are mathematics invented or discovered?

discovery or invention?

In the LinkedIn group about mathematics "Math, Math Education, Math Culture" Opher Liba asked an old and recurrent question in mathematics: Invention or Discovery? This was the title. Many people contributed to this interesting topic. I am not going to make a summary of all the relevant opinions, some of which were quite elaborated. Just let me highlight the new term proposed by Jonathan Visona: innovery (a mixture of invention and discovery). I will limit myself to reproduce my entry. 

I am one of those who think that mathematics is nothing more (and nothing less) than a language: http://www.cut-the-knot.org/language/MathIsLanguage.shtml

Is the language (theormems, propositions, corollaries) already in the grammar (axioms) that specifies it? Well, in some sense it is, but on the other hand you do not care for every possible sentece that can be expressed in the language (leaving aside incompleteness results), but for those sentences or sets of sentences (theories) that are of interest for some practical or theoretical reason.

My opinion is that mathematics are discovered, but the way in which we put everything together and make it "understable" is invented.

Today's quote naturally belongs to J.W.Gibbs: Mathematics is a language.