That’s just over an hour from now, and since I prepared opening remarks I thought it might be useful to post them here. I have now given six presentations, and each time I feel obliged to answer the questions in the first paragraph; but each time I come up with different answers. Rather than leave it up to chance, I have therefore decided to make an effort never to give the same answers twice.
The first question I’m likely to be asked about the book — the first thing the publisher naturally wanted to know — is “What is it about?” You’d think I would have a ready answer for that question, but in fact it’s actually the most difficult question of all, and the proof is that every time it’s asked I come up with a different answer. Today I’m going to start my presentation by answering an apparently quite different question, but equally natural, namely: “Why did I write it?”
I’ve given a number of different answers to that one as well, but today I’m going to try one that I think captures something common to all of them: I wrote the book as an act of free will. By this I mean something specific and possibly personal. For a very long time I have been acutely sensitive to the echoes of others in my speech; what Harold Bloom, in connection to poetry, called the anxiety of influence, but here operating in everyday life. What I mean is that I find myself speaking words that I have somehow absorbed through reading or through conversation or just from the environment, and in a way that bypasses the natural tendency to subject to analyze and criticism. I wanted to write a book about mathematics that does not simply repeat what everyone says, because I find that what everyone says, and what most mathematicians write, is in many ways deeply misleading. In this book I focus especially on the reasons given to justify pure mathematics, in terms of the good, the true, and the beautiful: mathematics is justified because it’s useful, because it provides a unique access to incontrovertible truth, and because it’s beautiful. These are not wrong, but the first two have little or nothing to do with the actual motivations of pure mathematicians, and if taken literally can lead to serious distortions and even ethical dilemmas; whereas the latter is too vague to hold up to scrutiny.