So many circular arguments. The Pythagorean theorem tells you that √2 exists, but not that it’s irrational.
As for the story, it’s apocryphal, not ahistorical, but even so, it was too good of a story not to tell my students when I taught Math for Liberal Arts Majors (the version I’d heard was that the proof was presented while the Pythagoreans were on a boat and they were so offended by the idea that √2 is irrational, they threw the guy off the boat. I would guess that of all the things I said in lectures for that class, this is the one that my students would be most likely to remember).
As for the story, it’s apocryphal, not ahistorical, but even so, it was too good of a story not to tell my students when I taught Math for Liberal Arts Majors (the version I’d heard was that the proof was presented while the Pythagoreans were on a boat and they were so offended by the idea that √2 is irrational, they threw the guy off the boat. I would guess that of all the things I said in lectures for that class, this is the one that my students would be most likely to remember).