[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.

[js1138]

Maybe both things are happening at the same time. ;^)

[js1138]

More seriously, for some people, truth, beauty, harmony, etc., have utility.

I can't think of how to distinguish discovery from invention in mathematics, but there is the problem that mathematical systems cannot prove their own truth. That seems a strike against the assertion that mathematics is God's alphabet.

[Alamo-Girl]

For the lurkers, I’d like to offer a few examples related to y’alls discussion of whether mathematics discovers or invents. I am a Platonist, so my examples are more favorable to the “discovered” column, but I'm sure lurkers will arrive at their own conclusions.

Did Euclid, Reimann, Schwartzchild discover geometries or did they invent them?

Does “threeness” exist separately from 3 chairs, 3 apples, 3 dogs?

Did Einstein discover general and special relativity or did he invent them?

As a Platonist, it's a bit tough for me to come up with examples that lean in the "invented" direction. Perhaps y'all can offer some?