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In mathematics, there is an unwritten rule that one is not supposed to write his or her own name (using initials or "the author" if necessary) or attach his or her own name to something (e.g., to have something named after you, someone else should first call it that).

A few questions:

First, is this rule, in some form, in fact written down somewhere? If so, where?

Second, what circumstances, if any, is it appropriate to use your own name?

Lastly, does the rule extend to other people referring to the originator of an idea and the idea? For example, is it appropriate to say "X proved the X Theorem."? Or does this make it seem as though (to a small degree) that X broke the unwritten rule? While less explicit, would it be preferred to say "X proved his/her theorem regarding Y on Z."?

I apologize for the "soft" question, but the discussion and answers are certainly appreciated.

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closed as too localized by Igor Rivin, Andreas Thom, Deane Yang, Mariano Suárez-Alvarez, Mark Sapir Mar 31 '11 at 2:17

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According to Shafarevich, Discourses on Algebra, Sturm used to refer to Sturm's theorem in his lectures as "the theorem whose name I have the honor to bear." – John Stillwell Mar 31 '11 at 0:13
Community Wiki? – stankewicz Mar 31 '11 at 0:14
As usual, rules like this are far from universal. Your mileage may vary, especially across cultures, whether they be national or mathematical. For instance, I've seen papers opening with the sentence "[Subject] was first considered by X in [X1]", where X is the (sole) author of the paper. I'm pretty sure that it wasn't conceit on that author's part; different culture, that's all. – Thierry Zell Mar 31 '11 at 1:08
I think this is a very nice question, why did you close it? Let's extend it in the following way: When and why does a theorem (or even a theory) become named after the person who proved it? There are many examples which may be discussed. – Martin Brandenburg Mar 31 '11 at 6:50
When I was a grad student, I sat in on a course on algebraic curves, taught by Zariski. He used the Zariski topology but never mentioned that it had his name attached to it. The next semester, Hartshorne taught a course (on algebraic surfaces, if I remember correctly) to essentially the same students. One of the first things he had to do was to tell us what that topology is really called. – Andreas Blass Mar 31 '11 at 13:16

I would avoid referring to your theorems by your own name unless they have become completely standardized as such. This is especially true when you submit a paper establishing a supposed new result since it will likely be considered presumptuous to assume that no one has already proven something similar. However, it would be awkward not to refer to your name in a theorem if it has become standard terminology. For instance, when Woodin proves results about Woodin cardinals, what else would he call them? To answer your second question then, I'd say you should do so when it is pretty much unavoidable not to.

On the other hand, it is perfectly acceptable to cite your own work, and you should certainly do this. When doing so however, I would avoid referring to yourself if possible. Generally, you can do this by saying "as shown in [n]" where n is the (alpha)-number for the article in your list of references.

As for referring to others' work, I think it is generally considered a compliment to name a property or a theorem after the person who introduced it. However, you need to do your homework first on this, making sure you attribute correctly. Also, you certainly can say "Name introduced such and such a concept in [citation number]," and this happens very often.

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There's a story that someone once asked Marston Morse what he was working on these days, and he pointedly replied, "My theory!" :-D (For some reason I think I heard or read this from Gregory Cherlin; I wish I could remember where.) – Todd Trimble Mar 31 '11 at 1:17
Coxeter has a paper "My Graph". (His name was attached to it by Tutte.) – Chris Godsil Mar 31 '11 at 1:21
Just about everyone else cals it "The Palais-Smale" Condition", but somehow it makes me a little uneasy to use that name myself, and I find myself still calling it "Condition C", the name Steve and I used for it in our paper that introduced it. :-) – Dick Palais Mar 31 '11 at 2:46
What I expressed here is my interpretation of the "unwritten" rules. Every "you should/need" was meant as "in my opinion, this is a good guideline to follow". As others have mentioned or alluded to, there are no universal rules. Separately, citing one's own work increases its exposure while citing others' work attaches proper credit and helps to make your research sound more informed. – Jason Mar 31 '11 at 20:31

Some additional remarks:

All you said are certainly only unwritten rules, not formal ones; just as there is no written rule or law that one has to be modest or polite. (With the possible exception that some journals might have a specific style regarding certain of these matters; however, if this is so a technical editor will take care of it or you will be made aware of it explicitly.)

I would not say 'X proved the X Theorem' but just as it feels redundant to mention X twice; but either 'X proved the following theorem' or 'the X theorem' are perfectly fine (in the latter case it should already be common to refer to this result as such or you should be in a position to feel comfortable to suggest naming conventions).

One additional point where I think it can make sense to deviate from the not mentioning the own name in a paper is when it would start to be complicated. What I mean is this, say you write all references in the form Authornames [number]. And the current paper is written by A,B,C who need to quote a paper by A,E,F and another one by C,G,H. Then avoiding the present authors name by saying 'E,F and the first named author [5]' and 'G,H and the third named author [7]' seems sufficiently inconvenient to warrant an exception.

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Any rule of writing should take a back seat to Rule #1: your prose should be clear, and if possible elegant. A writer shouldn't hesitate to break the other rules if it improves the result; a good writer will work wonders this way. – Thierry Zell Mar 31 '11 at 1:50

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