I don't remember many of the advanced algebra classes anymore and I wouldn't be able to tell you why precisely the polynomial equations of 5th and higher degree

I don't remember many of the advanced algebra classes anymore and I wouldn't be able to tell you why precisely the polynomial equations of 5th and higher degree aren't solvable in radicals (has something to do with sequences of normal subgroups, eh...) But studying advanced maths forced me to learn to think rigorously and take various minuscule details into account, and that skill is valuable.