- Feel Wonderful About Adding to Society’s Knowledge Base
- Discovered Applied Research is Both Useful and Interesting to Non-Mathematicians
- Found Applied Work is Fun!
- Learned About Real Applications of Mathematics
- Proving Helpful in Advising
I find it extraordinary and wonderful to be able to add to the knowledge our society has about a subject and to be able to discuss these new ideas with others who know the subject area. For myself, I am most amazed and pleased by the way a very difficult problem can be so difficult that one need not know too much before one knows something which no one else knows. With mathematical research that is purely mathematical, it is impossible to explain the research in a field to someone who hasn’t spent years studying that precise field. While this research can be useful and very challenging, it can be terribly isolated and isolating. The undergraduate research I’ve been involved in is anything but isolating. It is necessarily social in its implications and in its methods. And it’s fun.
As for my future students, this research experience has been the single best educator for me to be able to answer their most basic and vociferous question: “What is mathematics for?” Finally, I have a real experiential answer other than “it’s beautiful”. I can see myriad uses for the work we’ve done and the work we will do. I can now actually imagine what an “industrial mathematician” does. And I can better explain to someone who wants to know what they can do in the future, what opportunities they have.