I would like to deal with the problem of being neither an applied mathematician nor a pure mathematician, yet feel that I am a mathematician. Historical examples such as Newton, von Neumann, Turing and Watson-Crick will be discussed.  Also I will try to understand what I am doing now (mathematics?). I will go back to my Ann Arbor days 1948-1956 in these discussions. (Reception to follow in the Mathematics Department Atrium.)