Books

The Beginnings and Evolution of Algebra

We are indebted to Abe Shenitzer for translating this important history of algebra, written by two mathematicians associated with Moscow State University. It’s commonly known that in Russia mathematicians are admired and revered. There is poetry in the way the authors approach their subject and this translation has retained that poetry.

The Beginnings and Evolution of Algebra was a major influence on another book we recommend, Unknown Quantity by John Derbyshire. Indeed, Derbyshire has high praise for these women’s work and writings. The first few chapters of Beginnings and Evolution are just right for the early algebra student. Then it can be put on the shelf until the student graduates from high school and is ready for the poetry studied at the university level.

Bashmakova and Smirnova’s description of the Pythagoreans in the chapter on ancient Greek “geometric algebra” is representative of the in-depth studies they have made. Music is often linked with mathematics, for which the authors offer a clearly written explanation. Here they describe the Pythagoreans’ discovery of the ratios of musical intervals and the associated lengths of the strings on a musical instrument.

Reading about any subject from a variety of cultural viewpoints is crucial to the search for historical clarity. In this sense, The Beginnings and Evolution of Algebra is a particularly important work.

Author Isabella Bashmakova & Galina Smirnova
Publisher The Mathematical Association of America; 1st edition (January 15, 2000)