Math is a tool. It's orthogonal and used by all, not hierarchical above (or below) all of them..

http://euclid.trentu.ca/math/sb/misc/mathsci.html

    > The natural sciences investigate the physical universe but mathematics does not,
    > so mathematics is not really a natural science. This leaves open the subtler
    > question of whether mathematics is essentially similar in method to the natural
    > sciences in spite of the difference in subject matter. I do not think it is.

I'm not even including that famous Einstein quote about math.

Example: When you are doing math in economics you are not doing something that is even more foundational than physics.

Alternatively: mathematics can be seen as the science of structure.

http://web.maths.unsw.edu.au/~jim/structmath.html

what if the nature of the physical universe has no other reason to be as it is other than mathematical consequences of harmonies, resonances, balances, etc? In other words: if all that exists follows mathematical law, doesnt that make math part of the existential?

    > if all that exists follows mathematical law

As a thought experiment, try the opposite direction: Math mirrors reality, not reality mirrors math. I don't see electrons solving quantum equations - equations describe an electron. The cannonball follows a trajectory that we can describe using math - but it doesn't do math. Sure, you can say that it does, implicitly, but IMHO that's stretching it a bit, I don't see the value in such a metaphor.

From a certain level such questions become completely arbitrary and useless: Remember, it's your brain that interprets everything and you can just say whatever you want when there are no consequences.

> As a thought experiment, try the opposite direction: Math mirrors reality, not reality mirrors math.

If this was true, it would severely limit the usefulness of math. We'd see our predictability break down much sooner than we do actually. Read up on it here:

http://plato.stanford.edu/entries/mathphil-indis/

Why do you interpret my post as an absolute?

http://dilbert.com/strip/2015-06-07

I said - and I have no idea why I have to paraphrase my one sentence - to try a thought experiment, to see what happens when you reverse the direction.

Not to mention that you didn't really say anything? I have no idea what your point even is.

We don't have to make this thought experiment since we already know that it isn't the case - reality is a subset of what's mathematically possible. Finding that subset is what physics is concerned with.

Were you replying to me? I actually upvoted you, if it's meant to be a contradiction than I don't see it. I only just realized you may have been answering me since you used my words, but other than that I have no idea if that's true.

In any case, I should have read more carefully, because

    > reality is a subset of what's mathematically possible

does not mean anything. It's a grammatically correct sentence, sure, and that's all. The number of (grammatically) correct sentences is definitely larger than the number of useful ones though :)

let's just say it was a bit late in my timezone ;-).

I probably replied to the wrong post, but I wanted to say that math is in fact a tool for science - instead of being the most fundamental science itself. I've met some people, including mathematicians, who think that because everything can be described with math, it means that math is all that's needed to find the truth about reality. My point is that the process of appying math to find the model that best fits our own world is something that's outside of math itself.