As somebody who's studied some advanced maths, I think that their point is that abstract algebra is effectively a sort of secret maths techniques, sitting in plain sight but somehow sprayed with repellent or maybe equipped with a Somebody Else's Problem field.

I have had more than one afternoon where I learned a concept wholly from this sort of lecture. The ability to ask the professor questions can be useful, but almost all of my questions are actually answered by being more careful about listening to what they are saying the first time.