A lurking question, old as Greece, does ask:

Is math invention or discovery?

The answer’s both, but here the harder task

is knowing how it switches. So you see,

most truths are found with constructs, which in turn

are built from truths like chickens and their eggs.

One needs to know, should this fact raise concern,

that constructs can be daft; just logic’s dregs.

The truths discovered tell how to define

the structures that make math and world align.

Pythagoras’s theorem about lengths,

is one such truth that he (and others) found.

Observed, discovered, and through mental strength,

it was then proved with pictures that astound.

Much later mathematicians, minds alit,

would formalize, as sets, both “length” and “space”.

These constructs were defined so that by writ

Pythagoras’s truth remains the case.

That is, this “theorem” now seems just defined.

As such, one might then lose their peace of mind.

So in this world where "space" is formalized,

do all those pretty proofs now lose their charm?

Of course not! We all ought to realize

how “length” could change its meaning without harm

to mathematical consistency

in all the theory giving facts of space.

However, then these “facts” would hardly be

related to the nature we embrace.

And hence, a truth has told how to define

a structure that makes math and world align.