> I cannot resist joining in with a few quotations from the highly scholarly
> book:
>
> W Burkert, Lore and Science in Ancient Pythagoreanism, Harvard University
> Press, 1972.
>
> It is perhaps not the sort of tome that one would normally recommend to
> hard-pressed and overworked teachers, but its existence should be at least
> known to any historians of mathematics who set out to advise them on this
> particular topic. It is a very thorough study of the evidence concerning
> Pythagoras and Pythagoreanism, and it differs from many other such by
> taking the role of mathematics very seriously. (Van der Waerden was a
> friend and they apparently corresponded extensively. It seems to me that
> they must have disagreed over many issues, but in a thoroughly correct
> manner; I would love to see their letters.) Anyway here are just a few
> short quotations.
>
> To start with his general overall conclusion, and get it across quickly:
>
> "..., one is tempted to say that there is not a single detail in the life
> of Pythagoras that stands uncontradicted" (109),
>
> and
>
> "The apparently ancient reports of the importance of Pythagoras and his
> pupils in laying the foundations of mathematics crumble on touch" (415).
>
> One reason for the attraction of the usual story may be that
>
> "The discovery of the problem of the irrational in geometry, and the
> development of the ability to cope with it, is a fundamental accomplishment
> which holds a lasting fascination for modern historians of science. The
> tradition of secrecy, betrayal, and divine punishment provided the occasion
> for the reconstruction of a veritable melodrama in intellectual history"
> (455),
>
> and we all enjoy a good melodrama. But the reason why I am giving
> these quotations here is clearly explained by him:
>
> "What is the origin of the firmly rooted conviction that Pythagoreanism was
> the source of Greek mathematics? The question is easy to answer: it came
> from the educational tradition. Everyone comes upon the name of Pythagoras
> for the first time in school mathematics; and this has been true from the
> earliest stages of the Western cultural tradition" (406),
>
> for which opinion he cites the instances of Martianus Capella, Isidore,
> Nicomachus, Boethius, Gerbert, Copernicus Galileo,... So we, historians
> and teachers, may have manufactured this bit of history (and what others?).
> But at least we haven't here fallen into the sad situation described in the
> following quotation:
>
> "I often think it odd that it [sc. history] should be so dull, for a great
> deal of it must be invention." (Jane Austen, Northanger Abbey, Chapter xiv).
>
>
> Reviel Netz, author of an upcoming book _The Shaping of Deduction in Greek
> Mathematics_, CUP, sums it all up pithily:
>
> "Pythagoras the mathematician finally died in 1972!"
>
Dear David,
Why not, instead,
"Pythagoras, the mathematician, finally died in 1962" ?
Am I being too subtle?
With best regards,
Julio
> 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.
>
> David Fowler