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: 
First, Quine:
"..[If externally true] the definitions [of mathematical laws] would generate all the concepts from clear and distinct ideas, and the proofs would generate all the theorems from self-evident truths."
"...the truths of logic are all obvious or at least potentially obvious..[but] mathematics reduces only to set theory and not to logic proper."
-Epistemology Naturalized; Chapter 39.

The implications are bleak for the ontological objectivity of mathematics. For a fact to reduce to certainty one must present sensory evidence (to be "self evident"). Consider, I see that things fall to earth and stay there. I explain this to myself with physics. What I see is not physics. Physics is a framework invented to generalize what I am perceiving. 

A 1 and a 1 on a sheet of paper are not the same as a 2 on a sheet of paper. 1 is the smallest prime#, for example, while 2 is the smallest even prime, among myriad other differences. 

An apple on a table and an apple on a table is not the same as two apples on a table, as the set of two apples could be different apples. I cannot cube two apples, except to make pie. But I cannot make pi with an apple.

The value of a dollar is measured mathematically. But if humans disappear, the piece of paper remains, while the value disappears with humans. Things stick to the earth regardless of our existence, but the theory describing our perception of gravity does not. 

The epistemic objectivity of Mathematics is ontologically subjective. It exists only in our minds. Something that exists only in our minds can only have come into existence within our minds. Something that does that is invented.
If only we would get the question right, we may be able to get the right answer. The problem is, is invention discovery or creation? As a seven times patented inventor, I will tell you that invention is, at least to a great extent, discovery. As my patent agent explained, what is invented is a "method", a way of getting a job done. During the process of invention, one tries on a gazillion methods of getting the job done that don't work. When one does discover a method that does work, well, one has an invention.

The proof of discovery verses creation, is the proof of reproduction. When a person who has never seen a wheel before tries to solve the problem of causing heavy objects to move, he may very well re-invent the wheel. This happens all of the time with inventions. One comes up with a method of solving a problem, only to discover that someone else has patented that invention before him. Creativity is not like this at all. If two people truly independently come up with the same creative product, then their creative product is, well, simple. In fact programs are used to analyze college papers for plagiarization. They seek matches in a 7 word sequence because it is unlikely that two people independently come up with seven little words strung together the same way.

So let the question be, "is mathematics discovery or creation?" Ask the anthropologist to seek out the mathematical methods of other cultures. Surely these methods would be extreme subsets of our math. However, they still have some simple consistencies. Two plus two (though represented with different words) equals four. The fact that two cultures independently come up with the same logic sets establishes that mathematics is discovery, not creation.