ENV: Did anyone in particular, a colleague or friend, influence the conclusions you reach in these essays?
DB: No, I don’t think so. Daniel Gallin has been an influence on my thinking, but our friendship ended more almost thirty years ago, and so his influence is no longer of this time or place. Daniel introduced me to model theory. That was his gift to me. After studying with Church at Princeton, I regarded model theory as an immersion into cool water. Such ease, such elegance, such freedom! Had I stayed in mathematics as a research mathematician, I would have stayed in model theory. In the 1980s, I wrote a monograph for the Princeton University Press in which I reached the conclusion that mathematics has no applications beyond finger counting. I stopped for fear that I would find myself affirming that it has no applications at all, circumstances that would have made it difficult for me to justify my work. I never published the thing. It is still sitting in my drawer together with my short stories and poems. But in writing it, I found myself using model theoretic methods over and over again. I’ve not gone back to the subject. Just a few years ago, I tried to catch up, reading Wilfred Hodges’ Shorter Model Theory. Anyone who writes the shorter anything gets my vote.
It may seem odd to say that Marco had a la longue little effect on what I have written, but it is true. I loved the man; but what I took from our friendship and what I have written in these essays are two different things.
I have been influenced in a general way by a number of mathematicians: Daniel Gallin, as I have said, Marco, René Thom, Lipman Bers, Gian-Carlo Rota, and even Irving Siegel, whose friendship I acquired by correspondence. I admired these men, but by the time I came to write my essays, I had already developed my own way of thinking, and as often as not, what I took from them, now that I think about it, was as much an attitude as anything else. Gian-Carlo remarked to me once that mathematics was the last honest discipline. I was struck by the remark, one reason, of course, that Gian-Carlo made it; I thought then that it was true, and I think so now as well.
That is the kind of attitude I mean.