TITLE: When is it appropriate to entitle a paper "A note on..." or "On the ..."?
QUESTION [28 upvotes]: I rarely find modern research papers (on mathematics) that are less than 5 pages long. However, recently I came across a couple of mathematical research papers from the 1960/1970's that were very short (only 2-4 pages long). The authors of both papers solved very specific problems, and stopped writing (I guess) as soon as they were done. This made me realize that I very much like short papers! When possible, I will strive to do the same with my own future papers.
Sometimes one finds short papers that are entitled "A note on...". Since I am first of all not a native English speaker and also only a junior mathematician, I would like to know what you think about my questions/thoughts:
1) Is it a good (or bad?) idea to try to let the title of the paper reflect the fact that it is short? Are there any standard ways of doing this?
2) A paper which is entitled "A note on...", is it expected to be short? How short? Can a 50-pages long paper be "A note on..." or would that not be customary?
3) At least to me "A note on..." could give the impression that the paper is a survey article where no new material is presented, but I guess this need not be the case. When is it appropriate to entitle a paper "A note on..."?
4) When is it appropriate to entitle a paper "On the ..."?

REPLY [6 votes]: Historically, it was quite common to start titles with "on," much more so than it is today. Many classic works of science have such titles, such as
"On the Origin of Species," by Charles Darwin;
"On Growth and Form," by D'Arcy Wentworth Thompson;
"De rerum natura," by Lucretius;
"De revolutionibus orbium coelestium," by Nicolaus Copernicus.