I think it's a difficult question because it's really quite meaningless.
All of our logic, all of the way we think, is developed from our interaction with the universe, in very fundamental ways. I am in my bed. My bed is in my room. Therefore I am in my room. In this way our logic develops. Mathematics is the body of knowledge that grows from this logic. It is a human construct and it does such an amazingly good job of describing the universe because it grew from the structure of the universe. So when we find a surprising result and then find an example of that result in nature, we are even more surprised and get a feeling of being small surrounded by The Big Mystery.
"Was the math there or did we make it?" ignores the fact that we ourselves are a part of the mechanisms of the universe. To me, creating and discovering are the same. I am just happy I can take pleasure in the process!
(I suspect that the universe itself is an emergent phenomenum that comes from the simplest of rules, "1+1=2" or even simpler, like "1". It only really makes sense to me to think that the universe is just one particle.)
Agreed. Axioms are created, everything else is a property of those axioms and 'discovered.'
Those basic axioms tend to be the most useful in our universe, but they were still 'created.' We often define or create other axioms, for example, taxicab geometries are imminently useful for modelling paths in cities. We created the rules for the taxicab geometry, as with Euclidian geometry, but we didn't create the properties that emerge from those rules.
I think maybe the confusion comes from a misunderstood analogy: people think 'if you build a castle of LEGOs, you created that castle; aren't maths likewise created?' The misunderstanding is that mathematical theorems and properties aren't like the castle, they're like the potential to build a castle from those given LEGOs. The child created the castle, but she only discovered the possibility of building a castle, which always existed as a property of those LEGOs.