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
I have a suspicion that nonstandard analysis might be pedagogically superior in teaching high school calculus. But it is no more than a suspicion -- I have zero evidence to back that up.
@johncarlosbaez
@jswphysics @johncarlosbaez I had run into this book
https://en.wikipedia.org/wiki/Elementary_Calculus:_An_Infinitesimal_Approach
that was seemingly developed with that intent. From the article, it sounds like there were some limited attempts in that direction that had positive results but it was never widely attempted/assessed.
I assume there must be a fair amount of research into the pedagogy of teaching calculus, and I don't even know what the most common areas of student difficulty are.
@johncarlosbaez
