I remember proving my very first theorem. I also remember the very first time, twenty minutes later, that I helped a young person think more clearly about creating and communicating subtle but beautiful ideas. From that moment on I have been obsessed with the teaching and learning of mathematics.
I believe that learning is inexorably tied to communicating. Knowledge that cannot be expressed to another is not knowledge at all, and it is exactly the complex goal of communication that motivates and causes changes in understanding. As a result, my courses are structured like foreign language classes and would be more appropriately titled "Conversational Mathematics". Every day we practice the grammar and vocabulary of mathematics while participating in the society of mathematicians.
In my professional research, I am interested in enumerative geometry, meaning that I study ways to count interesting geometric objects. Much of modern mathematics is powered by the interplay of two major fields; my work lies at the intersection of algebra and geometry where there are many fruitful opportunities to look at the same problem from divergent perspectives.
- B.A., Williams
- Ph.D., Texas-Austin