 
Summary: Toward a Philosophy of Real Mathematics
by David Corfield
Cambridge University Press, 2003, 300 pp. $ 70.00 US,
ISBN 0521817226
REVIEWED BY ANDREW ARANA
When mathematicians think of the philosophy of mathematics, they probably think of
endless debates about what numbers are and whether they exist. Since plenty of math
ematical progress continues to be made without taking a stance on either of these ques
tions, mathematicians feel confident they can work without much regard for philosoph
ical reflections. In his sharptoned, sprawling book, David Corfield acknowledges the
irrelevance of much contemporary philosophy of mathematics to current mathematical
practice, and proposes reforming the subject accordingly.
Reading the introduction, it is hard not to be swept up by Corfield's revolutionary fer
vor. Most contemporary philosophical writing on mathematics focuses on elementary
arithmetic or logic, but that is not a representative sample of mathematical practice today
or at any time since Euclid. Corfield's push to widen the investigative reach of philoso
phers of mathematics will be welcomed by readers whose love of mathematics extends
broadly. But is this widening important merely because it may be more attractive to lovers
of mathematics? Or are there important philosophical questions about mathematics that
cannot be answered well without the widening?
