The book was reviewed by Pierre Kerszberg for Mathematical Reviews and by Michael S. Mahoney for American Mathematical Monthly. Mahoney says "The title should have a question mark." He sets the context by referring to paradigm shifts that characterize scientific revolutions as described by Thomas Kuhn in his book The Structure of Scientific Revolutions. According to Michael Crowe in chapter one, revolutions never occur in mathematics. Mahoney explains how mathematics grows upon itself and does not discard earlier gains in understanding with new ones, such as happens in biology, physics, or other sciences. A nuanced version of revolution in mathematics is described by Caroline Dunmore who sees change at the level of "meta-mathematical values of the community that define the telos and methods of the subject, and encapsulate general beliefs about its value." On the other hand, reaction to innovation in mathematics is noted, resulting in "clashes of intellectual and social values".
