### Greek history for idiots: Greediots and Pythagoras. 1: No axiomatic proofs in Greek math

Wednesday, March 18th, 2020### Greek history for idiots: Greediots and Pythagoras.

1: No axiomatic proofs in Greek math

Recently, I presented my talk on “Pre-colonial appropriations of Indian ganita: epistemic issues”. This was at a round table at IIAS Shimla which replaced the now-postponed conference on Indology.

The key point of my talk was that much present-day school math is an inferior sort of math which Europeans appropriated from Indian ganita without fully understanding it, and then returned during colonial times by packaging it with a false history and declaring it superior. A philosophical comparison between ganita and math was done in earlier posts and publications.

This post focuses on the false history aspect, going back to the purported Greek origins of the “Pythagorean theorem”.

**False Western claim**

Egyptians built massive pyramids very accurately. One would assume that to achieve that marvellous feat of engineering they knew the so-called “Pythagorean theorem”.

But in his book *Mathematics in the time of the pharaohs*, Richard Gillings speaks of “pyramidiots”: people who claim various sorts of wonderful knowledge is built into the pyramids of Egypt. Gillings’ argues in an appendix (citing the Greek historian Heath) that “nothing in Egyptian mathematics suggests that Egyptians were acquainted with…[even] any special case of the Pythagorean theorem.” Heath adds, “there seems to be no evidence that they [Egyptians] knew [even] that the triangle (3, 4, 5) was *right-angled*”. The Egyptologist Clagett chips in, “there have been exaggerated claims that Egyptians had knowledge of the Pythagorean theorem which is, of course, a formal Euclidean theorem of the Elements.”

First, Gillings, Heath etc. are not honest enough to add that there is no evidence for Pythagoras. Nor is there any evidence for the claim that he proved any sort of theorem. So, one should rightfully say, **“There ****have been persistent false claims about ****a ****Pythagor****as having proved**** ****a ****theorem, though there ****is no evidence that there was any Pythagoras ****n****or ****any evidence ****that he proved any theorem.”**

Obviously, Western history of Greeks is of very inferior quality, since the tacit norm is that stories about Greeks need no evidence and must be accepted on mere faith in Western authority: it is only stories about others which require evidence!

That is why I use the term Greediots to describe people who fantasize about all sorts of scientific achievements by Greeks without any evidence, starting from the “Pythagorean theorem”: if they can believe in that they can believe anything on their blind faith.

**Religious connection of geometry**

A key point: not only is there nil evidence for the story of the “Pythagorean theorem”, it is CONTRARY to all available evidence.

The Pythagoreans were a religious cult: their interest was in the connection of geometry to the RELIGIOUS belief in the soul as described by Plato, in Meno, Phaedo, Republic, etc. Anyone can check in two seconds this connection of geometry to the soul by searching for the 2^{nd}, 3^{rd}, and 4^{th} occurrence of “soul” in Meno, a primary source for Plato readily available online from the MIT repository. But for Greediots the story of a theorem is what is important: so they don’t and won’t check facts. (Is Plato evidence for Greek thought? If not, why has no one ever explained the grounds for rejecting Plato? And what are the other “reliable” sources, if any, for Greek history? )

Proclus, in his *Commentary*, explicitly asserts that this religious belief linking geometry to the soul was the sole concern of the Pythagoreans with geometry. **But Greediots not only have ****no ****evidence for their beliefs, they ignore all the counter-evidence.**

As Proclus further explains in his *Commentary **(*on the book *Elements* today falsely attributed to an unknown “Euclid”) the book does geometry with exactly the same religious concerns. The subtle issue here is to understand Egyptian mystery geometry (and related Greek mathematics) as a sort of meditative discourse which drives the attention inwards and away from the external world.

All this is explained at great length in my book *Euclid and Jesus: how and why the church changed mathematics and Christianity across two religious wars,* Multiversity, 2012. See the webpage, or look inside. But Greediots will be Greediots they not only have no concern with facts they will not tolerate a counter-narrative or allow any space for it.

**No axiomatic proofs in Elements**

The interesting thing is how this “virgin-birth history” propagated by Greediots creates false “facts”. Clagett’s claim that “the Pythagorean theorem…is, of course, a formal Euclidean theorem of the Elements” is one such false “fact” which is widely believed.

The real fact is **there is no axiomatic or formal proof of the “Pythagorean theorem” in the book ****Elements**** ****of “Euclid”**. One has only to read the book; its very first proposition has an empirical proof not an axiomatic one. But just as most people do not read Plato, most people do not read the *Elements*. They just naively assume that even if the myth about its author as Euclid is false, the myth about the book must be correct. (Ha, Ha, they don’t know how thick are the layers of church lies!)

After centuries, some including Bertrand Russell finally understood the absence of axiomatic proofs in the *Elements*. What is shocking is for how many centuries Western scholars collectively failed to realize that even the first proposition of the *Elements* is contrary to the myth of axiomatic proofs in it.