It can be hard knowing what is the appropriate length of a response to user[numbers]'s one line question

There are many of them

I'll keep that in mind.

I sometimes feel undergrad doesn't give a strong enough mathematical background, no courses in differential geometry, lie groups, functional analysis (at least in my experience)

I mean there are many universities, but that is my experience as well yes

Did things get better in grad?

This covers 2/3 of that

@Feynman_00 it did not