Disorderly presentation of a complex subject
Enlightening Symbols is a history of mathematics, in particular the history of how symbols have been created and adopted for various mathematical operations, functions, and concepts. As the subtitle indicates, much of the book is concerned with notation—such as, where did we get +, -, ×, and ÷—but that’s not the whole story. In the early portions of the book, Mazur talks about counting with fingers, sticks, and stones, and the use of the abacus. Ancient mathematicians didn’t even have numerals, at least not widely accepted ones. Early math texts, such as Euclid’s Elements, are written entirely in words. Mazur details how Arabic numerals spread and came to be accepted in Europe—except they’re not really Arabic numerals; they’re of Indian or Hindu origin. The book then goes into the history of algebra and how certain Greek and Latin letters came to be used in equations. Who was the first to decide the mathematical meaning of pi (π), for example?
I read quite a few books on the history of science, which has led to an interest in the history of mathematics. I’m also quite interested in different written languages, to which the subject of mathematical notation pertains. I wish this book would have stuck a little closer to its subtitle and focused more on notation. Mazur, however, keeps venturing into symbology and semiotics—how we process and interpret symbols. Towards the end of the book, he summarizes various psychological experiments concerning mathematical thought, and he gives his own epistemological theories about how the mind works. It’s a subject that clearly fascinates him, but that psychological content was far less interesting to me than the math history.
As a history, however, Enlightening Symbols does have its problems. While the table of contents indicates the book is organized roughly chronologically, Mazur jumps all over the place temporally. No matter what century he’s talking about, he constantly flashes back to earlier figures like Brahmagupta (c. 598–c. 668) and Al-Khwarizmi (c. 789–c. 850), creating a tangled narrative that’s really difficult to follow. In examining who was the first to introduce Indian numerals to Western Europe, Mazur seems to propose about 17 answers to that question. Some he disproves, but I couldn’t even tell you whom he finally settled on. I kept hoping for a chart, but when I finally got one, halfway through the book, it was still confusing. A simple timeline in list or table form would have been most helpful.
As a history, however, Enlightening Symbols does have its problems. While the table of contents indicates the book is organized roughly chronologically, Mazur jumps all over the place temporally. No matter what century he’s talking about, he constantly flashes back to earlier figures like Brahmagupta (c. 598–c. 668) and Al-Khwarizmi (c. 789–c. 850), creating a tangled narrative that’s really difficult to follow. In examining who was the first to introduce Indian numerals to Western Europe, Mazur seems to propose about 17 answers to that question. Some he disproves, but I couldn’t even tell you whom he finally settled on. I kept hoping for a chart, but when I finally got one, halfway through the book, it was still confusing. A simple timeline in list or table form would have been most helpful.
You don’t really need to know a whole lot of math to appreciate the history in Enlightening Symbols. I’m not up on calculus, but I could still roughly follow what Mazur had to say about the history of calculus notation. Some interest in linguistics helps. I’ll admit that I’m probably not qualified to review this book. If you’re reading this review at my blog, however, rather than reading a review in the Journal of Mathematics, then you’re probably in the same boat I am. I provide my layman’s perspective of the book, for what it’s worth, to help you decide if you want to read it.
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