[js1138]

Many working mathematicians have the notion that mathematics is invented not discovered.

I'm glad to hear that because I've suspected that myself. To believe this, however, you have to believe that some constraint is selecting useful inventions. I don't know how to conceptualize the selector for mathematical ideas, but I suspect it has something to do with usefulness.

[Doctor Stochastic]

Usefulness, beauty, consistency, amusement.

Of course, one tries to invent things that "agree" with the "real" world; at least in doing applied mathematics.

I'm in the "Math is Invented" camp. Mostly because, doing math seems more like invention than discovery to me.

[betty boop]

I'm glad to hear that because I've suspected that myself. To believe this, however, you have to believe that some constraint is selecting useful inventions. I don't know how to conceptualize the selector for mathematical ideas, but I suspect it has something to do with usefulness.

Somehow I think the opposite -- that mathematics is discovered, not invented. I think it has something to do, not with utility, but with the search for Truth.