Written: Oct. 8, 2020
I loved your piece here: https://sites.math.rutgers.edu/~zeilberg/Opinion174.html It was very comforting to read. My current research work centers around building new interpolating algorithms with clothoid and spherical clothoid segments. I am motivated more by the application in robotics, the practical side of the resulting algorithm more than austere mathematical beauty (although I do love it). In my own experience, it has been very useful for me to flirt with questions where I do not hope to have a rigorous guarantee that my technique will work in all cases but can still work 99.999% of the time in practice. Computer algebra lets a mathematician work a lot like an experimental physicist. In a lot of math culture, I find there is a growing divide between research mathematics and industrial/scientific questions outside of math. On one side, we have a lot of academic math preaching a kind of medieval theology of absolute rigor and truth, relying on pen and paper as much as possible. On the other end of the spectrum, we have a world with engineers, roboticists etc. working with very rough heuristics. I think a lot can be gained from these 2 extremes looking at each other and pushing forward a more experimental, algorithmic and semi-rigorous approach to mathematics.
-Alex