Chapter 4: Musings About Models and Modeling in Mathematics

As one who was a serious student of applied mathematics at a certain point in his mathematical life, and who worked on mathematical models for biological phenomena, I should know what a model is. Yet, I confess I have never fully persuaded myself that I really do. It is no wonder then that mathematical models and modeling were the subject of more than one conversation that I have had with Eva Jablonka. This was not only because of Jablonka’s longstanding interest in modeling in mathematics education, beginning with her doctoral dissertation; but also because of a philosophical temperament that allowed her to take seriously a simple question of the form (What is that, really?). After good conversations such as those with Jablonka, one was always left going over the arguments; thinking about what might have been added, or left out, a good example, a better example. In short, one continues to muse about the subject. It seems fit in this liber amicorum that I should give back to her, as a true offering of friendship, some of these musings on mathematical models; not a report of research results or a survey of current literature, but only the loose ends of a conversation with a thoughtful friend.