I disagree that there are "levels" of math as your post seems to imply. Yes, it's true that certain subjects are typically taught in a certain order (in the US

I disagree that there are "levels" of math as your post seems to imply. Yes, it's true that certain subjects are typically taught in a certain order (in the US at least) but that doesn't really imply that calculus for example is "higher" or more demanding than algebra or discrete math. There is professional, expanding-the-limits-of-human-knowledge level research being done in Algebra and Geometry just as there is in Calculus. Calculus is not the endpoint of math.