Boyer can write pretty well. His tendency to wax on about the virtues of the people he writes about can get annoying, but overall this probably works to make a more engaging style. This kind of writing style is entirely appropriate for a textbook designed to draw readers into the world of mathematics, but is prone to wide, sweeping generalizations and ill-supported assumptions and occasionally, factually incorrect statements.The reader who is serious about studying the development of mathematics will learn something from this book, but there are better places to learn it. Boyer, as indicated above, seems intent on "cleaning up" history to fit the nice picture he has of it. Unfortunately, merely reciting well-known mathematical legends does more harm than good; it obscures the real process of discovery, and the way mathematics has, and still does, develop.
There are errors in the book that indicate Boyer did not do his research. To keep this review short, Ill name one: Boyer credits Poincare with the Poincare disc model of hyperbolic geometry. Anyone that has actually looked at Riemanns very important 1854 lecture (one of the most important documents of 19th century mathematics) will realize this model is due to Riemann! Since Boyer spends quite a bit of time on Riemann, this is rather puzzling.
Boyer also relies on E.T. Bell for some biographical information. No serious historian of mathematics would (or should) reference Bell for biographies of mathematicians. Bells caricatures are entertaining, but do a disservice to the subject.
This book is only recommended for those who want to get a vague idea of the history of mathematics, but do not particularly care about the details being correct. For that purpose, Boyer does a better job than most.
Not for the serious student of history of mathematics
The best book on history of mathematics