David Eisenbud, one of the half dozen mathematicians featured in this documentary, identifies Paul Halmos’ complete commitment to all things mathematical, to all aspects of the life of a professional mathematician, as his defining characteristic. Indeed, Halmos’ intensity and his full commitment to the mathematical enterprise and community is patently obvious from the very demeanor of this recently deceased statesman of our subject as he answers question after question in a long interview that forms the core of the documentary.
Supplementary to this there are shots of others, former colleagues, former students, and so on, whose comments concerning Halmos, as Mensch, are both fascinating and poignant. I was particularly taken with the comments and reminiscences of the man Halmos himself described as his best student, Berkeley’s Donald Sarason, whose affection for his thesis advisor obviously remains undiminished over time.
The long interview itself is a marvelous thing: Halmos’ humanity shines through, as do the obvious qualities he was known for, be it though his writings, his talks, what have you: a man of strong and well-argued opinions, unafraid to state and defend them — keen to do so, in fact — and a meticulous craftsman qua mathematical scholarship. It is instructive to learn just how many pains Halmos took in preparing anything and everything, from an article to a book, from an invited address to a lunch time chat. It is indeed striking to learn from one of his colleagues at Santa Clara University that in her experience even witticisms and apparent small talk were preceded by considerable cogitation and preparation on Halmos’ part. No wonder that he came off as somewhat formidable to another of his former colleagues — but never so as to diminish their fondness for him: a wonderful tribute in itself.
In my opinion there are two most telling, or revealing, bits from the interview itself, standing out from among the rest. First, there is Halmos’ own estimation that the most important part of his legacy is his authorship of books and articles that succeed in presenting a topic “just so,” i.e. in a definitive, crisp, and clear manner, useful to his readers forever more. Second, at the end of the interview, Halmos proclaims without qualification that he is a totally convinced Platonist. Zowie!
It’s a wonderful documentary. Enjoy it.
Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.