I have a tendency to think, that here we need a rather precise meaning of math. On one hand, I tend to view mathematics (and logic) as a special facility of our

I have a tendency to think, that here we need a rather precise meaning of math. On one hand, I tend to view mathematics (and logic) as a special facility of our brains, which evolved to make sense of the surrounding world. For example, we essentially call geometries flat, which look like our local geometry. On the other hand, a intelligent entity which evolved in a curved spacetime, would have a brain to make sense of a curved spacetime and therefore would use a curved space as basis for its mathematics (in a similar fashion as we use |R^n as the standard example of a multidimensional space). But we can proof theorems about curved space (and this entity would be able to recognize theorems about Euclidian space as true. [1]) So to answer your question, mathematics [2] the craft, is very much shaped by nature. However there are apparently fundamental rules of the universe, which we would also call mathematics. [1] This sentence needs a qualifier, which should express that I am certain, to the extent that humans are a general intelligence. [2] Greek, something like 'the subject of study'