Science as a Medium for Friendship: How the Keller–Segel Models Came About

Abstract

I first met Lee Segel in the fall of 1968. Just a year earlier, Sol Rubinow had hired me to help set up a program in “Biomathematics” at Cornell University Medical College and the Sloan Kettering Institute, so when Lee joined us, I had a bit of a head start in thinking about what that word might mean. But truth be told, I hadn’t gotten very far. Perhaps it is fair to say that none of us had. I remember putting together a course for medical students on the subject (somewhere I still have the course notes), and it meant scrambling together a rather disparate collection of examples of biological problems for which we could show the usefulness of mathematics. Simple examples of dimensional analysis seemed like a good place to start; the Hodgkin–Huxley model surely needed to be included; Rubinow’s work on blood flow beautifully illustrated the extension of applied mathematics to problems in the life sciences; my own first efforts in modeling biological clocks offered a very different kind of example; and of course, there were always the classic examples of mathematical models in population biology (e.g., population genetics, epidemiology, and ecology). A good start, perhaps, but still a bit of a hodgepodge. What troubled me more, though, was that I couldn’t see how any of the examples I was able to find would hold much interest for working biologists—at least for the kinds of biologists I knew. Did they enrich our understanding of biological phenomena per se, and if they did, how? Admittedly, my experience in biology was pretty spotty—limited mainly to the phage group at Cold Spring Harbor, and a foray into molecular biology while a graduate student in theoretical physics, but I already suspected it might be better if our tools were to follow the problems, and not vice versa. The question of what an applied mathematician can do for biology seemed to me still very much up for grabs, and when Lee arrived for a sabbatical in the fall of 1968, with his family, this was the question that started us talking. How should one go about identifying problems in a discipline about which, we had to admit, we knew embarrassingly little—problems that could benefit from an application of our skills? How does one avoid the proverbial trap of the technician with a hammer in search of anything that looks like a nail?