[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?

[Doctor Stochastic]

Did Euclid, Reimann, Schwartzchild discover geometries or did they invent them? Invented. Same for Bolayi, Gauss, and Lobachevesky.

Does “threeness” exist separately from 3 chairs, 3 apples, 3 dogs? Yes, but it is an invented concept. Threeness as a concept is neither confirms nor denies the existence of three apples nor a pawnshop.

Invented.

One does try to make the inventions predict reality.

It can be a bit difficult to distinguish invention from discovery. For example, some sculptors say they are only bringing out or discovering a previously existing form in the raw marble. On the other hand, did Beethoven discover or invent his symphonies? Mathematics seems to have more in common with music than with trekking over the frozen wastes looking for a new island (at least on my good days it does.)

[forsnax5]

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?

It seems to me that mathematics is a combination of invented and discovered.

The relationship between the three sides of a right triangle certainly existed before Pythagoras came along, but he invented the formal theorum.

The map isn't the territory...

[edsheppa]

As a Platonist, it's a bit tough for me to come up with examples that lean in the "invented" direction.

How curious. I consider each of the ones you listed to be examples of invention.

[gore3000]

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

I think that Newton's and Leibnitz's coming up with calculus independently and at almost the same time is pretty strong proof that these mathematical theories are discovered.