History and Philosophy of Mathematics

Mischievous Eurocentrism 2: Euclid

Euclid is one of the pillars of the story that mathematics originated in Greece. But Euclid is a fake. Ask yourself: do you really know of any evidence of Euclid?

A few years ago, the late David Fowler, an authority on Greek mathematics, candidly and publicly admitted in response to my post, on the Historia Matematica discussion list, that “nothing” is known about Euclid.

The racist element of the Euclid story is brought out by Indian school texts which display images of Euclid (and various other “Greek” mathematicians) as Caucasian stereotypes. Note that even these sources now admit that Euclid was from Alexandria in Africa.  So how did they determine the color of Euclid’s skin? Such racist images from “reputed” Internet history sites like McAndrews lend a concrete reality to “Euclid” in the minds of young children. This conditions them lifelong to look askance at anyone who questions the existence of Euclid. This is the crux of propaganda–to make a large number of people believe something without evidence, and to make them believe that anything to the contrary is absurd.

More recently, on the Philomathes list, some people again started talking about this mythical Euclid using the terminology of “Euclid’s division algorithm” found also in many mathematics texts. This lacks elementary commonsense. How could an algorithm have developed with the clumsy Greek notation for numbers? Just try doing even a trivial sum like adding 17 and 23 in Greek numerical notation! So, I again reminded people that there was no evidence that Euclid even existed, and no non-textual evidence that Greeks ever used algorithms (and no evidence from any early texts).

One of the discussants pompously responded that he didn’t care whether or not Euclid existed, and that he was referring to the book with Euclid’s name in front of it, and the algorithm inside it.

I asked for the whereabouts  of such a book. Thus, the fact is that Euclid is NOT mentioned in Greek manuscripts of the Elements until the 18th c. which mention only Theon (an opponent of the church like his daughter Hypatia, and her successor Proclus). 

Since “Euclid” is mentioned only in post-12th c. Latin manuscripts, the most moderate hypothesis is that “Euclid” was a translation mistake for the Arabic “uclides”, meaning “key to geometry”. The Latin manuscripts of “Euclid” up to the 15th c. are all derived from Arabic, where ucli = key, while des = geometry. 

Naturally, none of the scholars in the Philomathes list was able to tell me the whereabouts of the “Euclid” manuscript in Greek from before the formation of the Arabic House of Wisdom. (The significance of this date is that then Constantinople was a tributary of Baghdad, and subsequently many manuscripts were translated from Arabic to Greek, including the Indian Pancatantra.) My point is that all these Arabic manuscripts were deemed to be of theologically correct “Greek” origin, when they were translated into Latin by Christian religious fanatics during the Crusades

Since nothing could be said in defence of “Euclid”, one Jeffrey Oaks launched a personal attack on me. Lacking any grounds to attack me, he invented all sorts of false opinions for me, which opinions he could easily attack. (This is a stock tactic used by Western theologians.)

My response to Oaks (given below) was ruled out by the “moderator” someone called Robert Eldon Taylor who, in a moment of candour, admitted to being just an “ignorant old man”. Taylor has racist sympathies, since he earlier disallowed me from pointing out the racist explanations offered by historians like Rouse Ball. On this occasion, Taylor happily allowed Oaks personal attack on me. What he disallowed was my response, presumably since his intention is to use the Philomathes list to propagate falsehoods. I was not allowed to correct Oaks’ falsehoods, even about my person, but was removed from the list—probably the first and last person to have been removed. The  justification given by Eldon Taylor: Oaks is an honourable man! (He did not add that I have the wrong color of skin.)

This is how Western historians actively cultivate and nurture  the falsehoods of racist history to this day: when someone asks for serious evidence (beyond worthless stray remarks in late texts) they attack the person with lies, and do not allow him a chance to correct those lies. Whiteside was not the first, and Oaks will probably not be the last.

Admittedly, some might consider Jeffrey Oaks a very inferior scholar who is not worth responding to.  But a similar thing happened also in the case of Atiyah: the Notices of the American Mathematical Society did not allow me a single opportunity to express my views. I hope you get the pattern.

So let us be clear: Western historians very well know that they are defending falsehoods. The point is not to convince them, but to expose them.

