It is an unfortunate fact that in the past opinions of cultural superiority permeated mathematics, specifically in the area of history. The thought processes that led to the dominance and exploitation of the colonial era led to the belief that all mathematics was invented in the areas described by the phrase “Western Civilization.” That is simply not true. That failing that is being remedied by books like this one.

The main thesis of *The Chinese Roots of Linear Algebra * is that some of the mathematical operations of matrix reduction and determinants were being used in China centuries (1,000 years) before their appearance in Europe. Hart performs a detailed examination of sections of the Chinese work *Nine Chapters of Mathematical Arts*, the first copy of which can definitively be dated as having existed as early as 100 CE. Given a problem with N equations with N unknowns, a primary tactic for solving it was the manipulation of counting rods according to a basic algorithm. Therefore, the device could be considered a primitive computer. Hart argues, and this seems logical, that the people that used them did not understand the underlying mathematics, but only moved the rods according to the given rules of computation.

Although the points are well made, there are times when the book gets tedious in that a problem is stated and then solved point by illustrated point using matrix reduction. One tactic that I liked is that even though I understand very few characters of Chinese, the sections of the work used as justification are included in their Chinese form. This is scholarship at its best, for it would allow people that can read Chinese to compare Hart’s interpretation with their own. Fortunately, the representation of basic integers in Chinese is easy to understand, so as long as you can mentally turn your head sideways, it is possible to follow the matrix computations.

Although gaps in the record occasionally require Hart to interpolate the processes, it is hard to doubt his conclusions. Matrix operations are based on repetitive and easily understood algorithms, so it is difficult to discern any alternate paths. This book is a worthy addition to the complete history of mathematics.

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.