Is mathematics invented or discovered? In physics for example, and in science in general, facts are "discovered" in the sense that they arise from observing nature. A particle is discovered if we can measure its existence in nature. A law is discovered if the predictions it makes are observed in nature.

Is this the case with mathematics? Is mathematics "invented", in the sense that we think up concepts and ways to relate them and all mathematical derivations are just toying with those base elements we made up, or "discovered", in the sense that there is some underlying fundamental "natural" framework we shed light on?

On one hand, one could think that mathematics is an invention, as it usually derived from a set of axioms and all we do is take those axioms as given and creatively work from there, but on the other hand, there seem to be truths akin to physical laws or constants. Take $\pi$ for example. Mathematicians in India computed the same number as Archimedes. If mathematics was just an invention by man, how could there be an agreement on this as there is with any other fundamental physical law? Same with the binomial theorem, for example. This suggests that mathematical truths are "discovered", not merely "invented".

In fact, does it even make sense to ask this? Is this an open philosophical question?
I would say, personally, that axioms are invented, and theorems are discovered (as a result of those axioms). Different people will probably have different opinions.

An analogy may be that by inventing axioms, we are planting the seed of a tree. The resulting tree that grows from that seed is the mathematical framework that is a result of our planting of the tree, but we didn't have a part in shaping each branch.
America was discovered.It was there when people lived in Europe but they didn't know about it's existence.When I was 6 years old I could certainly count up to 20.I surely counted 8 and 9.I did not know of course that 8 and 9 are the only consecutive powers but this was and is actually true.I know this is now a fact (thanks to Preda Mihailescu, 2004).It is the same thing with America.Mathematics is discovered.  

One more thing:You may destroy an "invention" such as the radio but you cannot destroy the fact that 8 and 9 are consecutive powers.Even if you destroy the radio the ability to construct one from the beginning will remain alive.
Certainly Mathematics is discovered.