Is this different from when I said: > It's not just physics that drives interesting math, and it's not just recently that this relationship holds When you say

Is this different from when I said: > It's not just physics that drives interesting math, and it's not just recently that this relationship holds When you say > So much of it was invented by someone just noodling around with numbers I think you're ignoring where the numbers being played with came from. Very rarely does someone just invent a fresh problem de novo and start messing with it AFAIK; the 'playful mathematics' approach is still reusing tools which were developed in application, just (typically) a long period of time after that original application. Euclid's geometry doesn't exist without the invention of a compass and rule for drafting. Yes he's playing with the concepts freely, but it's not just some arbitrary toy ideas, they're rooted in a practical reality (albeit deeply).