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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeJun 2nd 2013

    Euclid (Εὐκλείδης) was the ancient Greek version of Bourbaki.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJun 3rd 2013

    You really think so ? Euclid was a single person, wasn’t he ? Maybe you compare Euclid with Dieudonne, for exposition. But historians of mathematics consider Euclid having large own contributions, including the introduction of rigorous mathematical methods. In the times of Bourbaki, there were far greatest practitioners of rigour than him.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 3rd 2013

    Yeah, I don’t think the description of Euclid, while perhaps at least partly in jest, is all that useful or scholarly. Maybe someone who knows something about Euclid (maybe Toby in a different frame of mind (-: ) could add more here?

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeJun 3rd 2013

    But Bourbaki was a real person… just not that real person!

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeJun 3rd 2013

    He was a single person, if he was real. (He probably was. But I looked for clear evidence that he was, and it’s not there; the extant references are just too late to be sure. I was originally going to phrase it as ‘except that he was a real person’ but decided that I couldn't be certain.)

    • CommentRowNumber6.
    • CommentAuthorZhen Lin
    • CommentTimeJun 4th 2013

    How can be sure of even that? We often refer to Bourbaki as if he were a real person too – and it would not surprise me if a few centuries down the line only specialists know about the non-personhood of Bourbaki.

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeJun 4th 2013

    Good point; let's say, he was a single person if he was what people usually think of him.

    Wikipedia says that nothing is known of his personal life and the first references to him are from centuries later. Even the ‘royal road’ anecdote is apocryphal. So we really don't know!

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 4th 2013

    Of course, the “specialists” in this case don’t seem to treat the claim he existed as a real person with any particular skepticism either! So why don’t we just go along and say he existed, even though we can’t be completely certain.

    Although specific dates are impossible to ascribe, it seems to be agreed that Euclid of Alexandria flourished sometime around 300 BC, and worked and taught at the library at Alexandria. “They” say he received training in mathematics from students of Plato at Plato’s Academy in Athens.

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeJun 5th 2013

    If you’re suggesting putting such details in there, Todd, I don't mind a bit!

    • CommentRowNumber10.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 5th 2013

    Okay, I took a crack at this article. Please feel free to add further improvements.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2013
    • (edited Jun 5th 2013)

    Since “Euclid” is not defined in some abstract fashion but as “the author who wrote the Elements”, it seems to make little sense to me to claim that he might not have existed.

    Similarly I never thought it makes sense to argue, as some do, whether “Shakespeare” existed. To my mind, by definition both “Euclid” and “Shakespeare” existed, and the only remaining question rather is what else we can say about them with certainty beyond their defining property as the author of some text.

    If you think “Euclid” might not have existed, you would have to explain to me what you even mean by “Euclid”, for I wouldn’t know.

    • CommentRowNumber12.
    • CommentAuthorTim_Porter
    • CommentTimeJun 5th 2013
    • (edited Jun 5th 2013)

    I added a link to the St. Andrews history page on Euclid.

    @Urs: perhaps the question is what ‘type’ should be assigned to the term Euclid!

    • CommentRowNumber13.
    • CommentAuthorTobyBartels
    • CommentTimeJun 5th 2013
    • (edited Jun 5th 2013)

    I would define ‘Euclid’ as the mathematician who wrote the book that we know as the Elements, and there might not have been such a person. It's not so much that those books might have been written by committee, like Bourbaki's books were, but that the version that we know might have been added to and reorganised over the centuries. I don't think that anybody is seriously proposing this —it looks like a coherent whole in one hand—, but we just don't have the documentation.

    I used the phrase ‘a real person’. One would not say that Nicolas Bourbaki was a real person.

    William Shakespeare, on the other hand, is well documented as a person. People argue whether he wrote the plays attributed to him (and in fact he didn't write most of his last play, Henry VIII), not whether he existed. If we later learn that the person didn't write the plays, then we won't define ‘Shakespeare’ as the author of the plays but as the real person who took the credit.

    I cast doubt on Euclid's existence mostly as a joke, comparing him to Bourbaki (who certainly saw themselves as Euclid's successors, hence the name of their books). I originally wanted to say that he was real person (unlike Nicolas Bourbaki) but didn't feel that this was quite justified.

    • CommentRowNumber14.
    • CommentAuthorTobyBartels
    • CommentTimeJun 5th 2013

    I added a bit more to Euclid, particularly wrt rigour.

    I find it misleading to say that Euclid was ‘Greek’. He wrote in Greek and presumably visited Greece, but he apparently lived in Egypt. That's why I used ‘Hellenistic’ instead.

    • CommentRowNumber15.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 5th 2013
    • (edited Jun 5th 2013)

    the version that we know might have been added to and reorganised over the centuries

    There could be something to that. Although the analogy isn’t ideal, we could similarly contemplate the assertion “Homer is the author of the Iliad and the Odyssey”, where the poems were probably long in the making through oral-formulaic traditions which went through generations of story-tellers. The genius of Homer might then be in the careful selection and preservation of the best or most successful exemplars of hexameter verse (and still leaving open the possibility of improvisations here and there in the story by future story-tellers). (Note: I am not at all expert here! It’s just what I thought I had picked up from readings here and there.)

    There is indeed speculation that Euclid used treatises written by others, but here too he gets credit for his genius and taste for putting the best of these together while composing the Elements.

    • CommentRowNumber16.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 5th 2013
    • (edited Jun 5th 2013)

    I find it misleading to say that Euclid was ‘Greek’

    Hmm. I’m not sure. One of my sources says he received his mathematical training in Athens; it seems very plausible to me that he was “Greek” or perhaps more precisely Athenian by birth, and then moved to Alexandria in his maturity. But as I say, I’m not sure. Maybe you’re right to stay on the side of caution.

    • CommentRowNumber17.
    • CommentAuthorTobyBartels
    • CommentTimeJun 5th 2013

    I just finished the MacTutor bio of Euclid. They list Tyre (not Greek) and Megara (Greek) as the birthplaces given by ancient authors and also give reasons to doubt them both.

    I don't think that studying in Athens is much evidence that Euclid is from Athens at all. No matter where in the Hellenistic world he came from, Plato's Academy is where he would have wanted to go.

    • CommentRowNumber18.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 5th 2013

    Okay; thanks for looking into it. Whatever the case may be, I’m fine with changing to Hellenistic.

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