This post has its origins in a discussion that arose as a result of a very interesting post of Terence Tao. Both the post and the discussion can be found here . The post outlines a rather general idea, or trick, that can be used in many mathematical situations. With such tricks, it is usually difficult, and in any case not desirable, to formalize them as lemmas: if you try to do so then almost certainly your formal lemma will not apply in all the situations where the trick does. This has the unfortunate consequence that they are relegated to something like “folklore,” transmitted orally (to a lucky few) or rediscovered over and over again (the more usual experience).
Since tricks (or, to make them sound better, general research strategies) are very useful, and since it can be extremely illuminating to have them pointed out — Tao’s post is an excellent example of that — it would be highly desirable to have a lot of such tricks accessible in some convenient format. But what format? I take it as axiomatic that some kind of online resource would be ideal, but there are now many ways of collecting information online — in fact, many more than I know about. So I’d like views of other people.
To get the discussion started, here are a few views of my own. They are mostly criteria that I’d like such a resource to satisfy.
1. It should be a genuine collaborative effort, like Wikipedia.
2. It should have very high levels of quality control.
3. It should not be run in a dictatorial way.
These criteria are of course hard to combine: I have written them in what I consider to be their order of importance. Similar issues have been discussed at the n-category café here , and I recommend that discussion, but I think their needs are slightly different.
I don’t know whether it would be easy to set up, but the kind of idea I think might work is a Wiki where authors have full control over their contributions, but others are encouraged to suggest improvements (as happens in some of the comments on Tao’s blog entry). These suggestions could even be simple ones like, “I got a bit lost in the third paragraph — could you elaborate a bit?”
I think it would also be good to have some kind of certification process, so that the Wiki didn’t fill up with entries that were badly written or aimed at far too sophisticated an audience to be genuinely useful. A first approximation might be that if enough people wrote comments saying how great they thought the entry was then it would become an official “great entry.” But it is not obvious how to implement that in an automatic way (without a super-editor who judges which entries have reached this exalted standard). Alternatively, there could be something like an Amazon star rating, so that you could see which entries were generally thought to be good and ignore the bad ones.
Another issue is how to organize the entries so that people can look them up, or browse, in a reasonably systematic way. This could be particularly difficult for rather general tricks that are not tied to any particular branch of mathematics — a quality that many tricks have.