I think academic math has a problem where it’s more culturally valorized to *be really smart* than to teach well, to the point that effective communication actually gets stigmatized as catering too much to dumb people.
Having left academic math, I am no longer terrified of revealing my stupidity, so I can now admit that I learned intro probability theory from a class in the operations research department (that used an actual syllabus and lecture notes! unlike most math classes!), that I learned more about solving ODEs from my economics classes than from my ODEs class, that I only grokked Fourier analysis when I revisited it in a signal processing context, and that my favorite introduction to representation theory is Shlomo Sternberg’s *Group Theory and Physics.*
Concrete examples are easier for some people to learn from!
I think academic math has a problem where it’s more culturally valorized to be really smart than to teach well
I don’t think that’s the issue exactly. My guess is that academic math has a culture of teaching something quite different from what most applied practitioners actually want. The culture is to focus really hard on how you reliably prove new results, and to get as quickly as possible to the frontier of things that are still a subject of research and aren’t quite “done” just yet. Under this POV, focusing on detailed explanations about existing knowledge, even really effective ones, might just be a waste of time and effort that’s better spent elsewhere!
This matches my experience.
I think academic math has a problem where it’s more culturally valorized to *be really smart* than to teach well, to the point that effective communication actually gets stigmatized as catering too much to dumb people.
Having left academic math, I am no longer terrified of revealing my stupidity, so I can now admit that I learned intro probability theory from a class in the operations research department (that used an actual syllabus and lecture notes! unlike most math classes!), that I learned more about solving ODEs from my economics classes than from my ODEs class, that I only grokked Fourier analysis when I revisited it in a signal processing context, and that my favorite introduction to representation theory is Shlomo Sternberg’s *Group Theory and Physics.*
Concrete examples are easier for some people to learn from!
I don’t think that’s the issue exactly. My guess is that academic math has a culture of teaching something quite different from what most applied practitioners actually want. The culture is to focus really hard on how you reliably prove new results, and to get as quickly as possible to the frontier of things that are still a subject of research and aren’t quite “done” just yet. Under this POV, focusing on detailed explanations about existing knowledge, even really effective ones, might just be a waste of time and effort that’s better spent elsewhere!