[ArkyBeagle]

What's important is a familiarity and a comfort with rigor.

You don't have to be a genius to gain that. It might even be a liability - you don't have to follow the formula to get the right answer ( because you're impatient and want to go play outside ) ; you can just see the answer. This happened to me, and I spent a couple or four years as an undergrad undoing damage I'd done to myself that way.

I'd buy a lot more about what we think we know of human capability if there was even the most modest attempt to control for this factor.

I went to what used to be a "normal" school that had risen to university status. It still mainly taught teachers although I pursued a BSCS.

I asked the department chairman of the department why math was taught "from the wrong end of the telescope" and even he didn't really know why. I suppose the proofs course is no way to get buy in, but had I started with proofs rather than what they taught as algebra, I'd have had an easier time of it. I'd taken geometry but even algebra was still a morass, until I'd gotten a grounding in proofs.