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As someone who ended up majoring in pure mathematics, I always thought it was a shame that theres this wall of arithmetic and calculus between you and the first pure mathematics class.

I suck at those, but I do well with abstractions and proofs. Makes me wonder how many pure mathematicians the field misses out on.

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My university kept the pure math courses for "honors" students; I'm still outraged by this to this day. It's very misleading and as someone who didn't do great in the "regular" (i.e. rote repetition/memorization calculus and linear algebra courses), it kept me out until a prof in one of these classes introduced me to real math. At that point it was a much steeper learning curve to switch to the "honors" route but I'm glad I did it.

It does seem strange that you have to typically "pay your dues" with 4-ish semesters of calculus (calc i, ii, ii, diffy-q, and maybe pre-calc) before you take anything else. It's very strange as a gate-keeper to the subject.

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