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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.
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.
@Will, that puts you right there besides Legendre and his constant.
"God bless us, every Legendre's constant"
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.
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.
Well played, sir, well played.
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.
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".