04 October 2007

How we cite results

There seem to be some odd conventions in naming and citing mathematical results.

First, a result isn't necessarily named after the person who first discovered it. The canonical example is that there are about a zillion things which Euler and Gauss came up with which aren't named after them. (And yet the October 2007 issue of the Bulletin of the American Mathematical Society is entirely about Euler; the six full-length articles concern his work on infinite series, algebraic geometry (!), partitions, defining the derivative, compressible fluids, and incompressible fluids. This issue also includes Terence Tao's article What is good mathematics?, which I would recommend more highly if I hadn't read it already (it's been circulating since at least February). Part of this is probably the motivation to give more unique names to results: an example is Goldbach's conjecture, which I talked about in asking who gets credit for quadratic reciprocity, and which Euler actually conjectured.

Second, when more than one person proves a result, their names get smushed together into some new, hyphenated name which is grammatically singular. If Smith and Jones prove a theorem, it becomes known as the Smith-Jones theorem; then when people cite it, they'll say "as Smith-Jones proved" or "Smith-Jones shows, in [1], ..." This is despite the fact that there's no person named Smith-Jones! This of course gets even more confusing when one of the people involved has a hyphenated name; the canonical example is, I think, the Birch and Swinnerton-Dyer conjecture, which is a single conjecture, by two (not three) people, Bryan Birch and Peter Swinnerton-Dyer. My theory was that it's because the people who come up with these results don't seem like real people... until I caught myself thinking about the Stanley-Wilf conjecture yesterday. I have taken classes from both Stanley and Wilf, and I am very much aware that they are distinct people. Yet I still caught myself saying "So what does Stanley-Wilf say about this?" I suppose this is an abbreviated version of "So what does the Stanley-Wilf conjecture say about this?" but it still seems weird to me. Can any linguists weigh in on this?

Third, let's say that the aforementiond Smith gives a talk about eir theorem, which ey proved in joint work with Jones. Ey will write on the board at eir talk something like

Theorem. (Jones-S., 2007.) Let F be a foo. Then...

abbreviating eir own last name to a single initial. This seems unnecessarily modest to me; shouldn't Smith be proud enough of eir result to cite emself on an equal footing with eir collaborator? Fortunately people don't give joint talks, because then you'd have a talk by, say, Smith and Simpson, and you might see a theorem attributed to "S." (since neither one of them would want to write out their name) and you wouldn't know which one it was.

9 comments:

John Armstrong said...

Smith is proud enough, and is citing both authors equally. There's sort of a genteel modesty at play here. One doesn't just go writing your name up all over the board while one is talking.. it seems vain.

Actually, I go the other way and just don't cite the theorems I state that I'd proved at all. Then when someone asks (if they do), I get a distracted, off-my-stride, "oh.. that was me" before leaving the boring history and getting back to the interesting math.

D. Eppstein said...

I believe that, when properly formatted, there is a (hard to see) typographical distinction between multiple-contributor names and the hyphenated names of a single person: they use an en-dash rather than a hyphen. So it's Smith–Jones, but Swinnerton-Dyer.

Melanie said...

"So what does Stanley-Wilf say about this?" sounds like metonymy to me.

Harald Hanche-Olsen said...

D. Eppstein is exactly correct, except that the distinction between a hyphen and an en-dash is usually quite clearly visible. If not (as seems to be the case on this blog), I would consider that a bug in the font. (I am kind of sensitive to this issue , having a hyphenated name myself.) Fortunately, most fonts used on paper make the distinction sufficiently clear.

Anonymous said...

In your last example, shouldn't it be cites as S-S, thereby making it clear that both speakers were implicated?

Isabel said...

Anon,

my point is that one of the speakers there proved the theorem. (Say, Smith and Simpson are talking about their joint work, and they cite a theorem that Simpson proved a few years before which inspired the joint work.)

Isabel said...

d. eppstein,

I've seen that typographical distinction before, although I forgot about it while I was writing the post. But any notation that depends on typographical subtleties that are below the level most people will be bothered to think about is Bad Notation.

John Armstrong said...

Canonical Bad Notation:

$|\frac{\Xi}{\bar{\Xi}}|=1$

Ben said...

In the words of the late (great?) Serge Lang: "Your notation sucks."