a repository of mathematical know-how

Titles of articles

Titles of articles

I have only recently developed a conscious policy about the titles of Tricki articles – it's one that I was sticking to quite a lot of the time, but not always, and without really thinking about it.

It's that if your article is about a particular technique (as opposed, say, to a subject-area front page), then you should try to think of a good title that takes the form of a command. I feel that that is very much in the spirit of the Tricki: telling people how to do mathematics rather than just laying out some theorems, definitions and proofs.

For instance, an article I started is about the fact that combinatorial problems about sets can often be usefully generalized to problems about functions (with the original problem the special case of functions that take the values 0 and 1). A bad title would have been "Functional versions of combinatorial problems". The existing title is "Turn sets into functions". Somehow, commands seem much more memorable, and encapsulate better the point of the article.

I'm not saying that every article should have a title in the imperative. Sometimes it seems to be hard to think of a command that is sufficiently concise, and sometimes it is clearly not appropriate. I had to compromise in my most recent article (a stub), which I have called "Bounded functions that behave almost everywhere are Riemann integrable." I suppose I could have preceded that by "Exploit the fact that" but that would have been unwieldy so I decided to take that as read. Note that I didn't give it the "bad" title "A useful technique for proving that a function is Riemann integrable." Perhaps another principle could be that if a command doesn't work, then a one-sentence summary of the whole article is a good second best.

All this is motivated by the desire for the Tricki to develop into something like an expert system: as you browse the Tricki, there should be lots of commands out there vying for your attention, and your job is to decide which ones to obey. A second motivation is for the title of the article to give as good an impression as it can of what's in the article – this makes browsing much more efficient.

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