 
Summary: Plato's ghost: The modernist transformation of mathematics
by Jeremy Gray
Princeton University Press, Princeton, 2008
ISBN: 9780691136103, viii+515
reviewed by Jeremy Avigad
It only takes a few minutes on Amazon.com or MathSciNet to make the
case that Jeremy Gray is among the most prolific historians of mathematics
working today. Winner of the 2009 AMS Albert Leon Whiteman Prize for
notable exposition and exceptional scholarship in the history of mathemat
ics, his books and articles, and the many collections of essays that he has
edited, cover just about every aspect of mathematics in the nineteenth and
earlytwentieth centuries. It is therefore no small assertion to say that the
book under review, Plato's ghost, is his most farreaching and ambitious
work to date.
Gray's goal is to clarify the sense in which modern mathematics is "mod
ern," and explore the historical process by which the subject attained that
character. This goal is set out in the opening words of the introduction:
In this book I argue that the period from 1890 to 1930 saw math
ematics go through a modernist transformation. Here, mod
ernism is defined as an autonomous body of ideas, having little
