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Bourbaki, for example, is the name of a set of mathematicians, rather than a single person, under which several books were published.

Out of curiosity, I wonder if there is any historical evidence that makes one maintain that the author of the Elements, Euclid, is a single person instead of a set of ancient scholars?

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    $\begingroup$ See Euclid of Alexandria for some details on this issue. An "ultimate" evidence is not yet available, but the "Bourbaki-like" hypotheses seems hardly supportable. $\endgroup$ – Mauro ALLEGRANZA Sep 7 '15 at 12:07
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    $\begingroup$ Euclid as a group in the following sense: Euclid the real man collected results of many past mathematicians and placed them together in a book. $\endgroup$ – Gerald Edgar Sep 7 '15 at 12:47
  • $\begingroup$ There are really three separate questions one could ask: (1) Was there one person named Euclid? (2) Did that person write the entire text of the Elements? (3) What portion of the mathematical ideas expressed in the Elements, or of the manner of development, was original work by that individual? Simplicio's answer seems to show that the answer to #2 is no. Re #3, clearly some of the results were known before this period, but it would be fascinating to know whether an individual originated the idea of such a system of axiomatic deduction. $\endgroup$ – Ben Crowell Sep 8 '15 at 20:37
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    $\begingroup$ Re: Ben's #3. The idea of an axiomatic system definitely pre-dates Euclid. Aristotle discusses it at length a generation before Euclid, giving examples from mathematics in a way that makes it clear the idea was already widespread by then. Exactly when and where it arose is pretty hazy, with some combination of the Pythagoreans, early Ionic philosophers (Thales et. al.) and Egyptian mystery religions being suggested by the Greeks themselves. One imagines the idea was developed by all three before being formalized by the Athenians. $\endgroup$ – simplicio Sep 9 '15 at 14:04
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I too do not see any reason to doubt that the works of Euclid were written by one person, apart, naturally, from some interpolations. However, I must disagree with Konstantinos when he writes that “there is no known similar group of scientists in the ancient times”. The medical writings attributed to Hippocrates are well-known to have been written over a period of centuries and have very clear differences in content and style. But maybe medicine is not a science in the way that mathematics is.

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There's little question that some parts of "The Elements" were added by later authors. Heath's English translation gives a lengthy commentary on what is likely in the original work and what is known or suspected to be from later editors.

There were also two entire books tacked onto the end that were often attributed to Euclid, but are now generally recognized as being from later authors.

So in that sense the author of the Elements wasn't just one person. But there almost certainly was an actual Euclid who wrote the bulk of what's come down to us as The Elements. Pappus and Proclus both discuss him as an actual person, and while they lived several centuries after The Elements were written, we know they were drawing from near-contemporary sources.

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A "corporation" as Bourbaki is, from one perspective, a sign of great scientific progress: his great purpose was to unify somehow mathematics understood as a science that had acquired a vastness covering "many" quite developed branches each of which was autonomous. In contrast, unlike, in times of Euclid's purpose it was found in a unit just a branch of mathematics in different subjects but the same "spirit" which is ancient geometry.

It could be that Euclid was "A set of ancient scholars" as you imagine, I do not know but personally, I would say no, he was a genius of his time living in a single human body.

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Actually as Wikipedia mentions:

"This hypothesis is not well accepted by scholars and there is little evidence in its favor"

All evidence shows that Euclid was a real person.
Actually I am not sure if such an idea (of naming a group of scientists with an actual name) would be accepted at 300 B.C. and in addition, I do not believe there was such a big amount of mathematicians at this period (and so good).
Also,to my best knowledge there is no known similar group of scientists in the ancient times so why should "Euclid" be a group of mathematicians?
I believe he was a single person.

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    $\begingroup$ There may be no known group of scientists in the ancient times. However, attributing a work to a better known figure was common (like how Pythagoras continued writing after he died, and certain parts of the bible are supposedly written by the same author as another yet in a completely different style). I do not think Euclid was multiple scholars since those historians Wikipedia references probably have good reason to believe what they do, but the idea is not as farfetched as you may think. $\endgroup$ – Avatrin Sep 7 '15 at 12:54

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