is extremely sophisticated and designed for the mathematician who is thoroughly versed in advanced mathematics and complex music theory. The text is the result of the aforementioned global conference, which focuses on issues in the relatively new field of mathematical music theory.

It is impossible to summarize a work of such depth. Suffice it to say that abstract algebra, topology, number theory, geometry, and so on are all involved. If you are a serious devotee of musical-mathematical theory and have a very extensive background in both areas, the book will be a treasure.