Like most if not all people who are or were once college Math majors, I gave a lot of thought to the question “what is Math”, of which the “discovered or created” question is a significant part.
My conclusion then, which I still find true now, is that the most useful definition of Math is that it is
formalism. I particularly like the description of formalism in Hofstadter’s
Godel, Escher,Bach: that a particular formalism can be viewed simple as a collection of rules from manipulating strings of characters. That is what I believe Math is.
By this definition, Math is created. Although it is very useful in describing discovered and discoverable things (eg: the physical universe), it is also useful in describing physically impossible things that, in the usual sense of the word, can never be discovered.
Just my opinion, of course, though, having a diploma with “Math” printed on it makes it an arguably an “expert” opinion.
