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I recently watch this recording (in French) of a talk (La mathématique expérimentale) given by the mathematician Vladimir Arnold. There are some rather surprising claims about math history. One of them concerns Euclid's geometry (see the video at 49:53, for about ten minutes). It is claimed that Euclid's axiomatisation of geometry actually comes from the Egyptian mathematics, through the teaching of Pythagoras of what he learnt in Egypt (then recorded by Euclid in his Elements). From I what know about Egyptian's mathematics, I find the claim rather suspicious, but I wanted to check just in case.

Is there an Egyptian origin known, or at least suspected, of Euclid's axiomatisation of geometry?

Edit: I add the link mentioned by José Hdz. Stgo below for an english written source of Arnold's ideas, Some excerpts from V. I. Arnold's "Yesterday and long ago" on the origins of mathematics.

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  • $\begingroup$ There are sources regarding Ancient Egyptian mathematics but not wrt the axiomatic approach. See e.g. Bartel van der Waerden, Science awakening (1954) (original edition 1950). $\endgroup$
    – Mauro ALLEGRANZA
    Commented Jul 25 at 13:42
  • $\begingroup$ See hsm.stackexchange.com/questions/391/… $\endgroup$
    – Gerald Edgar
    Commented Jul 25 at 15:15
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    $\begingroup$ No, there are no Egyptian sources with anything of the sort, or even secondary Greek sources that would suggest it. Pythagoras's visits to Egypt are semi-mythical and the consensus of historians after Burkert is that he did not do any mathematics at all, see McLarty's answer. Arnold and Mishchenko make a lot of surprising claims about history they really should not make. $\endgroup$
    – Conifold
    Commented Jul 26 at 4:42
  • $\begingroup$ What I find the most surprising is how Arnold is precise. He even mentions differences between the Egyptian's axiomatisation and Euclid's axiomatisation, a statement being an axiom on one side and a theorem on the other... $\endgroup$
    – AGenevois
    Commented Jul 27 at 9:23

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Arnold was one of 20th century's greatest mathematicians. This does not necessarily mean that he was a careful mathematical historian. I personally lost my patience with his history when I read his denigrating comments about Leibniz.

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There are certainly accounts of how Thales studied under Egyptians and how Euclid eventually collected and organized Thales's accounts.

Update: research on Thales clarifies why Arnold's claim is technically incorrect but thematically probable. Thales is credited with bringing Egyptian geometry into Greece.

This geometry was not axiomatic. Therefore, Euclid's axiomatization is not Egyptian. However, the origin of one of his sources is probably Egyptian because Thales is believed to have studied under Egyptians, though he didn't write a book about it that can be used as a primary source, etc.

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  • $\begingroup$ If you intend to argue that Thales brought an axiomatic treatment of geometry back from Egypt, your source says the opposite: "In The Elements, Euclid collected, organized, and proved geometric ideas that were already used as applied techniques." Thales is mentioned shortly afterwards, but as someone who, like Euclid, enquired into why things were true and who "became a celebrity in Egypt" for doing so. Egyptian mathematical practice is explicitly contrasted with that of Thales and Euclid. This is very much the standard story, not Arnold's version. $\endgroup$
    – Will Orrick
    Commented Jul 30 at 12:01
  • $\begingroup$ I did not intend to argue that, but my source is more suggestive than oppositional, and it suggests that Thales was one of several people, including Euclid, who can be credited with treating applied mathematics more systemically and thereby enabling Euclid to bring those recordings closer to an axiomatization, which is what is interesting. Thales is credited with bringing Egyptian mathematics into Greece: plato.stanford.edu/entries/presocratics Is the axiomatization Egyptian in origin? No, but are some sources for Euclid's increasingly axiomatic treatment Egyptian? Yes. $\endgroup$
    – Paul Chubinski
    Commented Jul 30 at 17:27
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    $\begingroup$ I think it needs to be emphasized that (1) there is a two and a half century gap separating Thales from Euclid, (2) many of the stories told about Thales (and about Pythagoras) have a legendary quality, (3) our knowledge of Greek mathematics is extremely fragmentary, (4) our knowledge of Egyptian mathematics is even more so. $\endgroup$
    – Will Orrick
    Commented Jul 31 at 12:14
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Actually, Arnold was only drawing from Proclus Diadochus, who wrote the following in his Commentary of Euclid's Elements (Book 1):

We must next speak of the origin of geometry in the present world cycle. For, as the remarkable Aristotle tells us, the same ideas have repeatedly come to men at various periods of the universe. It is not, he goes on to say, in our time or in the time of those known to us that the sciences have first arisen, but they have appeared and again disappeared, and will continue to appear and to disappear, in various cycles, of which the number both past and future is countless. But since we must speak of the origin of the arts and sciences with reference to the present world cycle, it was, we say, among the Egyptians that geometry is generally held to have been discovered. It owed its discovery to the practice of land measurement. For the Egyptians had to perform such measurements because the overflow of the Nile would cause the boundary of each person's land to disappear. Furthermore, it should occasion no surprise that the discovery both of this science and of the other sciences proceeded from utility, since everything that is in the process of becoming advances from the imperfect to the perfect. The progress, then, from sense perception to reason and from reason to understanding is a natural one. And so, just as the accurate knowledge of numbers originated with the Phoenicians through their commerce and their business transactions, so geometry was discovered by the Egyptians for the reason we have indicated.

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After these Pythagoras changed the study of geometry, giving it the form of a liberal discipline, seeking its first principles in ultimate ideas, and investigating its theorems abstractly and in a purely intellectual way. It was he who discovered the subject of proportions and the construction of the cosmic figures.

Source: https://mathshistory.st-andrews.ac.uk/Extras/Proclus_history_geometry/

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    $\begingroup$ Doesn't this passage suggest that axiomatization started with Pythagoras? I don't see anything about an Egyptian axiomatization or about Egyptian axioms differing from Greek ones, so I don't see how Arnold could have been basing his ideas about an Egyption axiomatization on Proclus. (In case it's not completely clear from the question, Arnold really was making such strong claims, as you will see if you watch the linked video or read the linked excerpt from Arnold's book.) $\endgroup$
    – Will Orrick
    Commented Sep 13 at 17:30

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