I never said that.
Yet, you would not know that the Pythagorean Theorem is truth without the mathematic proof
Mathematical proof are theorems. Theorems are not facts. They are true within the mathematical working model based on axiomatic assumptions in all cases. They do not describe reality.
If reality happened to correspond to the axiomatic assumptions involved in a theorem, then the theorem will describe the factual reality, but only under those conditions (in Pythagorean case a natural object would have to be triangular and one of its angles would have to to be an exact [to the nth decimal], perfect 90 degrees).
Of course there are no true 90 degree angles in nature; they "exist" as conditional axiomatic assumptions in Euclidean geometry, and therefore the theorem does not correspond to reality. So the Pythagorean Theorem does not apply to the real world, describe reality, or 'prove' it. It's pure theory.
These are real world quantities and real world geometries
Geometric shapes are perfect assumptions. Classical geometry is an idealized system which does not quantitatively or otherwise correspond to the real world, and is therefore only an approximation of it; it is an approximate description of the world.
The system is true only in its idealized form, but the real world is not ideal.
If you cannot accept mathematic proof, then your problems are moreso with logical proofs - and any argument you make fails by your own test
Logical proofs also operate in an ideal environment of assumed axiomatic "truths." That's why so many believers find logic dear and near when it comes to "proving" God logically. Such proofs are theorems under assumed conditions, and have no bearing on the real world, nor can they be verified in the real world for that reason.
My arguments are not logical but empirical. Empirical proof is the only proof. All else is theoretcial. An optical engineer can tell you that his system (on paper) will be diffraction-limited to the edge of the image field, but the final wavefront that reaches the focus depends on much more than theoretical design.
My tagline is pure empiricism. The world is the way it is even if it is not logical. We can't argue with the world logically.
You have thoroughly dug yourself into a hole.
If you have a measuring device capable of measuring distance and angles to a significant degree of "real world" accuracy, will the Pythagorean Theorem apply to the real world, describe reality to the same degree of accuracy as you are capable of? Using these measurements and mathematics can you prove it in the real world? Why?