I still believe in this general concept, but for a wiki-type site to be successful it must reach the stage where people think it is worth contributing. Since writing a good Tricki article takes a bit of work, the motivation to do it has to be particularly high. And it seems that it is not high enough for the site to have taken off. I hasten to add that I myself am just as guilty as anyone else — after an initial burst of articles I got distracted by things like Polymath and, dare I say it, conventional research, and haven’t written a Tricki article for well over a year.

During that time, a new factor has come into play: Mathoverflow. For the Tricki to be successful, it had to do something that Wikipedia doesn’t do. And now, to be successful, it would also have to do something that Mathoverflow doesn’t do. This is a serious point: I used to think that one of the main functions of the Tricki would be to make it much easier for people to find out what was known about a problem, but Mathoverflow seems to me to be a better way of doing that.

What I’m asking for here is a bit of feedback. Is the Tricki useful even in its very small and incomplete form? Is there, at least in principle, still a niche for the Tricki, or is it squeezed out by Wikipedia on the static side and Mathoverflow on the dynamic side? Should the Tricki just be allowed to die a dignified death? (Of course, the existing articles might as well stay there, so this would be more like the death of a certain dream.)

Here are a few miscellaneous thoughts.

1. Perhaps some kind of reputation system would provide just enough extra motivation for people to want to write articles. (However, this becomes more problematic when it comes to major edits of existing articles.)

2. Perhaps the Tricki could, at least initially, achieve some success by restricting itself to one or two technique-heavy areas of mathematics such as extremal combinatorics. I have a theory that the success of Wikipedia is partly due to the fact that it has reached the point where the default is that it has an article on something, so that if it doesn’t then that is perceived as a gap that needs to be filled. I think people are in general much more motivated to complete a task that feels as though it is well over 50% done than to do the earlier work.

3. I am prepared to have another blitz on the Tricki (though I make no promises about when), but I don’t want to do so unless it is actually going to be useful to people.

4. I think that there are at least some questions the Tricki might be more suitable for than Mathoverflow. I’m thinking of questions along the lines of “This problem that has just emerged is of a kind I haven’t seen before but it feels as though people ought to have thought about similar things; what should I do now?” Obviously Mathoverflow would be useful for some such problems, but sometimes they are a bit too vague, sometimes one might have a subproblem that one does not wish to make public, and sometimes they may be sufficiently easy that one would prefer just to look up the answer rather than bother other people with the question.

5. If the Tricki became more complete, then one could browse it more systematically than either Wikipedia or Mathoverflow. One could for example decide to read up on all the standard techniques in some subarea.

6. Perhaps part of the reason the Tricki hasn’t taken off is that a high proportion of the existing articles are about undergraduate-level mathematics rather than research-level mathematics. Eventually I would hope for both, so it seemed natural to start with low-level articles and work up, but this may have given a misleading impression of what a complete Tricki would be like.

I’ll leave it there. My two main questions are (i) whether it would be worth my while to put some more effort into the Tricki and (ii) whether there is any chance that if I did so then eventually it would continue to grow without substantial input from me.

### 49 Responses to “Is the Tricki dead?”

1. Vineet Says:

I am not a mathematician, but I think it’s great – ‘How to solve it’ exemplified!

Most text books, however good, typically have concepts and examples, but rarely, if ever, tricks. Especially for someone who is trying to learn serious math, it opens up a whole new way of looking at the problems – which may be part of the toolkit of a practising mathematician but not obvious to an outsider.

• a blogger Says:

I agree with you! but wise man always said! learning by reading oops typos 😉 I mean learning by doing 😉 anyway great articles professor Gowers 😉 I should visit more often at least from 0 to hero hopefully 😉

PS . just kidding 😉

2. Greg Graviton Says:

First of all, I think the quality of the articles on the Tricki is excellent and well worth preserving in form or another, for instance the discussion of homology as “linear combinations of level lines (lines/surfaces where a function is constant)”. Most importantly, you can’t find this stuff elsewhere except in informal discussions with other mathematicians. There ought to be a place to make that public.

Concerning the format, I think the current technology of the Tricki fails to deliver your original “promise” of a powerful search function, that somehow helps you from nothing to a trick that applies. This is a hard problem, it’s not sure whether it can be solved with computers, and bolting the Tricki on top of a Drupal installation apparently does not really solve anything. (On the technology note, note that MathOverflow was programmed from scratch as well, so a fresh start is quite unavoidable, not to mention that even small issues in usability (e.g. sluggish to load) matter a lot.)

Then, there is the “bandwidth” problem of human communication. The fastest way to convey a mathematical concept or trick is to present it to your colleague on the blackboard. It takes very little effort on your part because a lot of information per time is being exchanged: mistakes, mnemonics, steps are weighted by difficulty and importance, questions can be asked, etc. etc. In contrast, the amount of information that a written article can transfer is very small and it takes a lot of effort and skill to maximize its utility.

