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Maybe we need some replies on current scholarly thinking.

(Judging from some replies here, many of us are still using the myths current 100 years ago.)

Is it true (as I have heard) that most, if not all, of the things attributed to Pythagoras and the Pythagoreans were, in fact, due instead to someone in Plato's school? Someone who promulgated these ideas many years later, adding the attribution of "Pythagoras" (a famous personage of the remote past) in order to lend credence to them?

And, if so, what are some good things to read about this?

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Yes the stories of Pythagoras that were common a few decades ago have all been been disproved, largely by Walter Burkert in Lore and Science in Ancient Pythagoreanism (1972). In short, Pythagoras never thought about any of the mathematics attributed to him. Consequently he gave no mathematical theory of music, never said all is number, and never contemplated a harmony of the planets.

The place to start reading about this is Burnyeat's concise review of later lighter books, including Pythagoras and the Pythagoreans: A Brief History by Charles Kahn. The review is linked by Gerald Edgar, http://www.lrb.co.uk/v29/n04/mf-burnyeat/other-lives. Burnyeat bases his review on Burkert's book. Since then Leonid Zhmud has urged the opposite, saying Pythagoras did pursue mathematics. But the review at https://web.archive.org/web/20141018100000/http://bmcr.brynmawr.edu/2014/2014-08-30.html shows Zhmud also attributes essentially all of the specific traditionally Pythagorean mathematics to later Pythagoreans, not to Pythagoras himself, and the review shows problems within Zhmud's argument.

I do not entirely trust any current attempt to find how the mathematics was produced, but the other thing to read is David Fowler's book The Mathematics of Plato's Academy (1987).

The books by Burkert and Fowler are no light reading.

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    $\begingroup$ Given the absence of sources it seems to be quite difficult to prove that Pythagoras did think of something. But how can it be proved that he did not think of something? $\endgroup$ – user2255 May 19 '15 at 17:13
  • $\begingroup$ @FranzLemmermeyer He never existed. $\endgroup$ – user85798 Feb 19 '16 at 16:12
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    $\begingroup$ @Sekots Neither do you. $\endgroup$ – user2255 Feb 19 '16 at 17:16
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    $\begingroup$ @FranzLemmermeyer See Burnyeat. In short: the sources closest to Pythagoras don't mention any math; the mathematical sources closest to his time show no knowledge of what he is later alleged to have found; later ancient sources differ wildly as to what math he knew; the sources attributing mathematical interest to him have clear agendas; and they do not have even the small air of historicity that some ancient sources do have on other topics. An analogy: if I claimed Gauss had a secret proof of the ABC conjecture, how would you prove he did not? $\endgroup$ – Colin McLarty Feb 26 '16 at 14:09
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    $\begingroup$ @FranzLemmermeyer Nothing that is even attributed to Pythagoras anytime near his life suggests he ever thought about math. And the math attributed to him would require techniques which no one is recorded knowing about near his time. If you still see no analogy, I hope you'll glance at Burnyeat. $\endgroup$ – Colin McLarty Feb 26 '16 at 17:54
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I'd like to present my point of view on the history of Greek mathematics from Thales to Euclid, which differs from Colin's.

What we know about Greek mathematics we have learnt from sources that were written after 300 BC, and of course we do not have any originals but copies of copies of copies. In particular, everything we seem to know about Thales or Pythagoras is second hand knowledge coming from histories composed at least 200 years after their death. Just because legends about Pythagoras have been embellished a few centuries later does not mean, however, that there is no substance to these legends at all.

This means that there are many possible interpretations, all of which are more or less compatible with the "facts". The two extreme positions are held by Burkert, who views Pythagoras as some kind of medicine man, and e.g. by Zhmud (Pythagoras as a mathematician). Just because they are extreme does not mean that they must be wrong, or that the truth lies somewhere in between. But there is certainly not an unanimous opinion concerning the "historical truth". For a balanced view (whatever that means) one may consult Kahn's book "Pythagoras and the Pythagoreans".

In my opinion, honesty requires using the phrase "we do not know for certain" a lot more often than did historians in the last century. There is an "ignoramus" in history of mathematics, and unless someone comes up with a time machine, there also is an "ignorabimus".

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  • $\begingroup$ Two more: during the 1920's [somebody called] Isidore Levy published books (in French, archive.org) about the legend of Pythagoras, later mentioned by EM Butler in her Myth of the magus; most recently we have Gabriele Cornelli's Pythagoreanism as an Historiographical Category 2013. $\endgroup$ – sand1 Feb 28 '16 at 22:39
  • $\begingroup$ @sand1 Could you summarize Cornelli's conclusions? $\endgroup$ – Colin McLarty Mar 7 '16 at 13:38
  • $\begingroup$ sorry for the delay; there is a short & excellent B.Mawr review (BMCR 2014.10.22) ; whith few facts there is much room for of interpretations so history depends on who writes it $\endgroup$ – sand1 Mar 13 '16 at 14:48

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