Another thing to say is that the software that Alex and Olof have used to write the Tricki itself is Drupal, which is freely available. So it could in the end be that those wishing to serve broader educational ends would be better off just writing something specially tailored to their needs using Drupal.

Although the Tricki itself will emphasize “method over matter,” the design or specific features of the Tricki could be adapted to broader educational ends.

For example, an analogue of arXiv.org with Tricki-style comments and cross-links could serve browser-formatted lecture notes and collaboratively evolving textbooks. Authors would set the policies for community changes to and comments on their own articles, but other works might be almost completely “open,” as with Wikibooks.

Automatic or relatively painless machine translation between online and conventional formats (*eX, PDF, etc.) might also be useful for converting existing manuscripts, editing articles elsewhere, stripping comments, feeding journals, making hard copies, generating slides for class, etc.

The Sage developers may be able to help with embedding Sage expressions and plots into Tricki pages. Presumably, live objects would absorb non-trivial server-side resources, but perhaps they could be hosted remotely.

In a subjunctive mood, I suppose. Much praise to those who toil tirelessly for the Tricki.

http://www.mathlinks.ro/ ,

might enjoy the Tricki. Apparently, many current, former, and future Olympiad-caliber competitors and problem-solving enthusiasts — not to mention budding mathematicians — use the large and very active MathLinks forums to discuss problems, techniques, etc. Depending on the level of the Tricki, they could benefit from and contribute to it, or perhaps spin off a Junior Tricki.

Incidentally, maybe another description of this trick is, “Often it’s enough just to look at zero,” another example being that if you want to prove that you can’t expand a vector in two different ways in terms of some spanning set, then it’s enough to check it at zero, or that to prove that a linear map between Banach spaces is continuous it is enough to prove that it is continuous at zero.

Harrison, thanks for that interesting comment — I had a look at the TV tropes Wiki. As an experiment I decided to look for a very common trope: the police detective, not the main character, who reveals that he is on the point of retirement, at which point you know that he is doomed to die before the end of the film. I clicked first on “death” and then found a long list of names of tropes. One of them was called “retirony”. I thought it looked promising, and indeed it turned out to be exactly the trope in question. But this felt like a bit of a fluke, as for many of the trope names it was not possible to guess even roughly what the trope was that they were describing. But I definitely agree with your main point, that Tricki users will find solutions to these difficulties. At this stage my priority is to make people aware of the problem, and to urge people not to be satisfied with what I would regard as unsatisfactory solutions to it. In other words, I’m very happy to rely on our collective ingenuity, and that is one of the major ideas of this Tricki, but I want to make it as clear as possible where this ingenuity needs to be applied. Once the site is up and running this will of course be much easier, and I expect there will be surprises in store — some things working better than expected and others less well.

I feel as if this is a question that the “tricki community” should ask itself collectively. Wikis, of course, work on the same logic as open-source software and prediction markets; not only does pooling everyone’s work or knowledge or bets allow the resources to come together in one place, but the end result tends to approach some sort of optimum over time. A sufficiently robust system, in other words, will take care of these types of problems itself (i.e., by allowing articles to shift focus over time, so that something that starts as a specific example can become more general, and an over-general article can split into several new, more focused, ones).

However, I find that unsatisfactory, partly because I’d like a way of finding the trick by describing the trick, and not by using some name of a theorem.

In reference to the general problem of navigation on the Tricki: the TV Tropes Wiki is another collaborative wiki that deals with subjects for which there’s no good naming convention; it divides its pages in several different ways (so that you can get to a given trope page from the page for a series in which it’s used, or from a list of tropes for its medium or genre) and has a lot of index pages, so that if a trope exists it’s possible to find it fairly quickly.

So, while I’m not sure that “describing the trick” is entirely feasible, it’s certainly possible to reduce ambiguity. In the example you give, our hypothetical user might find the add-a-linear-function trick by first looking at the index on “Reduction Tricks,” tricks for reducing one problem directly to another, and then to “Transformation Tricks,” which involve performing an operation on the object under consideration so that it has a certain desirable property. Or perhaps from “Reduction Tricks” the user could click on “Reduce to special cases” and from there link to the Rolle’s theorem trick.