First of all, you are wrong about the Pythagorean theorem being universal. There are spaces where the Pythagorean theorem doesn't apply.
Second of all, if we are going to have a rational argument about this... it will a mathematical argument, not a philosophical one
. The mathematics is important to this discussion... whether or not there are "philosophical" principles is irrelevant.
The question of whether all mathematics is philosophy is silly. It doesn't impact the life of a mathematician in any way however you decide to settle this meaningless questions. Calling a mathematician a "philosopher" doesn't at all change how she does her job.
However to confuse philosophy with mathematics is foolish. You can get a wrong answer if what you are "philosophizing" isn't mathematically sound.