You think Mathematicians in general have people skills? Most Mathematicians i met were good people but they definitely kinda lived in their own world, they were super helpful, but only if you explicitly asked for their help.
The issue today, IMHO, is that every university is looking for professors who are "good at research" (meaning, they can win grants), and teaching is not even a secondary or tertiary thought (if a thought at all). The last four professors we hired in our STEM department could barely speak English (I am in the states), let alone get points across or create examples. You know what they can do well? Write grants that get awarded.
Research and teaching are both important, and a smart university tries to use its professors' talents most effectively.
I studied at the VU, where Andy Tanenbaum, writer of a ton of famous CS books teaches. Of course I followed his classes. His books are excellent, but his classes are basically him reciting his books from memory. The jokes are literally identical.
At some point, more and more of his classes would be taught by Maarten van Steen instead; he's an excellent teacher who really knows how to engage the students and make them think about problems, instead of merely telling them the answer.
There was another professor who, as far as I know, didn't do any research at all; he just taught a ton of classes.
A professor who is great at one thing is not necessarily good at something else.
People skills? The informal prereqs/expected background for a class should be listed in the syllabus. Lack of "mathematical maturity" is a non-answer, they should make it clear what sort of math knowledge that refers to.
I disagree. 'Mathematical maturity', to me, means:
There is no specific advanced prerequisite knowledge, but you need to be able to follow something technical.
As an example: you'd reasonably expect a student with mathematical maturity to know what a set, the Cartesian product of two sets, and a function are. That's high school level math.
From there you can define a ring and a module over a ring, in like 5 mins.
So at that point the Prof, strictly speaking, told you everything you need to know to start studying modules.
Of course, many students will be like whaaaaaa?! When a ring is defined. But here's the point: Mathematical maturity does not mean that you already know what a ring is, but when the Prof defines a ring, you are following along.
Anyway, my point is that there is nothing specific that you need to know.
Mathematical maturity should be well defined if you are using it as a prerequisite. Mathematicians, of all people, should be good at coming up with such precise definitions.
Some people are better with math than others. Undergrad math majors thought the major was pretty easy. Many of us in engineering majors--who weren't that bad at math (it was a good school)--could no more have graduated with a degree in math (or physics) than have flapped our arms and flown.
Maybe the class did have pre-req? I mean i think it is obvious that a class called "Hard problems in combinatorial optimization" is aimed more at future Mathematicians/Computer Scientists than people who want to take it for the fun of it.
I felt this in Spain. In my little local university it seemed like they were gatekeepers. Some professors were hostile and treated you like if you were dumb.
It didn't help that I went to uni at 24 IIRC while I was working my ass off, so I wasn't that happy to put up with the BS.
It seems less like gatekeeping and more like "I'm struggling for my life to climb this mountain on my own, and I'm not strong enough to drag up your dead weight up behind me. I'll train you if you seem to have the aptitude and drive to eventually become a useful partner in my struggle, but I'm not going to waste my life energy on people who will never be anything more than dead weight."
Calling it gatekeeping seems like a fish complaining that the birds are gatekeeping the sky. The sky is open for anyone, but only if you have wings to fly.
