23 September 2009

Eponyms in mathematics

Let S be the standard Smith class of normalized univalent Matcuzinski functions on the unit disc, and let B be the subclass of normalized Walquist functions. We establish a simple criterion for the non-Walquistness of a Matcuzinski function. With this technique it is easy to exhibit, using standard Hughes-Williams methods, a class of non-Walquist polynomials. This answers the Kopfschmerzhaus-type problem, posed by R. J. W. (“Wally”) Jones, concerning the smallest degree of a non-Walquist polynomial.
This fake abstract of a paper is from Merv Henwood and Ivan Rival, Eponymy in Mathematical Nomenclature: What's in a Name, and What Should Be? (PDF), from the Mathematical Intelligencer in 1980. It sounds to me like slight caricature -- but only slight. Henwood and Rival point out that such names are lazy. Names have at least two important functions -- to describe and to label -- and eponyms only label.

Perhaps such abstracts would be more common in areas which are small enough that all the major players talk to each other. I imagine that Smith, Matcuzinski, Walquist, etc. know each other.

Also of interest is David Rusin's list of eponyms occurring in the MSC classification. These names in general seem a bit less obscure than the names one would find in the abstract of a random paper, which isn't surprising as they're names of concepts big enough to get areas named after them.

(And can someone confirm or refute the story that Banach, in the paper in which he introduced Banach spaces, called them "spaces of type B" in an effort to get them named after himself? I've heard this one a few times but always unsourced.)

9 comments:

unapologetic said...

How does "ring" label? "algebra"? "loop"?

Michael Lugo said...

I wasn't saying that all non-eponyms label.

Michael Lugo said...

Where by "label" I mean "describe". (I suspect that's what you meant as well, although I don't mean to put words in your mouth.)

unapologetic said...

Yes, sorry, confusion when retyping three times because blogger decided it wasn't going to take OpenID

Todd Trimble said...

The story seems to be that people were already beginning to call them Banach spaces; Banach referred to them as spaces of type B out of modesty. See here (page 124 of Limaye's Functional Analysis).

s said...

Similarly in statistics, Akaike referred to his criterion as "An Information Criterion" or "AIC"

CarlBrannen said...

The eponymous names always bothered me particularly in algebra as I was always having to look up definitions in the back.

Algebra always made sense to me, it's what you do in algebra class with x's and y's. Rings make me think of the integers modulo a number as being a ring of numbers so I think that's okay. And loop is a sort of modification of a ring.

Ben said...

In "History of Class Field Theory", Keith Conrad mentions that Dickson did something similar when defining what are now known as cyclic algebras:

"Dickson called these 'algebras of type D,' but the hint did not have long-term influence (unlike Banach's 'espace du type B). They are no longer called Dickson algebras".

justsalt said...

You are right. No more eponymous names! From now on it should be the "right-triangle" theorem. What does "Pythagoras" mean anyway?