The Stanford Encyclopedia of Philosophy has a long article on Pythagoras that doesn't mention the whole rutti-tutti-irrationality issue. http://plato.stanford.

The Stanford Encyclopedia of Philosophy has a long article on Pythagoras that doesn't mention the whole rutti-tutti-irrationality issue. http://plato.stanford.edu/entries/pythagoras/ http://plato.stanford.edu/entries/pythagoras/ They do say that we don't have anything written by Pythagoras or his contemporaries--the earliest extant works mentioning him were written more than a century after his death--and then a lot of people attributed their own views to Pythagoras to give themselves the benefit of his fame. So it's really hard to know what the historical Pythagoreans did or believed. I think it is safe to say that if the Pythagoreans kept the irrationality of √2 a closely guarded secret, it wasn't their only closely guarded secret.