Would you say math was discovered or invented?

[NeutronStar]

I can see how such views might develop if one only works with numbers, and never has to verify predictions.

I too fully understand where the pure mathematicians are coming from. However, I also firmly believe that pure mathematics could be both, logically abstract, and ontologically correct. So I don't understand why mathematicians don't strive to make it both logically abstract, and ontologically correct.

Well, actually, I do understand why the mathematical community historically went down this path. I just disagree with the direction that they have chosen to take. What I don't understand is why the scientific community isn't in an uproar about it.

Who is at the helm of the mathematical community? Any why have they chosen to completely ignore the original historical foundation of mathematics? (i.e. The observed ontological quantitative properties exhibited by the universe?)

To answer my own question, I believe it was their thirst for some idealized logical purity that is disconnected from physical reality. Personally I think that notion is absurd. The quantitative properties of our universe exist because the physical universe exists. Any attempt to try sweep that under the carpet is nothing short of silliness.

It's just plain silly. It really is!

More importantly, as we continue down this path we will get further and further away from ontological truths. All aliens will recognize numbers like π and e because these quantitative relationships arise from ontological situations.

But will all aliens agree with the axiom of the existence of an empty set? No. Why not? Because that's strictly a human invention that is actually quite ontologically incorrect. Aliens would laugh at such a notion as being a display of our ignorance. The aliens will, however, understand the concept of a set itself, because that is ontological. They will just have to explain to us that we don't fully understand the concept of sets, and then show us why it is ontologically incorrect to claim that an empty set can exist.

I'm not even an alien and I know that much!

In fact, whenever we ask whether we are inventing a concept, or discovering it, I think it is a good test to think in terms of extraterrestrials. Would they come to the same conclusions? If so then it must be a discovery. Or might they think up something else? If so, then we must be inventing an arbitrary concept.

 

[Hurkyl]

My response here.

 

[Icebreaker]

If aliens may not agree with some axoims, then it's possible that some theorems as well and, from there, our entire math structure. Meaning that they might have a different math system than ours, and therefore, math is invented, not discovered -- for it to be discovered, it must be universal.

 

[selfAdjoint]

If aliens may not agree with some axoims, then it's possible that some theorems as well and, from there, our entire math structure. Meaning that they might have a different math system than hours, and therefore, math is invented, not discovered -- for it to be discovered, it must be universal.

Not so, just because the medieval Europeans didn't know about the New World didn't mean it wasn't there, nor that the geography they did no was wrong. Just because mathematicians have only discussed certain systems and there are other systems yet unkown to us doesn't invalidate the systems we know. Mathematicians are continually dealing with aliens who discover different systems and new perspectives on old ones. It's called the younger generation.

 

[Icebreaker]

Exactly, it is not invented because one of the two must be "wrong", and therefore there must be a true and universal answer.