Avi, I never looked into what was R Meir’s motivation to learn from Acher? Did Acher have Mishnayos that others did not? Did he have his own logical approach? Maybe he was quoting Aristotle and R Meir found it as interesting as Rambam did?
> what Pythagoras and Euclid believed?
Personalities would not matter in pure math. A proof stands on its own. But other sciences are not that simple, especially in pre-experimental times.