The remote video experiment was a general success, I think. I was gone just long enough for my group to work on the project just to the point of feeling frustrated and hamstrung (which is, sadly, the primary feeling of doing math research). I was expecting them to feel that a little sooner in the program. I tried to set the project up so they’d have plenty of opportunities to feel confused, overwhelmed, and unsure of what to do next. That’s not because I’m naturally sadistic or uncaring; that’s because I want them to have a real research experience, and these feelings are part of the process. To become a researcher, you have to learn to live with doubt and uncertainty — and then to get to work. I also want to give them a taste of criticism and rejection, because that’s part of the process, too. But ultimately, I want them to learn a lot of math and discover something new. They’re on track to meet both of those objectives.
However. Having said all of that, I want to be supportive and helpful, too. I’ll prepare a few lectures on related algebra topics (tensors products of modules and complexes) and give them a little homework to do. Again, this mimics research: when you realize you have to learn something new to start working on a problem, it’s a relief. Working through the basics of a theory is like classwork, and by the time you’re doing research, you’re good at classwork.
I’ve also tried to rephrase the research problem a few different ways for the students, based on what they’ve described to me. The point here is to try to help them interpret the problem in a way that will lead to a specific course of action. I’m being purposefully vague about what they’re doing; as I keep telling my math friends, you’ll just have to wait for the paper for the full picture. Consider this blog one long teaser.
As for my work… Before I left last week on my personal trip, I finished editing my parts of a paper and sent it off to my coauthors for their next turns. Phew. One item off the to-do list. I also made some progress on writing a project description for a grant proposal. I struggle with writing grants; finding the appropriate level of assumed knowledge on the part of the reviewers trips me up.
Time to get my homework done for tomorrow!