Claremont Center for the Mathematical Sciences

Alvin's life in mathematics is exemplary for two reasons: he insisted, and he persisted. He insisted that mathematics is something that people do, it is inseparable from people. And he persisted and persisted! In the spirit of Alvin's example, I will try to lead an informal conversation, linking two well-known controversies: The first controversial issue is about the many different approaches and styles to college math teaching. Noteworthy examples are from Emil Artin, Alonzo Church, William Feller, Robert Lee Moore, Richard Courant, George Polya, and Clarence Stephens. On the other hand, there is a controversy in the philosophy of mathematics about the nature of mathematical entities or \objects." Mathematical entities might actually be self-subsisting, external, outside of space and time (\Platonism"). Or they might just be arrangements of arbitrary symbols to form \patterns" (formalism, structuralism). Or they might be concepts, shared by thinking human beings (humanism). Is there an important linkage between these two controversies, about the teaching of mathematics and the nature of mathematics?