I too have Burkert at my side right now. I don't see how anyone can fail
to be impressed by his
Lore and Science in Ancient Pythagoreanism.
Perhaps he is a wee bit too much of a nay-sayer for my taste. He does
allow himself to say that the best attested teaching of Pythagoras is
immortality and transmigration of the soul.
I found it helpful, long ago, to read two chapters of
The Presocratic Philosophers
of Jonathan Barnes right after reading Burkert:
From the first volume: Chapter VI: Pythagoras and the Soul
and
From the 2nd volume: Chapter IV: Philolaus and the Formal Cause.
It gave me more hope than I got from Lore, Lore though is a better work.
Perhaps you don't agree about the worth of the Barnes accounts.
at the end of your message, you wrote
> It is not that that I just want to destroy all of these great stories; I
> want to replace them by others that are mathematically just as good or, as
> I think, even much better (though they don't yet come along with such a
> dramatic cast list). I don't pretend that my version is 'true'; in fact I
> don't really know what that word means when used in this context of early
> Greek mathematics, for which we have almost no reliable evidence.
I think that you have the passion of the true historian to avoid saying
anything that doesn't have sufficient evidence, but you are certainly good
at making the most interesting speculations, which are backed by evidence
that we do have.
I love the factorial sign at the end of the quotation of Netz:
"Pythagoras the mathematician finally died in 1972!"
1972! is in the very far future, and I am glad that Pythagoras, as a
mathematician, still has that long to live.
Best wishes,
Sam Kutler