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Is this question acceptable?: Why is "abelian" infrequently capitalized?

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    Not much more to it than that. My spidey sense says it's poor form to ask a question like this but I can't fathom what to add by way of motivation or background.
    • CommentAuthorWill Jagy
    • CommentTimeNov 4th 2010
     
    seems alright to me, I guess it's a question of how creepy the answers become. Do we usually capitalize Gaussian, Riemannian? Since it is no longer a proper name as such, maybe it depends on the fame of the individual. In effect, it may be the frequency of use of the name that reinforces the idea of capitalizing the adjective form.
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    I remember a professor of mine once told me that if you became a famous mathematician, you got something named after you, and if you became REALLY famous, they'd do you the honor of uncapitalizing your name. Obviously this is not a highly-adopted convention (maybe "algorithm" counts? Have I seen "artinian"?), but amusing nonetheless.

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    In my first abstract algebra course I remember the professor explaining it pretty much exactly as Cam says. Having something named after you is relatively common. But once you've become a part of the fabric of mathematics, your name starts to be uncapitalized.
    • CommentAuthorHarry Gindi
    • CommentTimeNov 4th 2010 edited
     

    @Cam:

    Debacker told my class the same exact thing two years ago when he introduced us to some basic group theory. It is tradition that "abelian" is not capitalized.

    • CommentAuthorWill Jagy
    • CommentTimeNov 4th 2010
     
    Once in a class on general relativity we had maybe a dozen new tensors with names one day. I asked if I could have one named after me. My adviser nominated one, it turned out to be identically zero. Good times.
    • CommentAuthorMariano
    • CommentTimeNov 4th 2010
     

    @Will, that puts you right there besides Legendre and his constant.

    • CommentAuthorWill Jagy
    • CommentTimeNov 4th 2010
     
    • CommentAuthorHarry Gindi
    • CommentTimeNov 4th 2010 edited
     

    "God bless us, every Legendre's constant"

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    If only you could patent 0, Will, you'd be rich.

    The most interesting GR class I had was the day after I shaved my head, and Werner Israel decided to tell us about the "black holes have no hair" theorem.
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    I've heard professors suggest alternative conventions (consistent with "abelian" and "artinian"), e.g., don't capitalize when the name is modified to form an adjective. These seem somewhat inconsistent with current practice, though.

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    As to whether the question is acceptable on MO, I'd be happier if it were broader, something along the lines of, "Are there any rules to determine whether mathematical concepts named after mathematicians should be capitalized?"
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    I've also heard the adjective rule before and seen people write e.g. "euclidean geometry" or "cartesian square" which seems nonstandard to me.
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    I think that if you can say X is (term) without the noun following it, it is generally left uncapitalized. So, notice, for instance, "the ring X is noetherian", "the ring X is artinian", "the group X is abelian", "the square F is cartesian", "the square F is cocartesian", etc.

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    Dear Scott, the suggestion you mention is amusing if you know that Emil Artin's ancestors were Armenian and had as patronym "Artinian" which was then Germanized to "Artin". By the way Bourbaki is no help in this case because in French adjectives or adverbs derived from proper names are never capitalised: vous parlez français, un sénateur gaulliste, des coordonnées cartésiennes, un revêtement galoisien, et donc (obligatoirement) un anneau artinien et un groupe abélien. But if the adjective is used as a noun, it is capitalized: j'adore les Américains et les sites américains ( surtout l'un d'eux!).
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    Steve's question is a good one. Is there really a rational explanation why it's "abelian", "noetherian", and "artinian" but "Euclidean", "Riemannian", and "Lorentzian"? The only pattern I see is that algebraists like to use lower case and the geometers like to capitalize.
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    "God bless us, every Legendre's constant"

    Well played, sir, well played.

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    • CommentAuthorWill Jagy
    • CommentTimeNov 5th 2010
     
    The MO question seems to be going well. With Georges' example in mind, what would we do with d'Artagnan?

    http://en.wikipedia.org/wiki/The_Three_Musketeers
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    D'artagnan?

    • CommentAuthorWill Jagy
    • CommentTimeNov 5th 2010
     
    Hi, Gretar. Not a mathematician, fictional or otherwise. He's the young man who meets the three musketeers. Whenever I have heard the name pronounced it was a sort of dartan-yan sound, French and all. So I was thinking of d'Artagnanian as amusing.

    Here we are, movie with Chris O'Donnell as d'Artagnan:
    http://www.imdb.com/title/tt0108333/

    There have been many movies with that character, in many languages:
    http://www.imdb.com/character/ch0006263/
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    Hi Will. Thanks for the info, but I think you misunderstood a rather silly joke on my behalf :) You asked " what would we do with d'Artagnan?" and I jokingly answered by capitalizing the d, and uncapitalizing the A.

    • CommentAuthorWill Jagy
    • CommentTimeNov 5th 2010
     
    Oh, crap. I was not expecting that. You are simply too clever for me. And if you had put in enough explanation to remove all possibility of misinterpretation it would have weakened the joke, so there's no way around it...I put something like this as a comment after one of my MO questions, roughly that there was a American comedian named Red Skelton, if he found that nobody seemed to have gotten a joke he would say "I just do 'em, I don't explain 'em."
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    Ack Gretar, you've just reminded of my trouble recently when writing a proposal. I had to format the list of references alphabetically by author, and wasn't quite sure whether d'Alembert goes under "D" or "A".

    • CommentAuthorWill Jagy
    • CommentTimeNov 5th 2010
     
    I have figured it out. I assumed that since it was the first, and only, word of the sentence, D'artagnan was naturally capitalized. So it is only half my fault for not noticing the lower case 'a. Something along the lines of "I nominate D'artagnan" would have worked. I am redeemed, at least a little.

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