For ready reference, my response to Oaks, and Oaks personal attack on me, are reproduced below. Oaks has given what might be called a “mathematical proof” of the existence of Euclid—for he has completely disregarded all empirical facts, twisting them just as he pleases! For example, my claims about “Euclid” are all drawn from my peer-reviewed publications, the empirical existence of which Oaks denies! One can understand Jeffrey Oaks’ anxiety for peer reviewed publications, since, despite being a professional academic, he managed just one mathematics publication in 17 years (according to Google Scholar). Perhaps that is why it did not strike him that I put my paper on Euclid on the net (http://IndianCalculus.info/Good_bye_Euclid_journal.pdf)  because I am interested in being read, not merely in being published with the social approval of peers! (This paper too was presented at a confernce and is due to be published.) Or perhaps Oaks meant to insinuate that the referees had the wrong skin color?

The last part of the response below is of independent interest, because it shows that “Archimedes” too is just a myth.

All best,

C. K. Raju

============original response=======

From: c_k_raju@..

To: philomathes@yahoogroups.com
Subject: Re: [philomathes] Euclid?
Date: April 23, 2008 4:02:11 AM

Jeffrey Oaks response is amusing.

I asked for evidence about the whereabouts of a Greek manuscript which has Euclid’s name in the front of it, and which comes from before the time of Bayt al Hikma. Noticeably, no one on this list has supplied evidence of such a manuscript, for no such manuscript exists. 

Instead, Oaks choses to launch a personal attack on me. I take this personal attack as a conclusive admission of his failure to find the evidence I had asked for. This is a classic tactic: if there is no evidence, attack the person who asks for evidence.

Here too he can do no better than to thoroughly misrepresent my opinions, by suggestion and innuendo. Indeed he makes out my opinions to be directly contrary to what I have stated in print. (I had already provided him a reference, which has further references to my published work.)

I take this as an implicit admission on his part that he found himself unable to contest any of my actually stated opinions in print, and therefore was compelled to attribute to me by innuendo an opinion which I do not hold but which he could easily attack. 

I see no possibility of misunderstanding. Even in this discussion, I had clearly stated that all existing Greek manuscripts of the Elements known until the 18th c. claim to be derived from Theon. Perhaps the history that Oaks believes in is built on the kind of logic where “Greek” can freely be conflated with “Euclid” since “non-Greek” with Indian. 

In fact, I am on record that the Elements reflects Egyptian mystery geometry. Here is what I said in my recent book (Cultural Foundations of Mathematics, Pearson Longman, 2007, p. 25) 

“In particular, there is the erasure of Egypt. Herodotus informs us not only that the Greeks learnt geometry from Egyptians, but that they also borrowed most of their religious practices from the Egyptians. From this perspective, Proclus’ philosophy of the Elements makes it just a continuation of Egyptian mystery-geometry texts, and there is no clear evidence of what, if anything, the Greeks from Pythagoras onwards added to this tradition.”

Whether Oaks finds this too difficult to understand, or whether he is deliberately misrepresenting me, I see no point in discussing anything further with him.  

C. K. Raju

P.S. Oaks says
*I presume here that Raju is not a woman.
Oaks’ level of humour and history seem to be about on par, and equally full of biases. 

===Jeffrey Oaks’ personal attack on C. K. Raju======

From: oaks@uindy.edu
To: philomathes@yahoogroups.com
Subject: Re: [philomathes] Euclid
Date: Tuesday, April 22, 2008 11:52 pm

If C. K. Raju would like us to seriously consider the proposition that
what we call Euclid’s _Elememts_ did not originate in Grece, but perhaps
India, then he* should write an article for a refereed journal with his
evidence.  In particular, he should (1) find a way to explain all the
references to Euclid’s book in other ancient Greek sources (there are
probably dozens).  In particular, he would have to assert that in all
those manuscripts, some medieval scribe has inserted such references,
or, in the case of Proclus’ _Commentary_, show that the entire book is a
medieval forgery.

Once this is accomplished, he must (2) provide positive evidence that
the Elements was *not* originally composed in Greek.   This will be
tough.  Consider the following, from al-Nayrizi’s Arabic commentary on
Euclid’s _Elements_ in the 9th c.:  “This is the abridgement of the book
of Euclid on the study of the elements preliminary to the study of plane
geometry…This is the book which Yahya bin Khalid bin Barmak ordered to
be translated from the Roman into the Arabic tongue…” (Anthony Lo
Bello’s translation.  I have two editions of the Arabic text, and this
is a faithful translation.)  By “Roman” they of course meant the Eastern
Roman Empire, known to us as the Byzantine Empire, where Greek was the language spoken.

Lastly, he must (3) show that the book was originally written in India. 
What eveidence there is for this I cannot say.

