[defrost]

> The Pythagorean theorem makes more sense as something we have discovered, or the inner corners of a triangle add up to 180 degrees (half a circle);

These are literal examples of things proven to be true constructions as a result of Axioms (of a Euclidean Geometry).

> The simple answer is that math is simply a feature of the universe.

If (big if) in fact the physical universe is a Euclidean universe (and not, say, just a tiny bit hyperbolic [1])

[1] https://www.maa.org/book/export/html/115525

> If mathematics were constructed, we are essentially taking on faith that mathematical properties in the physical universe just so happen (by coincidence) to correlate with the mathematical principles we have invented.

Err, no.

The mathematics we as human have constructed is a superset of the physical universe - the mathematical world embraces much more than the mere confines of the physical world we can kick and observe across.

Indeed we have constructed various mathematic worlds that are at odds with each other - some my have application in this physical universe which then precludes others from also corresponding to the same.