Timeline for Why is "abelian" infrequently capitalized?
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13 events
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| Dec 28, 2020 at 7:59 | history | edited | J. W. Tanner | CC BY-SA 4.0 |
corrected spelling
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| Nov 6, 2010 at 18:00 | comment | added | Michael Hardy | @KConrad. I don't find your comment cogent. The word "red" in "a red house" is simply an adjective. The point was that the term "Cauchy sequence" can be viewed as a compound, rather than viewing "Cauchy as an attributive adjective (which of course could then also be used as a predicate adjective). I don't think that position is silly. But it may be an attempt to push back the tide with a pitchfork. | |
| Nov 5, 2010 at 20:21 | comment | added | KConrad | Michael: it is a little silly to say a sequence can't be Cauchy. A red house is also a house that is red. A Cauchy sequence is also a sequence that is Cauchy. Someone who says that is not a good way to write should be reminded that words can have more than one meaning (a name vs. an adjective). | |
| Nov 5, 2010 at 18:26 | comment | added | Ketil Tveiten | @Sándor: Yes, it was a bad example. I suppose I should have said 'Lorentzian' or something else. Also, in case it wasn't obvious, the comment about shift keys was tongue-firmly-placed-in-cheek. FOr what it's worth, I have no problems with decapitalising words like this, nor with using e.g. 'Cauchy' as an adjective. It makes life easier. | |
| Nov 5, 2010 at 17:31 | comment | added | Deane Yang | I found "Killing" to be seriously confusing when I first saw it used as an adjective. | |
| Nov 5, 2010 at 16:27 | comment | added | Spiro Karigiannis | Regardless of the reason, if there are more proper names floating around, it seems to me more likely that people will "recognize" them as proper names, and capitalize them. In fact, it was at least a year after I first saw the word "abelian" that I even realized that it was named after Abel. If geometers did not capitalize "Killing vector field" then no one would know there was a guy named Killing... | |
| Nov 5, 2010 at 16:26 | comment | added | Spiro Karigiannis | @Deane: I didn't notice your meta post. But there may be more to the "culture" than that. I may be totally wrong here, since I haven't been immersed in pure abstract algebra since the first year of graduate school 13 years ago, but it strikes me that in geometry, there are many more things which are named after people, compared to algebra. For example, almost every "curvature" I can think of (and there are many...) other than the mean curvature is named for somebody. This might be because there are more distinct objects in geometry than in algebra? | |
| Nov 5, 2010 at 16:20 | comment | added | Sándor Kovács | @Ketil: Cohen-Macaulay is never used as "Cohen-Macaulayan", so this isn't a very good example. Also, I think that many of these words were already used one way or another much before shift keys were invented. | |
| Nov 5, 2010 at 15:57 | comment | added | Deane Yang | Spiro, that was exactly what I said on tea.mathoverflow.net! | |
| Nov 5, 2010 at 15:46 | comment | added | Michael Hardy | Many people write "This sequence is Cauchy" rather than "This sequence is a Cauchy sequence", treating "Cauchy" in effect as an adjective rather than treating "Cauchy sequence" as a compound noun. I've heard it objected that no sequence is Cauchy (Cauchy was a person) but some sequences are Cauchy sequences. And similarly with "Cohen--Macaulay", etc. | |
| Nov 5, 2010 at 15:10 | comment | added | Spiro Karigiannis | Speaking as a geometer, we use "Riemannian". "Euclidean", and "Hermitian" all the time. Also, the adjective "Euclidean" has been around much longer than "abelian" or "artinian", so familiarity can't be the entire answer. I think it has more to do with culture of algebraists versus culture of geometers, but I may be wrong, and I'm curious to see what others think. | |
| Nov 5, 2010 at 14:51 | comment | added | Steve Huntsman | Gaussian integer. | |
| Nov 5, 2010 at 14:46 | history | answered | Ketil Tveiten | CC BY-SA 2.5 |