In this thread with @johncarlosbaez I was mentioning how when I first encountered Category Theory it seemed like little more than a curiosity (for my purposes, as a physicist), even though mathematicians seemed excited about it.
I had almost the opposite experience with Nonstandard Analysis (i.e. the hyperreal numbers), in the sense that I bumped into this notion, read a bit about it, and it sounded potentially quite useful. Physicists tend to talk in terms of infinitesimals anyway, so a framework where that could be done rigorously seemed useful, and I was curious if it might provide nice ways to think about other things such a path integrals or even renormalization. But the only mathematician I talked to about it dismissed it as basically a curiosity. I believe the way he put it was that it was "just a trick to avoid an extra quantifier in in proofs."
Now I'm curious if that is the consensus among the #physics and #mathstodon folks around here or if people see it as a practically useful tool.
#math #maths
QT: https://qoto.org/@internic/110639879113598032
@internic - A few people have tried to use nonstandard analysis to prove theorems in analysis that haven't succumbed yet to traditional techniques. I've mainly seen this in attempts to make interracting quantum field theories rigorous - this subject is full of unsolved problems in analysis. But none of the nonstandard attempts have made much progress. And that makes sense to me, since I don't see how nonstandard analysis would help much here.
@johncarlosbaez Are there areas where you would expect (at least intuitively) there to be more likely to be of some practical use or not really?
