[Doctor Stochastic]

Many working mathematicians have the notion that mathematics is invented not discovered. (I don't remember what these are called.) Others (the Platonists) believe that mathematical objects exist independent of being discovered. The problems raised by the Axiom of Choice make both positions uncomfortable.

What's funny (to me at least) is that many non-mathematicians tell me that they support the Platonist line, but they balk at saying the complex numbers exist. I'm not sure if this group of people accept vector spaces or abstract groups.)

[Alamo-Girl]

Thank you so much for your post and for the background and explanation!

For lurkers who are interested in learning more on Axiom of Choice

From all that I've read, I must be Platonist. That may be because of my overarching interest in geometry.

[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.