> there is a very ancient philosophical debate about math as a "discovery" versus as an "invention."

Yes, and it's a super interesting idea & debate too. Not to get too far off topic, but I'm a little bit more of a mind that representations are invented, while many fundamental truths are discovered (and can only be expressed through representation).

One math example that for me relates to software just a tiny bit, and illustrates why this is a debate is the 0^0 problem. We've mostly figured out how to better classify and represent that, but not before having big arguments where smart people say 1 and other smart people say 0. Mathematicians and programmers have mostly picked a convention, even though both answers are right depending on context. I would call that picking of a convention part of the "invention" side of math, as is calling it indeterminate.

But yeah, agreed, invention and discovery are both weird and problematic when you talk about math.