Something I often wonder, as I want to one day be a math prof...
As far as credential go: most Junior colleges require a Master's degree, and, as far as I know, Universities require a PhD.
i could probably easily solve 95% of the problems in any calculus text (except very hardcore old-school ones like hardy's a course of pure math) in a day or less. in spite of that i don't think i know math well enough to be a math prof. i'm sure everyone knows someone who has picked out typos in math texts. well i would say someone knows math REALLY well if they can find a mistake in the statement of a theorem (ie the book says something that's false like omitting some condition), fix it so it says something true, and then fix/rewrite the proof. i can find typos but i've never spotted a mistake in the statement of a theorem. i guess mistakes like those are rarer though. anyway that's the kind of critical thinking & autonomy it takes (i assume) to get a PhD, which is part of what someone has to do to become a prof.
way back in 1st year my physics prof told me that physics is extremely competitive; the guy whose office was next door worked at CERN as an experimental physicist for 8 years before becoming a lowly assistant prof at the university. i assume it's roughly the same in most other fields.
But I think Physics is a touch more competitive than Math.
Besides, things like what you mentioned are laregly stuff which can be learned.
My 70 year old Number Theory prof said that to be a professor in math, you need to pick a field and then get good at it.
He is an algebraist and really only has a passing knowledge of the geometric domains of math beyond some finite geometries(undergrad type stuff), and even those he is not to good at anymore.
gone are the days of Gauss, Leibniz, Able, and Euler when a mathematician can have a day job and dabble in many different fields of math in their spare time and bring to light many new ideas.
As most professors in the sciences... you must ... well, devote you're life to it to be good enough. I mean really, you take 10 years worth of college courses to get a Phd for a reason...
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