First of all, math is not just numbers. Probably, most of math only deals with numbers indirectly. Think of geometry class. Is it really about numbers? No, it's about shapes. You could certainly interpret it in terms of numbers and numbers are sort of there in the background, but when you think of geometry, you don't start thinking of explicit numbers like 5, 15, or 186285, you think of circles, squares, lines, etc. So, I always find it a little annoying when non-mathematicians tell me "oh, so you're a numbers person" because that is only part of math (and one of the least interesting parts, to my mind), and most of a mathematician's thinking doesn't explicitly have anything to do with numbers. I find it annoying, not just because it's inaccurate, but because it sounds like they think mathematicians just sit around adding and subtracting really, really big numbers and computing pi to a bazillion decimal places, which is just sort of degrading because it's much more interesting than that (well, SOME of it is, anyway).
Archimedes changed the way we looked at geometry, mainly (maybe numbers, too, but I think that's less important). Also, I'm not sure importance of discoveries is related to their difficulty in any clear-cut way. Some people are just in the right place at the right time when they make an important discovery.
The type of scale you mention would suffer from the same problem as IQ. It assumes that people can be ranked in a linear order, which can become silly if you take it too far. For example, my PDE prof was better at certain kinds of very computational PDE research than I will ever be, but my visual reasoning ability was much greater than his, so we have wildly different levels of ability in tackling different kinds of problems. To some extent, if you're good at one type of math, you tend to be good at other types of math, but that doesn't mean there is no such thing as having different strengths and weaknesses.
Why do people vary so much in their math acumen? Is it nature, nurture, or a combination of both?
No one knows, but obviously it's a combination. Understanding math is something you learn how to do, though. I think my own ability was greatly increased by reading Visual Complex Analysis (I was about 21-22 at the time) and following its example.
I'd rate myself about 8.5, considering I got a PhD in math and proved a few new theorems in topological quantum field theory. People who make really revolutionary discoveries typically are quite a bit above my level, even though I am capable of proving theorems that no one else knows. Maybe you could say 9 is like a typical research mathematician, and 8 is like the typical math PhD. But I wouldn't take this scale seriously, other than your own personal use, if you want.
