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I have heard the phrase "first-class mathematician" bantered about in various halls and articles, and in particular, McTutor states:

Euclid may not have been a first class mathematician but the long lasting nature of The Elements must make him the leading mathematics teacher of antiquity or perhaps of all time

My question is: why might we exclude Euclid from the category of first-class mathematicians?

I know this is a soft question as the label "first-class mathematican" is an old, but (apparently) poorly defined, term. Yet still, perhaps there is a reason for the analysis about Euclid I am missing. (I say `old' because Gauss is reported to have said that if Euler's formula $e^{i \pi} + 1 = 0\,\!$ "was not immediately apparent to a student upon being told it, that student would never be a first-class mathematician.")

Let's try a couple 'definitions.'

Nowland's "A Chronicle of Mathematical People" states

By this time, Hurwitz had established a record of publishing important papers, marking him as a first class mathematician.

This implies important papers and/or numerous papers might be a test. Surely Euclid's texts (especially the Elements) that were used and emulated for centuries would be 'important' and his texts together give him numbers. So this must not be the test applied to Euclid by MacTutor.

On a discussion board I found

By first-class mathematician I mean someone who delivers a "significant" new unification of previously disparate topics or delivers a previously unanticipated result. My definition is "significantly" wooly to be contentious.

Yet again Euclid's Elements seems to stand as "a significant new unification of previously disparate topics." In fact, what work stands close to it in those centuries?

Perhaps the reason Eulcid might not be 'a 'first-class mathematician' is just the fear we might accidently label a 'mere' archivalist or librarian `first-class mathematician,' and this might happen by mistake since we know so very little about him directly. Maybe. Or am I missing something that would omit Euclid from the first class mathematicians?

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This question strikes me as too subjective and argumentative for math.SE. –  Qiaochu Yuan Apr 9 '12 at 22:11
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Agreed; which justifies closing votes, but I don't see how it would justify downvotes, to be honest.... –  Arturo Magidin Apr 9 '12 at 22:15
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The Elements is thought to have presented and organized material that was discovered by others, including the axiomatic method. In a technical sense, the theorems in the Elements are relatively simple compared to other works of the Greek school on conics, mechanics, incidence geometry, and number theory. This is not surprising for a work that sets down the basic foundations of a subject. –  zyx Apr 9 '12 at 22:23
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I can’t add anything myself, but the question of whether Euclid was a main contributor or more of a compiler seems to me to be of historical interest; any relevant links or references would be appreciated. –  Brian M. Scott Apr 9 '12 at 22:59
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Rota: "4 You are more likely to be remembered by your expository work" alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-lessons.html –  yasmar Apr 10 '12 at 7:41
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closed as not constructive by Benjamin Lim, GEdgar, Matt N., Hans Lundmark, Asaf Karagila Apr 10 '12 at 9:51

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