/math/ - Mathematics

Both, depending on how you think about it.

We have Axioms, which are things we hold to be true, but cannot prove. For instance, the idea that two parallel lines will either intersect 0 times or infinite times.

If we choose different axioms, we would still arrive to the exact same conclusions (which is a pretty good indicator that the truths are objective), but our proofs for those theorems would be radically different.

The patterns that emerge from a collection of axioms are indeed objective (in that no one else can derive different results from them) and natural (since many natural processes behave according to these patterns regardless of whether anyone has studied them.)

Choosing a set of axioms which gives a good balance of generality and usefulness is an art, so they seem more like inventions. For example, topological spaces are pretty general, so they don't have the nice properties that Hausdorff spaces have, which itself is pretty broad compared to metric spaces, which have a great deal of structure and nice properties. But Euclidean spaces, although having tons of organization, cover a very small portion of useful mathematical objects.

However, since some collections of axioms give a surprising amount of results over other less elegant attempts, one could argue that they would be invented anyway at some point, so they are discovered rather than invented.

I'm a graduate student in mathematics, and can confirm that all our perspectives, even through reason, are incapable of reaching higher reality. Sorry meat monkeys, but we're all shit stains.

As far as the "real" axioms go, it can be imagined otherwise. By that I'm talking about the axioms that are talked about today, not the commutative property of the integers. When it comes down to it, the mathematical community decides something that it decides is "cool" or is a good direction to rock with and rolls with it. Perhaps this is for lack of another viewpoint, but I don't think there are many mathematicians that will say mathematics is a fundamental property of the universe, other than from our perspective. Of course, higher level physics is based on all of this so what you have been told as true could very well be meaningless. Who cares, live your life.

>>328

At what point does a sentence arise out of mere description and into modeling?

At what point does modeling accelerate the repeatability of things?

At what point does the repeatability of things result in the influence of distant objects upon each other?

At what point must the repeatability of things be measurable through the manipulation of symbols in order for the universe to exist?

Answer those questions and you'll know if math runs the place. Nitpick, of course, is whether our current math is anything like the math the universe uses, and even so if we're constructing it correctly and completely.

>>337

A sentence doesn't model anything until it is interpreted in a model, for instance the sentence "multiplication is commutative" is meaningless until you clarify what it is you're talking about multiplying. So in some sense you have to pair the sentence with a structure in order to decide whether it has any sort of meaning beyond expressing some abstract property. I have no idea what you mean by repeatability of things.