>>12881028First, there is no generally accepted definition of math. So deciding whether math is a science or not will depend on your definition.
However, there are a generally accepted definitions of science. Science deals with empirical data and falsifiable claims about the universe.
I'd argue that most people would define math in a way that it's not a science.
If I want to know if 123 + 456 = 579 or not, I'm not going to run experiments, I'm just going to calculate it.
If I want to know if the Collatz conjecture is a theorem or not, I won't run experiments, at least not physical experiments. I might do a lot of computations, but even that would just to build my intuition. At the end of the day, I'll need a proof, no matter how much data I have.
Personally, I define math as the study of analytic statements. Things that are "true by definition". For example, if you define 1 to be "a number" and 2 to be the number that comes after 1 and "something"+1 to be the number that comes after that thing. Then 1+1 is 2, by definition.
If you define 3 to be "a number" and 100 to be the number that comes after 3 and "something"*20 to be the number that comes after that thing. Then 3*20 is 100, by definition. It's just that these definitions suck because these symbols already have other implicit meanings by convention.
Analytic statements contrast synthetic statements, statements you can't prove/disprove with definitions alone. For example, "My chair is black". Even if you know what chair and black means, to know if this is true or not you'll have to step outside of your mind. You'll need to look at my chair or something.
But like I said, that's just my personal definition. Our desire to study analytic claims about numbers comes from them being really useful in practice. So you could argue that there's a link of some sort between math and the real world, which I agree with, but then we'd be talking about philosophy of mathematics instead of mathematics.