Related is the question of rewards. It’s rewarding to publish a paper (career) or book (fame), and it’s rewarding to talk to other people (see MathOverflow). There is no reward associated with a tricki article, also because the appreciation by a reader happens at a different time than when the article is written.

However, I think there is room for the Tricki as a “MathOverflow for intuition questions”. The idea is that a Tricki article could be initiated as a discussion between people and then transformed into a proper article by volunteers. By the way, this is how the community wiki feature of StackOverflow/MathOverflow was originally supposed to work. I think it’s still possible to do that, albeit with a software that encourages the corresponding behavior better than MathOverlfow currently does.

Again, note that building such software and community is a very hard problem! A simple wiki software probably won’t cut it, simply because it doesn’t encourage the right behavior. To get an impression of its hardness, remember that Wikipedia’s success could not have been planned, it was just the fittest to survive, and that MathOverflow didn’t get the community wiki thing right either. This is not intended to discourage, I’d just like to point out that a successful Tricki probably needs more cleverness than is apparent at first.

3. Roy Says:

I think that the Tricki is important, and I think it is going to be useful, but it will take time. http://www.scholarpedia.org can both an example and a solution, it is peer-reviewed wiki (at least this is how I see it), wiki just in the sense as free on the web with self-references, but written by professionals. Because it is peer reviewed it grows more slowly then Wikipedia (obviously). There I am not sure how propose the topics in the Tricki anybody should write and peer-review will make it “publication” so this both give a solution to the credit and set the growth rate to be slow. But it requires a journal-like system of editors etc’. I think this is also a good thing because it will share the work load and will give a system to transfer the title and the responsibility for the project to be functional for many years.

4. Xamuel Says:

Very ambitious and difficult goal here.

One of the problems I see is, you almost have to already know what trick you need before you can search for it.

Take for example the problem “Prove every vector space has a basis”. If you don’t already know how to do it, you aren’t likely to know to search for keywords like “make something maximal”, “extend something one thing at a time”, much less “Zorn’s Lemma”.

If I were designing the Tricki, I would set it up like this. There would be articles for individual problems, and articles about techniques. The former would link to the latter. I would then fill it up with as many “stock” problems (mostly from undergrad math) as I could. Essentially it would be like exampleproblems.com, except, instead of just giving the solutions, it would link to the pages for the techniques used in the solution. As the number of problems grew, this would be much more efficient than ultimately writing the same techniques over and over and over (which is what you’d do if you took an exampleproblems.com site to its logical conclusion).

So for example it would have a page “Prove every vector space has a basis” which would in turn link to “How to use Zorn’s Lemma” as well as maybe “Partially ordering sets by inclusion”, and any other technique pages that might be relevant.

5. Terence Tao Says:

One of the reasons that MathOverflow works so well is that it takes full advantage of Metcalfe’s law. If N people ask questions and N people read the site to answer questions, there are O(N^2) opportunities for a question to be answered.

In contrast, to write a Tricki article, one of N people must come up with the idea and then write at least a stub article, and so there are only about O(N) opportunities for such an article to be created.

That said, just because a site is not highly active in traffic does not mean that it has little value. Tricki pages still come up in web searches, and I link to them sometimes on my blog. If at some point in the future some research group would like to collect a focused set of tricks on some mathematical topic, there is now a ready made location for them to do so if they please. And at some point in the future, perhaps when technology improves to the point where a better platform becomes more evident, the existing content might someday be migrated to a more lively forum.

6. Rune Says:

Perhaps the easiest thing to do now to test whether Tricki will work is to restrict its scope to a small field, such as extremal combinatorics, as you suggest. Even if very few people contribute and Tricki is doomed to failure, at least you’ll end up with a decent collection of tricks in Extremal combinatorics. In the worst case, if you end up having to shut down Tricki, a decent collection of tricks in a small area can be published to help folks in that area. A random collection of tricks in all of mathematics will serve little purpose.

Yeah I think Terrys comments are good ones. Tricki can be quite useful when your thinking about a trick. It takes time for such things to get enough data, I believe for instance that a lot of good Phd students procrastinate by writing wikipedia articles! One commenter made the point that ‘how to solve it’ is exemplified. Perhaps there could be a system where you type ‘traffic modelling’ or ‘kirchoffs laws’ and a list of related tricks comes up like Operations Research results. The programming problem is highly non trivial as you well know. I think the Tricki is worthwhile, guess I’ll need to procrastinate from my Masters by writing something for it!

8. John Says:

Tricky has been very useful for me. The lucidity and the insights offered by the articles on stationary phase and other topics in Fourier analysis are not matched by any existing textbook that I know of. Reading a tricki article is the next best thing after listening to an expert mathematician explaining things. One issue with tricki is that certain areas of mathematics, like Algebraic Geometry or Algebraic Number Theory are under-represented.

