[somenameforme]

I'm speaking of math majors, or fields with a heavy math requirement, of course. Diff eq is not required anywhere, as far as I know at least, for non-technical majors. As for the army, I wouldn't just hand-wave away soldiering. You're talking about people being put in high pressure situations with ever-shifting dynamics, potentially against a human adversary, where lives are at stake. And they think everybody except the bottom ~32% of society is fit for this task.

I'd certainly expect an average person who dedicates his life to mathematics to end up with a higher than average IQ largely because while IQ is a useful measure, it's not an independent g factor. Studying mathematics is going to absolutely help train your brain in many areas that are also beneficial for performance in IQ exams. So for instance, some studies have shown that each additional year of education, relative to a fixed base, can causally contribute 1-5 additional IQ points. [1] So our person in question would almost certainly expect to see a significant and measurable IQ increase.

And FWIW I'm rather on the opposite extreme of those who argue for some sort of tabula rasa. I fully acknowledge dramatic innate differences between individuals, but I'm largely arguing that such differences only become major factors for people who approach their genetic potential in something, which most people will never get even remotely near, simply because the amount of dedication and sacrifice it takes is something that very few people are willing to accept.

[1] - https://pmc.ncbi.nlm.nih.gov/articles/PMC6088505