28 of 31 people found the following review helpful
on September 12, 1999
Ever since the first explosion of mathematics in the West, some 2500 years ago, philosophers have wondered from whence does mathematics arise? For most of this time, and for most of these questioners, the answer has been some form of "platonism" - some variation on the view that numbers and other mathematical "objects" exist in a transcendent realm, a priori to, and independent from the material world. Throughout history, several attempts have been made to articulate a coherent alternative to this essentially religious view. At last Brian Rotman has succeeded in this task - and the view he offers is astonishing in its elegance and satisfaction. A truly brilliant and deeply important work, Ad Infinitum should be required reading for all those interested in the philosophy of mathematics.
1 of 1 people found the following review helpful
on July 5, 2010
Terrific little book with a strange new vision of what counting is. Rotman not only lays out an alternative theoretical account of what it means to do mathematics, but, by sketching out a type of non-Euclidean arithmetic, goes ahead and does a little bit on the sly. In the end, this is very lucid, accessible, and thought provoking way to stop simply taking infinity for granted.
on February 13, 2014
I read Rotman's "Becoming Beside Ourselves", and really liked his out-of-the-box ideas. In this book, Rotman's perspective is unique and though-provoking. This book challenges many old math ideas and shatters the metaphysical, mystical, Platonic backdrop that no one would have dared question, until recently, as new thinkers have begun to shift the dialog.