A man wishing to prove, by the authority of Pythagoras, that he had formerly been in the world, while another would not let him finish his argument, the first speaker said to the second: “It is by this token that I was formerly here, I remember that you were a miller.” The other one, felling himself stung by these words, agreed that it was true, and that by the same token he remembered that the speaker had been the ass that carried the flour.

-The Notebooks of Leonardo da Vinci Vol. 2 by Jean Paul Richter pg. 350

The necessity of establishing the core ideas that Leonardo da Vinci was a Pythagorean is because it fits into the matrix of many unsolved dilemmas and paradoxes.