My friend Amelie and I have been talking about our summers, and in particular the differences in our research came up. She's on an interdisciplinary engineering team working on blimps, and I'm doing math research that has many applications but isn't really applied in and of itself.
It turns out that my team is working on a problem that is harder than we expected. We're looking for a number of different pieces, and we've found that having any one of them would allow us to find all of them without too much work. The problem is finding one, and we're a bit stuck. There are directions that we're exploring, and we've confirmed a lot of the work that we've found in literature, but at this point it doesn't feel like we're going to be able to make much progress, and we'll probably end up pivoting to a related but more approachable problem.
Amelie's reaction when I told her this was that math research seemed pretty scary, that in her kind of research, maybe there's one way she would prefer to do things, but really she could come up with six different ways. If something doesn't work, there are other ways to accomplish the same task. But when we're stuck, we don't necessarily have that option. We try to find ideas for new approaches or information from doing more literature review and from discussions with other people, but sometimes that doesn't lead to anything helpful.
We're looking for closed forms of certain expressions, and we're not even sure they exist. We know that if they do exist, they're far from elegant, but we don't really have ideas for proving the closed forms don't exist, either. So we're reading, trying to follow lots of trails, and talking to our liaison a lot for suggestions on directions to go right now and about possibilities if this is just too intractable.
