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When reading on the topic of Ancient Egyptian geometry by Ancient Greek philosophers, there is a certain sense that this is quite a thriving discipline that seems comparable to the type of geometry done in Greece at that time. E.g., Diogenes Laertius' Lives of Eminent Philosophers :

And Pamphile relates that he, having learnt geometry from the Egyptians, was the first person to describe a right-angled triangle in a circle, and that he sacrificed an ox in honour of his discovery

or Clement of Alexandria' Stromata

"I have roamed over the most ground of any man of my time, investigating the most remote parts. I have seen the most skies and lands, and I have heard of learned men in very great numbers. And in composition no one has surpassed me; in demonstration, not even those among the Egyptians who are called Arpenodaptae, with all of whom I lived in exile up to eighty years."

or in Iamblichus' Life of Pythagoras :

But it is said that he very much applied himself to geometry among the Egyptians. For with the Egyptians there are many geometrical problems; since it is necessary that from remote periods, and from the time of the Gods themselves,[38] on account of the increments and decrements of the Nile, those that were skilful should have measured all the Egyptian land which they cultivated. Hence also geometry derived its name. Neither did they negligently investigate the theory of the celestial orbs, in which likewise Pythagoras was skilled. Moreover, all the theorems about lines appear to have been derived from thence.

This seems to give the impression of some geometry (and astronomy) with some theory behind it, and from various other quotes, partly done by the priestly class.

However, the actual geometry that seems to exist in surviving documents like the Rhind papyrus or the Moscow papyrus, seem to be fairly utilitarian texts on the topic, being mostly either scribal exercises or practical computations, which do not seem to have much hints of such things.

Am I perhaps overinterpreting what is said in those sources? Are there any other documents which would be more in line with this interpretation? Is it maybe just that such documents did not survive at all, or were not even written down? Or is it maybe even the case that most of these are legendary, as many of these texts are written much after the period in question was concerned (from around 600 BCE to 300 BCE)?

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    $\begingroup$ Its strange to us today, but formal mathematics (as opposed to the more applied stuff seen in the Rhind papyrus) seems to have been done largely or entirely orally. Note we see this in Greece as well as Egypt. The Pythagoreans had a prohibition against writing down their discoveries and indeed, we have basically no writings from classical Greek mathematicians, nevermind Egyptian ones. Almost all of our knowledge of Greek mathematics comes from later Hellenistic authors or earlier philosophers like Plato & Aristotle using math as examples of general philosophical principles. $\endgroup$
    – simplicio
    Commented Jan 10 at 15:37
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    $\begingroup$ Clement's passage is him quoting Democritus, Arpenodaptae are usually translated as rope-stretchers, as Greeks called Egyptian land surveyors, Iamblichus refers to land measuring as well. Right angles and triangles were used by land surveyors and in construction. So the quotes suggest the same practical focus that we find in papyri. Even early Greek sources describe the more theoretical geometry of fellow Greeks differently. $\endgroup$
    – Conifold
    Commented Jan 10 at 23:14
  • $\begingroup$ @Conifold The Democritus quote specifies he's talking about "demonstrations", so while the name Arpenodaptae might well have its origins in practical measurement, the quote suggests they'd moved on to what passed for formal mathematics circa 400 B.C. $\endgroup$
    – simplicio
    Commented Jan 11 at 14:24

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Greek writers of Hellenistic times indeed had a tendency to claim that mathematics and astronomy came to Greece from Egypt. This has no conformation whatsoever. Modern studies show that mathematics and astronomy in Egypt were in very primitive state, in comparison with Mesopotamia and Greece. On the other hand, these Hellenistic sources do not mention Mesopotamia (Babylon), while there are documented cases of transfer of important scientific knowledge from Babylon to Greece. Notice that all those Hellenistic authors who claim that there was a substantial influence of Egyptian mathematics/astronomy are not mathematicians or astronomers themselves, so they probably did not understand the subject.

The reason of this confusion is unclear. As an example, all Hellenistic sources tell us that Thales traveled to Egypt to learn mathematics. On the other hand these same sources say that Thales surprised Egyptian priests when he showed them how to measure the height of a pyramid. Modern historian comments: "And what could these priests possibly teach Thales?"

