Very good point. A professors job should be foremost to teach. Research and chasing fame should come second. In my opinion, universities have flipped this on its head. They've allowed and in some ways forced professors to relegate teaching to a level of "by the way". Students pay and go to university to learn from teachers, not to subsidize researchers. There's something very wrong when a University places more emphasis on research than in teaching students
There are research universities and teaching universities. If you want to go to a college that focuses on teaching calculus 101 they exist though I don't know why as a budding mathematician you'd want to sprint full speed away from doing real mathematics.
The research has to be done somewhere. It's supposed to be subsidized by the public or private donations but funding is regularly and methodically cut so the only remaining reliable source of income is tuition which ends up having to pay for both.
Not an ideal situation but unless Americans start deciding research is worth paying money for (unlikely) it's what we have.
Umm why? For the most part a professor is a talking text book that stands in front of the class. You can go download charismatic people with fancy approaches to the material online. However, I don't think this really makes much of a difference (choosing the right curriculum does though).
The one place I've seen professors have real impact is in their ability to both answer innovative and novel questions and convey a sense of excitement and interest in a subject. While these only affect a small fraction of any given class they are the important value add and they are what someone who is personally passionate about the field and deeply knowledgeable about it brings to the table.
Worse, what seems like "good teaching" can often reflect a counterproductive attitude to the subject.
Everyone I know who has become a mathematician has done so DESPITE (not because) of their pre-college teachers (some have had the good fortune to run into one or two exceptions but still struggled past teachers who attempted to ruin the subject). These teachers were chosen entirely for their teaching ability but to no avail since without the perspective of a research career they weren't teaching people how to duplicate a computer algebra system instead of understanding the math. Focusing on accurate symbol manipulation and memorization is in active tension with understanding but is an easier rote to solving the kind of problems you can ask on AP tests.
College students are big boys and girls. They can read the damn textbook if needed. I spent an entire semester at caltech (my most productive one) without attending a single class (I had my friends turn in my homework in section). However, having professors available who could accurately convey (through course content, discussion and even research projects) what a discipline was about was invaluable.
Let's give up the charade people and let professors play videos of better speakers in lecture but lend their expertise to answering questions and talking to students.
