I don’t have to prove theorems to be a mathematician
I’m giving a talk at the Joint Mathematics Meeting on Thursday (it’s a 30 minute talk that starts at 11:20am, in Room 2 of the Upper Level of the San Diego Conference Center, I hope you come!).
Thinking about that talk brought something up for me that I think I want to address before the next talk. Namely, at the beginning of the talk I was explaining the title, “How Mathematics is Used Outside of Academia,” and I mentioned that most mathematicians that leave academia end up doing modeling.
I can’t remember the exact exchange, but I referred to myself at some point in this discussion as a mathematician outside of academia, at which point someone in the audience expressed incredulity:
him: Really? Are you still a mathematician? Do you prove theorems?
me: No, I don’t prove theorems any longer, now that I am a modeler… (confused look)
At the moment I didn’t have a good response to this, because he was using a different definition of “mathematician” than I was. For some reason he thought a mathematician must prove theorems.
I don’t think so. I had a conversation about this after my talk with Bob Beals, who was in the audience and who taught many years ago at the math summer program I did last summer. After getting his Ph.D. in math, Bob worked for the spooks, and now he works for RenTech. So he knows a lot about doing math outside academia too, and I liked his perspective on this question.
Namely, he wanted to look at the question through the lens of “grunt work”, which is to say all of the actual work that goes into a “result.”
As a mathematician, of course, you don’t simply sit around all day proving theorems. Actually you spend most of your time working through examples to get a feel for the terrain, and thinking up simple ways to do what seems like hard things, and trying out ideas that fail, and going down paths that are dry. If you’re lucky, then at the end of a long journey like this, you will have a theorem.
The same basic thing happens in modeling. You spend lots of time with the data, getting to know it, and then trying out certain approaches, which sometimes, or often, end up giving you nothing interesting, and half the time you realize you were expecting the wrong thing so you have to change it entirely. In the end you may end up with a model which is useful. If you’re lucky.
There’s a lot of grunt work in both endeavors, and there’s a lot of hard thinking along the way, lots of ways for you to fool yourself that you’ve got something when you haven’t. Perhaps in modeling it’s easier to lie, which is a big difference indeed. But if you’re an honest modeler then I claim the difference in the process of getting an interesting and important result is not that different.
And, I claim, I am still being a mathematician while I’m doing it.