Hellenistic historians never mention any specific important contribution of Egyptians to mathematics or astronomy. Just the general statements that founders of Greek exact sciences, Thales and Pythagoras "traveled to Egypt to learn the wisdom of Egyptian priests". What could they possibly learn there remains a mystery.

Ptolemy, an astronomer who worked in Egypt at the time of the Roman empire, and whose works are our principal source of knowledge about ancient astronomy, frequently refers to Babylonians and never on Egyptians.

References:

O. Neugebauer, The exact sciences in antiquity,

O. Neugebauer, A history of ancient mathematical astronomy,

B. L. Van der Waerden, Science awakening.

This last book discusses exactly this question: "What could Greeks learn from Egyptians?" in the last section of Chapter I. The author mentions other opinions on the question as well.

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    $\begingroup$ They do also mention Mesopotamia (or more specifically Chaldea), I just did not include it in the quotes here. $\endgroup$
    – Slereah
    Commented Jan 11 at 14:45
  • $\begingroup$ Did you mean confirmation when you typed conformation in the second sentence? $\endgroup$ Commented Jan 11 at 18:09
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Although the Greeks are credited with the discovery of mathematics, this is clearly not the case. The discovery of number and geometry ranks as one of the greatest discoveries. It was already there by the time of the Babylonians and Egyptians. Who and when these two disciplines were discovered is very likely lost to time, although we do have evidence like the Ishango bone which shows tallying was known back in 20,000 BC and with the Lembobo bone, possibly to 40,000 BC. Both of these were discovered in Africa.

Although a lot of Babylonian and Egyptian mathematics may look primitive compared to the later developments of Greek mathematics, the key thing is that it came later. The important thing is that it was a vigorous field that seeded future developments. And of course the development of key concepts like length, angle, area and volume were hugely important, although I don't expect that they were discovered by the Egyptians but probably predate them.

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  • $\begingroup$ Can the person who downvoted or placed a delete vote, please explain why? $\endgroup$ Commented Jan 12 at 12:58
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    $\begingroup$ I did not vote on your answer, but I can explain what I disagree with. First of all, you treat Egyptian and Babylonian mathematics together, while they are very different, and the question was specifically about Egyptian mathematics. Mathematics/astronomy in Babylon was indeed highly developed, unlike in Egypt. Second, the Greeks can be really credited with "invention of mathematics" because all pre-Greek mathematics was lacking a crucial ingredient, namely proof. This is what makes mathematics special and different from all other kinds of knowledge. $\endgroup$ Commented Jan 12 at 14:26
  • $\begingroup$ So, if mathematics is understood in the narrow sense, as based on mathematical proofs, then the Greeks indeed invented it, and everything else can be called "pre-mathematical knowledge". And this "pre-mathematical knowledge" achieved a high degree of development in Babylon. But nothing comparable comes from ancient Egypt. $\endgroup$ Commented Jan 12 at 14:29
  • $\begingroup$ @Eremenko: I happen to disagree with a number of assertions that you are making. First, I am not treating Egyptian and Babylonian mathematics together because I am not intending to write a treatise discussing their similarities and differences. What I am duscussing is mathematics before the Greeks and you will see that I have mentioned the earliest evidence we have for mathematical thinking. This is why I mentioned Egypt and Babylon as they are civilisations that preceded the Greeks. Though of course the list goes on - the Assyrians, the Phoenicians, the Canaanites ... $\endgroup$ Commented Jan 12 at 14:38
  • $\begingroup$ @Eremenko: I also dispute that proof was new with the Greeks. First, the notion of evidence, proof and demonstration was well known before mathematics. It was understood for example in law. And it was from law that these ideas were imported into math and physics. This is why we say, "a law of nature". Once they were imported they began to develop in a way peculiar to this field. But again, this is nothing new since every field develops methods peculiar to itself even when importing ideas from an adjacent or far away field. $\endgroup$ Commented Jan 12 at 14:42

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