Towards a Philosophy of Real Mathematics

Rating:
Summary: A philosopher with a real interest in mathematics
Review: Philosophy of math has long been obsessed with questions like the existence of numbers and the set-theoretic or logical foundation of the discipline. A century ago, top level mathematicians like Weyl, Hilbert, and Brouwer were engaged in some of these problems. But today's mathematics has largely moved on to other issues. This book is an attempt for philosophy to catch up with these developments.
I have to admit that I was less interested in the chapters on automated theorem proving and conjecture formation. So I read the introductory chapter (which should be comprehensible for a general audience) and then jumped to the later chapters which I find particularly intriguing. In these chapters, Corfield touches several modern areas of mathematics (such as algebraic topology, category theory). These are fields that do not lend themselves well to armchair philosophy, and it is reassuring to know that Corfield has a degree in math from Cambridge University. At times, the book gets technical, not in terms of formulas, but in terms of advanced mathematical concepts that are being discussed. Still, the gist gets conveyed. This makes the book an excellent read.

For those interested, there is a long review of the book on John Baez' home page, under "This Week's Finds in Mathematical Physics (Week 198)".

B. Schölkopf