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.
I think it's hard to say. If you believe that mathematics has been discovered, you must assume that "something" is out there, something we can interact with, of which we have been unable to prove existence so far. 

However, even assuming that there are ideas out there, I believe that there is no reason to think that humans should be, in any way, able to understand them. As David Deutsch famously said, the fact that we understand the laws of Nature, is pretty much like saying that you land on another planet, and find aliens completely able to speak to you in english. 

Last but not least, it is possible that our models of how the Universe works are completely wrong. Hence, we are talking about ideas derived from our models that may be, ultimately, way off the truth.