[klt0825]

"Do you think maths is discovered or invented?

To tell you the truth, I don't think I know a mathematician who doesn't think that it's discovered."

Anyone else struck by this? It has really never occurred to before that I've always assumed that we were simply discovering math versus creating it.

[kxyvr]

Well, I suppose it's a philosophical thing, but I don't subscribe to the discover point of view. However, to be clear, I don't think there's anything wrong with this viewpoint.

For me, math is a set of rules that we know to be consistent. Based on these rules, we put together new constructions that obey this framework. When I prove a theorem, I don't really internalize it as discovering something that was already there, but as putting together a new creation based on a set of tools that I already have. As the author of the result, I have the flexibility to be as creative as I want in how I prove the result and that creativity has an affect on how people view and internalize the theorem. I mean, if someone writes a narrative story we could say that the story was always there and that they just discovered it in a sea of words. Again, there's nothing wrong with that point of view, but I prefer to say that the person created the story.

[arctangent]

Opinion isn't as clear cut as Wiles makes out. There are definitely opposing viewpoints.

This would be a good place to start: https://en.wikipedia.org/wiki/Philosophy_of_mathematics

[OscarCunningham]

Perhaps it would be correct to say that we discover mathematical objects but invent theorems about them.

[psychometry]

Gödel would have probably answered the opposite way, as would I think many logicians.

[fmoralesc]

Gödel was a platonist.

[boomzilla]

So are logic frameworks discovered or invented? Are true/false values discovered or invented?

I think the question whether math is discovered or invented is silly. It is both.

[Retra]

We create the language and methodologies while we discover the relationships. It's both, as mathematics requires both.