I am not a great mathematician. I have many deficiencies. The deficiency I am going to focus on today is that I am not very good at generating my own research questions. But I have some ideas on how to get better below.
(Note: I am not a great mathematician, but I am an okay mathematician. This is because I have some amount of the most important quality for a mathematician: tenacity. I am not work efficiently and I may not have the background I should, but I am willing to sit down most every day and work. This is really huge).
First, I went to the Zassenhaus Group Theory Conference last weekend (I am one of the giants in the back of the picture). I was reminded how important these conferences are. For one, I got a lot of ideas for research questions from listening to other presenters speak. Some of these ideas were given to me directly by the speaker, and other ideas were tangential to what the presenter was actually discussing. But I also was a presenter, and I presented on a problem that I am stuck on. I received several great suggestions on how to proceed.
Second, I have been working with a collaborator for the past semester on a problem. Something clicked today about one problem I have: I search for a solution a little too directly. But reading my collaborator’s ideas, I realize that he plays with the ideas much more, collecting a bunch of ideas that may or may not be useful to the problem at hand. This seems like it would be enormously useful, and I am shocked that I do not do it already.
My goal is to play more. This is what I ask my students to do, and they sometimes just do not get it. Apparently, neither do I. I am hoping that
- I can work past this and
- I can learn what it took for me to work past this, so that I can help me students to learn to play more.