So until the appearance of Raju’s article, we can all go on assuming
(correctly, I would say) that Euclid is the author of the _Elements_,
and that he wrote it in Greek sometime before (or contempoaneous with)
Archimedes.  I personally don’t care who wrote the Elements or where. 
Currently the evidence overwhelmingly points to ancient Greece.
On another note:  there is no lack of brilliant scholars in India which
the West has acknowledged for some time.  The most important that I know about is Panini, the 4th c. BC linguist who created an artificial
language which is capable of generating all (and only) proper Sanskrit
sentences.  His work is so profound that linguists today are still
mining it for new ideas.  Although western scholars have been in
possession of his text for a long time (> 100 years), it is only very
recently, since the 1980’s, that certain aspects of his thought are
coming to be understood.  Panini’s is the only premodern scientific work
(of which I am aware) which is still the source of new insights.  No
research geometer reads Euclid for ideas anymore!
—Jeff Oaks
*I presume here that Raju is not a woman.

=====Raju’s earlier response
From: c_k_raju@…
To: philomathes@yahoogroups.com
Re: [philomathes] Euclid
Date: Tuesday, April 22, 2008 1:31 pm

Jeffrey Oaks wrote:
> In _On the Sphere and the Cylinder I_, Archimedes writes
> “…through the
> second <proposition> of the first <book> of Euclid <=
> Elements>…”

Let us look at exactly how inaccurate your statements are, for you will agree that with the help of  inaccuracies almost anything at all can be established.

I will take just one example.

 You say Archimedes mentions Euclid. That is very imprecise for a variety of reasons.

First, when you say “Archimedes”, you are actually referring to a manuscript from the 14th c. or later. It requires a giant leap of faith to connect this manuscript to Archimedes, from some 1600 years earlier, since there is no continuous intervening tradition. Further, the claim about this linkage was first made at a time of intense religious fanaticism, during the Crusades and the Inquisition. The same Western historians who make such claims would clamour for evidence if such a claim were made with regard to any other tradition. Surely, the demand for evidence is not merely a weapon to be selectively used against non-Western history?

 Let us, however, for the sake of argument, take the giant leap of faith required to believe this highly improbable claim that the 14th c. manuscript of the Sphere and the Cylinder was somehow connected to Archimedes. What exactly is the nature of the connection? You use the text as if it was a verbatim record, as  if every word and remark in the manuscript accurately reflects what Archimedes said. (That is somewhat more ambitious than using a current text with no intermediate connecting texts as a verbatim record of what Haroun al Rashid said 1300 years ago.)

 The assumption that the book was blindly but accurately copied out, without change, for the intervening 16 centuries is contrary to the merest commonsense. There is no known text which has been thus copied out without change—not even scriptures like the Bible for example. But this hypothesis, contrary to commonsense, and not known to be valid even in a single real case, is implicit in every one of your claims. So, it seems you are confounding myths, internal to a culture, with history which must proceed from evidence which is convincing also to others.

 In the particular case of Archimedes the situation is somewhat worse, for people in the time and place assigned to Archimedes wrote on papyrus, which was expensive, and easily destroyed. So, for a book to be preserved it would have had to be frequently copied out. Why would anyone go to the trouble and expense of copying it out if it were not of current practical use? Just for the benefit of future historians was it? And, if the material were of current use, why shouldn’t it have been continuously updated to reflect the latest developments to make it more useful? In short, common sense tells us that the extant text of “Sphere and the Cylinder” reflects the understanding of the 14th c., not of the time of the Archimedes. Any assertion to the contrary requires solid proof which is missing.

 As already pointed out, claims based on such texts are contrary to the non-textual evidence.

 However, to return to the text, the extant text of Sphere and Cylinder, attributed to Archimedes by Western historians, does NOT mention Euclid. It only mentions the Elements. In the context of the current discussion, that is a big inaccuracy to confound the Elements with Euclid.

 Also why only one isolated citation? After all, there are so many opportunities in that text where the Elements could have been similarly cited. Further, the citation is in a modern style, and such was not the custom at the time of Archimedes, since texts were not standardised then. So the citation is obviously an interpolation (even after granting the various  giant leaps of faith required to connect the rest of the text to Archimedes). Others have made this point long ago.

So the “Archimedes” citation of the Elements (not “Euclid”) is clearly spurious, and not suited to any sort of critical history. Since the “Proclus” citation of “Euclid” mentions the “Archimedes” citation, that must be from an even later date (perhaps 16th c. CE) and is equally an interpolation.

 Finally, notice the way you proceed. When the myth of “Euclid” is challenged, the demand for solid proof is side-stepped by appealing to further myths (about Archimedes, which, in turn, would be supported by further myths and so on). This is an approach typical of mythology.

 All best,

C. K. Raju



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