[leftcenterright]

What makes you consider it a "discovery" instead of a creation of us humans?

I am more on the side of seeing maths as a precision language we utilize and extend as needed, especially because it can describe physically non-existent things e.g. perfect circles.

[esperent]

I rather think the discovered/invented thing is just semantics.

You can say that literally anything was "just discovered".

Thriller by Michael Jackson? Those particular ordering of sound waves always theoretically existed, MJ and various sound engineers just discovered them, they didn't create anything.

The cappucino? It's just a particular orderly collection of chemicals, such a collection always theoretically existed. Those baristas are explorers, discovering new latte art shapes, nothing creative there.

Cantor's diagonal argument? Yep, those numbers where just waiting to be discovered and written in that order.

And so on. The entire argument is meaningless, pointless philosophizing. Nobody wastes their time saying latte art was discovered rather than invented, but somehow when it comes to mathematics this is considered a deep and worthy discussion.

[dgfitz]

To me, the difference is: the way to __make__ music was invented, it was already there to be discovered.

Didn't mean to rub you the wrong way.

[frontfor]

I like to think of axioms as "created" while the consequences (i.e. theorems) of said axioms are "discovered". You can't create logic consequences (conclusions) given a set of axioms, but you can certainly create the axioms (premises).

[mjburgess]

It's not clear to me why people think perfect geometries do not exist, they occur all the time in physics.

Of composite matter, sure, because it's composite in a certain sort of way, you do not get perfect circles. But the structure of macroscopic material does not exhaust the physically.

Even here, one could define some process (eg., gravitational) which drives matter towards being a perfect circle, because perfect circularity is a property of that process. This is, as a matter of fact, true of gravity -- if it weren't we'd observe violations of lorentz invariance, which we do not.

[IAmBroom]

Perfect in a single-body universe, perhaps, but the gravity field of a particle is perturbed by other nearby particles - where "nearby" is relative to precision desired - and therefore never a perfect sphere.

Or, to put it another way, so-called "perfect circles" exist in a real, 4-D, wibbly-wobbly gravity-distorted space, and are no longer perfect Cartesian circles.

They still only exist theoretically; not in practice.

[woopsn]

When was the circle discovered? When it became essential to physics?