As late as the fall of 2012 I thought the book would be called “How to Talk about Mathematics
at a Dinner Party.” Someone for whom I have enormous respect thought that was a bad idea: it would make the book “sound too flippant.” He was right: I didn’t want that. So why are there so many tongue-in-cheek passages and patent absurdities?
The first and easiest reason is that in writing the book I was reacting to the earnestness of so many popular books about mathematics. I don’t deny that the practice of mathematics can be uplifting, but not in a quasi-sacred sense. It deserves to be better known that the professional lives of mathematicians involve a lot of silliness. At one point I quote the great mathematician (and notable wit) Jean-Pierre Serre to the effect that nothing is easier than making an auditorium full of mathematicians break out in laughter. He’s right, and in my experience the effect crosses nearly all cultural boundaries. I won’t venture an explanation — there must be a good one — but I did want to make the book an accurate representation of the mathematical life, and the choice of (not too flippant) tone felt like the right one.
The second reason is defensive. In seeking the origins of some of the notions and assumptions that we have assimilated, usually unconsciously, in the process of becoming mathematicians, I did a fair amount of historical research and textual analysis, but nothing that meets the minimal standards of professional scholarship. The tone was chosen to ward off accusations that I was claiming competence on questions for which I lack the requisite training. It’s a signal that the material I am presenting may well be interesting (I hope it is), but the reader is free not to take it too seriously.
Then there were first-hand reports of genuinely absurd situations, usually based on a complete misunderstanding (on the part of people in positions of power or influence) of what mathematics is actually about. (I’ll return to how I understand what mathematics is about in a future post.) In these passages the humor flows from the situation; the author’s job was simply to observe.
The last (and most serious) reason for the tone is that I found it the best way to avoid certain predictable controversies. Philosophers spend their professional lives debating whether mathematics is invented or discovered; sociologists argue over the relative importance of internal disciplinary norms and external (“social”) factors; historians argue about nearly everything. In writing about mathematics (or any intellectual discipline) one is always at the risk of being seen to come down on one side or the other of the most visible controversies, and the failure to criticize one position is often taken as evidence of support for the opposing position. But I wanted to talk about something else, and I am convinced that the material I chose to cover is more relevant to the actual practice of mathematics than the questions that (many) philosphers and sociologists and (some) historians get so worked up about. I also think it’s more interesting. Still, I felt I couldn’t help alluding to these controversies — because it’s even less desirable to be seen as an ignoramus than to be seen as too flippant — but I hoped to make it clear that I could write about mathematics without taking positions on these particular issues, while not dismissing the serious intentions of the partisans of one side or the other.
That list doesn’t exhaust the possible answers to the question in the title. The text frequently departs from the conventions of scholarly gravity; but in most cases this is purely for stylistic reasons.