Yeah, they made a symmetry argument, a series expansion argument, and a law of sines argument. None of those require the Pythagorean Theorem and are all separately proven. There may be a reason that it's wrong (I'm not a mathematician but the article's author is).
So, they showed why the sum of squares is true for the hypotenuse of a triangle. It's even an exact proof rather than a limit argument. That I could follow the steps, and other mathematicians seem unaware of this combination of tools makes it seem relatively novel.
Speaking as a mathematician with a PhD, you're wrong about proofs. You're wrong about this site, which intends to promote a curious and celebratory attitude towards knowledge. Ironically, it is you who is displaying the hateful attitude that you bemoan. Please adjust your attitude, or see yourself out.
And do re-read the article; the author is attempting to reconstruct their proof without seeing it. You're attacking the students without even seeing their work. Incomprehensible.
So, they showed why the sum of squares is true for the hypotenuse of a triangle. It's even an exact proof rather than a limit argument. That I could follow the steps, and other mathematicians seem unaware of this combination of tools makes it seem relatively novel.