[bbor]

Well put, but sadly I must disagree heartily. Mathematics is half of what drives/guides/underpins natural science, but it is not itself a natural science.

As Kant teaches us in A Critique of Pure Reason, mathematics is the cultivation and extension of intuitive intellectual tools. This puts it in natural opposition to philosophy (which deals with conceptual intellectual tools) and natural science (which deals with the empirical nature of the Actual world). None of them would be very useful without the others, but that does not mean that we should abandon the distinctions, imo.

That article is great, but I think the immediately preceding sentence is telling:

  Earlier that year, his father had died, and Pasten found himself turning to math for comfort. “I found mathematics really helpful for that,” he said. “Mathematics is not just about…

To put it bluntly: I think that’s just cope. Again, I absolutely agree that mathematics can be useful for natural science, but we need to look no further than the multitude of mathematically-consistent models of the universe to see that it is not itself natural science.

[youoy]

Yes! I agree with you, mathematics is not a natural science. You can study the physical reality or the intellectual reality, mathematics would be closer to the intellectual reality.

I guess this points back to the eternal debate about if mathematical objects are invented or discovered. If they are discovered, then that would mean that there is an underlying truth/semantics behind the mathematical formalisms. So in that case mathematics studies and interacts with reality. Take for example Calculus and Newton and Leibniz [0] who invented/discovered calculus independently.

I will let you decide on what side of the debate you feel more comfortable :)

[0] https://en.m.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calcu...