It is important that mathematics students appreciate their subject has a past. It is equally important for non-mathematicians to appreciate that mathematics has exerted a significant influence on human history. It is extraordinarily difficult to write a good history of mathematics, and a good textbook is even harder.
Victor Katz does an excellent job, and I would not hesitate to base a lecture course on his book. It covers most of the main events and personalities - including the role of women and third world countries, and it manages to convey their importance in terms of the subject itself rather than mere political correctness. About time: Sophie Germain, for instance, belongs in any history because she was a superb mathematician, not because she was female. And during the Middle Ages, it was the Islamic world that carried the torch of mathematics: Europe was too busy peering up its own religious fundamentals.
This 800-page book is clear and readable, tackles conceptually difficult topics and makes a fair stab at the modern era.
Ian Stewart is director, Mathematics Awareness Centre,University of Warwick.
A History of Mathematics: An Introduction
Author - Victor J. Katz
ISBN - 0 321 01618 1
Publisher - Addison Wesley
Price - £25.95
Pages - 800