My belief (I call it a belief, because I haven't done rigorous research to confirm it; it is based on what I learned during studying physics) is that all early,

My belief (I call it a belief, because I haven't done rigorous research to confirm it; it is based on what I learned during studying physics) is that all early, 'basic', mathematics was invented (or discovered, I don't want to get into that) to describe nature. Initially, the natural numbers were nothing but a convention to describe and differentiate between sets of multiple objects that were to be considered equal for the purposes of discussion. IV apples vs. V apples. II rocks vs. VII garments (of course, the Romans didn't invent this, but I find it a distraction to use 'our' Arabic numerals). Another example: Newton invented differential calculus specifically to describe nature. Shortly after that field was invented, mathematics in it would be done for it's own sake, but that doesn't detract from the fact that originally it was meant to describe nature. More recently, mathematics has been invented before it was shown to be applicable to physics. What I earlier meant is that this may be a result of the origins of mathematics and doesn't prove what it seems to imply.