Spent five minutes, five increasingly frustrated minutes, flipping through an uglily typeset pre-TeX book of mathematics in front of the copier. Was searching for Lemma 5.1; was hampered in this by the fact that the book had nine chapters and the numbering of all results got zeroed at the beginning of each: Lemma 5.1 could be the first in the fifth section of the first chapter; or in the fifth section of the second chapter, and so on.
Well, could have been, except that after all that flipping found out only one chapter had five sections.
It did not have the lemma it was supposed to have.
Curses, foiled again.
After a while of brimstone and keyboard-smashing, the reason became apparent: in my previous pursuits, I had written down the equivalent of “this result, here nicely proven for our current purposes, is basically Lemma 5.1 of RandomItalianMathematician’sBook” when I should have written “Lemma 3.1”.
The lesson of this is not that I should be more careful — a nice lesson of universal value that would be! — but rather that it is ugly, maddening, counterproductive and reference-killing to reset your result numbering at the beginning of each chapter. It is insane to use a method that n-furcates the easiest, simplest method of reference, and necessitates page number or some other contrivance for accuracy.
Also, it may be insane to use the word “n-furcate” without provocation, like I just did.