Meaning in Mathematics – John Polkinghorne (Ed.) ***
In this book a number of leading mathematicians, philosophers and physicists, each contributing a chapter, offer us a range of reflections on the philosophy of mathematics, looking at, for example, the extent to which mathematics can be considered objective, and the issue of discovery versus creation in mathematics.
I really liked the format of the book. Each chapter is followed by a brief commentary by one of the other contributors to the book, with these commentaries providing alternative ways of looking at a particular issue, and encouraging the reader to engage in the debates. Further, the chapters are bite-sized and self-contained, and I enjoyed picking up the book to read, say, a chapter or two, before coming back to it later.
There is an occasional problem with the shortness of the chapters. This is that sometimes there isn’t enough room for ideas to be gently introduced to those of us who aren’t professional mathematicians or philosophers. Despite the book’s aim of being accessible to the layperson, at times it is just too much like an academic book to be considered good popular science.
Some contributions are not as dense as others, however. Marcus du Sautoy, who has perhaps had more practice than some of the other contributors in writing popular science, has written a very easy to follow chapter. And I particularly liked his idea of reconciling creation in mathematics with discovery – whilst all mathematical ideas already exist ‘out there’, in a Platonic sense, waiting to be discovered, mathematicians are still engaged in creative processes, in the sense that they have to choose, often for aesthetic reasons, the most appealing and useful ideas from among the much more banal.
Altogether, then, this is an interesting and thought-provoking collection, which does however suffer from being a little too difficult in parts.