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: 
I consider an answer too simple if it just affirms one of the alternatives and negates the other.

Naming just a few eminent contributions to mathematics: Complex numbers, set theory, theory of schemes. E.g., the concept of a set has been invented by Cantor, it did not exists before. After the basic concepts like set, power set, cardinality etc. had been invented, the Continuum Problem was discovered, hidden deep in these concepts. 

Therefore I compare mathematics to a game like chess: Inventing new mathematical concepts is like creating new rules of the game. Playing a match means to discover the consequences of the rules and to solve the problems posed by the rules. 

My conclusion: The rules of the game of mathematics have been **invented**. Following the rules mathematicians then **discover** some challenging matches.
Every mathematician can only discover mathematics.

Yet, mathematics is an invention.

And this is no contradiction.

Mathematics is fundamentally dependent on the human mind, and more particularly on human deductive logic and on the human perception of the real world, so it is a sort of invention of the homo sapiens species, not one of individual mathematicians. Human mathematicians are unable to invent anything logical which does not follow logically from human nature.

Thus, every mathematician can only discover what is already there, implicit in human nature, and since the mathematicians we know of are all humans, they will discover or rediscover the same things.

This is why mathematicians come to believe that it is a given, hence the Platonist view.

The Platonist view is wrong because while mathematics is given to every mathematician, it is not given to the human species. It comes with, or is part of, its own nature, so to speak. Human mathematics does not exist outside the human mind.

The human species is itself implicit in nature, so human mathematics is implicit in nature, but it is set out according to human logic and human perception of the real world. So, at best, the Platonist world is nature itself. This is clearly not what mathematicians mean by "Platonist", but this is the only reasonable option.