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.

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