Question: What would it mean to say that mathematics was invented and how would this be different from saying mathematics was discovered? 

Is this even a serious philosophical question or just a meaningless/tautological linguistic ambiguity?

Answer: 
Mathematics is a lot of things: there are basic/complex entities/structures, proof strategies, algorithms, formal manipulations... in order to try to answer your question I think we should make some distinctions between different matematical entities/activities where the "creative" part of the thought is more or less relevant. Moreover some parts of mathematics seems to be neither discovered nor created, they seem to be just "given" embedded in our natural language grammar.

Some examples of math entities/activities that:

* *seem embedded in our grammar*: classical logical operators, classical deduction rules, tautologies, natural numbers
* *seem more discovered*: non-trivial general fact in a given structure (ex. fermat's last theorem), finding general patterns, classifications, finding counterexamples
* *seem more invented*: definition of new non-trivial structures (ex. complex numbers, quaternions), finding new non-trivial proof strategies.
My view on it is that Mathematics is a system invented by humans to represent things we otherwise can or cannot perceive. For example, we can perceive an object through vision and know it's a triangle, however, our vision alone does not tell us the length of the legs of the triangle. We need math to represent that for us.

JUst to further my point, consider Calculus. Two people who were on completely different sides of Europe, Leibniz and Newton, created a system that that both do the same thing. For Newton, f'(x) is the same as Leibniz' df/dx. Both of them yield a function that represents the slope at any given point on the original function, f(x). They invented a system to represent something we otherwise couldn't perceive (which was pre existing - The shape of a mountain should be enough to prove that the slope exists naturally), the only difference was their notation.