Pythagorean problems are set so often in examination questions (often as a multiple of 3-4-5 sides) that it's refreshing to see the whole tired non-learning undermined by a young student:
who was prepared to risk a zero mark for a great joke.
Adepts of the Inner Circle know one other thing about Pythagoras: that he eschewed rather than chewed broad beans (Vicia faba) and forbade his (many) followers from eating them either. He had many followers because he was the leader of a cult that insisted on all sorts of weird restrictions, dietary and behavioral. Such restrictions are familiar at second hand to most of my readers in the 'sacred cow' of hindus and the laws of kosher which insists, among very many other things, on two sets (milky and meaty) of china to extrapolate inconveniently from the law (Exodus 12:19) "Thou shalt not seethe the kid in its mother's milk" to make eating lasagne, as traditionally rendered in Ireland, impossible. Me, I don't eat broad beans either: I was talking about haricots (Phaseolus vulgaris) last week, now there's a bean for heroes.
When scientists of a certain type hear about these quirky cultural proscriptions, they assume that there is a rational basis, which has become opaque through the passage of time, and see it as their job to bring that reason into daylight. So the cow is sacred because hindus used them to plough, if you've eaten your tractor you cannot sow seed, so there is nothing to harvest and everyone dies. Even if you've eaten all of last year's corn don't eat the cow. The same people salute the wisdom of Moses in recognising (empirically rather than microscopically) that pigs carried the nematode Trichinella spiralis and saving his people from a lifetime of chronic nausea, vomiting, sweating and diarrhea followed by intense muscular pain, difficulty breathing, weakening of pulse and blood pressure, heart damage and kidney malfunction.
The Pythagoreans' refusal of broad beans is mapped, by the loose-ends school of science, onto the observation that the frequency of Glucose-6-phosphate dehydrogenase deficiency is rather common among the people of the Eastern Med, where all the Pythagoreans lived. There is evidence (PMID 10916676) that G6PDH deficiency confers resistance to malaria (which even today kills more than a million (mostly black) babies each year. So the side-effect that a) some people with the deficiency b) IF they are exposed to broad bean pollen or eat the beans THEN they develop a hemolytic anemia (their red blood cells get destroyed), is a small evolutionary price to pay for lowering the chance that your kids will die of malaria. Favism causes maybe 4000 deaths a year, although there are quality of life issues that need to be factored in. It is obvious-to-all-thinking-people that Pythagoras (probably a G6PDH- sufferer himself) sorted all this out in his capacious brain and, just like Moses, issued a diktat to make the benefits accrue to the illiterate and those not so smart as the boss. What a guy!
Except that he didn't, or at least we have only the most tentative evidence that he did. Nothing written by Pythagoras has come down to us. The first written sources seem to have codified a miscellany of oral traditions about 150 years after his death. Among these was Plato's pupil Aristotle, who in Islamic and later medieval philosophy and science was the greatest of the ancient sages. Aristotle notes the prohibition and advances a number of reasons why P should have had a bean in his bonnet. One of these being that the sprouting bean looks like a foetus (see left) and no civilised Greek was a cannibal. Aristole's pupil Aristoxenus OTOH "denies that Pythagoras forbade the eating of beans and says that he valued it most of all vegetables, since it was digestible and laxative”. Aristoxenus grew up in Tarentum in Magna Graecia (now Taranto in S Italy) just down the road from Croton where Pythagoras spent most of his life, so may have a richer a source of oral tradition than Aristotle in Athens. You should really follow this up in Carl Huffman's excellent and compendious essay on Pythagoras for the Stanford Encyclopedia of Philosophy.
In science we sometimes have theories that have the Ring of Truth but turn out to be wrong. Nature is the ultimate arbiter of what is true. In The Arts, there is no such authority, so your opinion is as good as your reputation and that hinges on how well you interpret the data - and whether you come from Oxbridge of course. The data on Pythagoras are few, fuzzy and a long time dead, so it's easy to say things that sound credible but don't bear scrutiny. As scientists, there is no credit in duffing up The Arts Block for being unscientific. Contrariwise we can learn from such stories to be really careful, nay critical, about out own cherished hypotheses.