I’ve been doing some soul-searching lately. and landed on a good way to satisfy any latent academic urges I feel: contributing to libre math software
In particular, I’m taking a course in “modern control theory”, and will be using Matlab quite a bit (much like vector calculus literally grew out of the need to understand electromagnetics, I think a significant part of Matlab grew specifically to accommodate this type of engineering).
I used software called Sagemath/CoCalc to investigate a few topics in pure math previously. It’s built on top of Python and completely libre. It’s pretty good for a lot of algebra and number theory mathematicians care about, but can get pretty sparse outside of that. The creator, William Stein, seems pretty cool but bummed; I’ll always remember a status update where he declared the software a failure because he couldn’t compete with banks etc in terms of paying math graduates to work on the software
Sage doesn’t seem to have any control theory toolbox whatsoever, and I’m thinking I might like to see how much of this sort of thing I could implement in Sage and actually learn how.. software works, to the point that I could actually clean my shit up and get it included in Sage; you could replicate what was done in Matlab with similar effort. I haven’t done an in-depth search to make sure this functionality isn’t present, but the top hit for “sagemath transfer function” is a 7 year old thread
This only occurred to me recently, but it feels infinitely more meaningful than whatever academic research I could ever produce, so I’m thinking I might give it a real shot.
If you're not familiar with Arthur Whitney, you would find him and his work fascinating. It's very much for-profit, I'm afraid. But he's an absolutely brilliant mathematician and programmer, who did a lot of work in terms of bringing various aspects of math into computing.