9. Spencer Says:

While the reputation and medals thing is a big part of MO, I’m not sure it would work that well for The Tricki. It’s nice and only realistic to have a (more often than not) polite competitiveness on MO, given that it’s all about answering questions, but Wikipedia works very well in that you feel the goal isn’t to best satisfy the “question-asker” but to somehow contribute to the “higher goal” as it were of having a complete encyclopedia like you say. So you are motivated to all work together to improve the quality of Wiki rather than to best your rival question-answerer. The former seems more appropriate for Tricki, I’d say.

I like the idea of your point 2.: This could really work. Members of the field, as it were, would feel more obliged and motivated to contribute and critique entries and the job feels like it could be accomplished (i.e. get up to a good standard) more easily. Also, if it did take off, say in Extremal Combinatorics, then other fields would want in! So that as soon as it was seen to be successful, it would multiply.

10. Lukasz Grabowski Says:

I also think restricting to a specific subfield, say “Extremal Combinatorics”, is a good idea.

For me rather than looking for solutions of the problems I’m working on, it’d be much more interesting to see whether The Tricki could be used as a “hands on” introduction to a subject.

As noted by others, it seems normal that one learns about tricks and general point of views mainly from discussing with other people and only after that by dwelling into research articles to extract details.

For me this is the main reason I’m not even thinking about working on problems from some distant branches of maths if there’s noone around who’s already an expert in them. It would be very interesting to see if one could, to some extent, use Tricki instead.

11. Gordon Royle Says:

I don’t think static can ever match dynamic, except for basic facts (dictionaries, atlases, wikipedia) or technical things (manuals, documentation, recipes)

Much of it is due to, or stems from, the N^2 phenomenon that Terry referred to, but I think that there are additional factors involved.

A problem posed to MathOverflow attracts a range of knowledgeable (or at least, helpfully speculative) responses from multiple responders, all customized to the level of understanding, or viewpoint, or application that the original poster displayed in their question.

A static article, no matter how good, reflects one viewpoint, expressed at a particular level of sophistication that may or may not match that of the reader.

MathOverflow is beautifully set up in a technical sense, it has sufficiently restricted scope that many professional mathematicians can at least browse it, and it taps into the natural desire of people to help others and be acknowledged for that help.

• gowers Says:

I agree in the sense that I don’t think that the Tricki should try to compete with Mathoverflow on Mathoverflow’s territory. But the Tricki could I think aspire to compete with, say, textbooks, which are extremely static. But maybe that needs to be demonstrated clearly before one can hope for the site to become successful. (This is related to the points made by Spencer and Lukasz.)

• Mark Bennet Says:

Perhaps the ideal motto of the Tricki (which I find fascinating) is derived from the famous Freeman Dyson “gaussian unitary ensemble” comment – the kind of thing that is mentioned in passing in a lecture or seminar – the stuff which will be in textbooks in 10 years time.

The original ethos seemed to me to be “Here is a technique which really ought to be applicable more generally, why not see if you can use it?”

It seemed to me to be pretty much orthogonal to “here are techniques for algebraic geometry/extremal combinatorics”

12. Ross Snider Says:

As an undergraduate student interested in complexity and a number of topics in pure mathematics, I’ve found browsing the Tricki both useful *and* fun. This is because (for me) the Tricki does something that Wikipedia/Google and Mathoverflow don’t do. Specifically, I am interested in learning different tricks and techniques (in addition to facts), but I don’t know their names! And since I don’t have specific problems in mind to solve I can’t ask a question on Mathoverflow! I can (and do) lurk cstheory and Mathoverflow, but this really isn’t as efficient as browsing the Tricki.

Unfortunately, the TCS section of the Tricki isn’t populated. Oh well. I’ve been checking back every once in a while just in case. Thanks for initiating it! 😀

13. obryant Says:

I confess that although I’ve been aware of the Tricki since before it went live (and abstractly like the idea), I’ve never actually read any of its articles. I like the idea, but for some reason I can’t put my finger on the Tricki hasn’t entered my day-to-day consciousness the way Mathematica, Wikipedia, Mathworld, and MO have.

14. Gil Kalai Says:

My impression is that the tricki serves quite a different purpose compared to MO. It is possible that a post on a mathematical blog or rarely a specific answer on MO can be polished into a tricki post. Maybe as an intermediate stage towards writing a full tricki article one can link to such posts inside the tricki. Probably tricki’s post are supposed to be more definite and polished, so it is quite natural that progress in creating the tricky will be slow. Of course, a tricki article (as wikipedia articles) can be quite useful for MO participants.

Regarding the specific questions:
(i) whether it would be worth my while to put some more effort into the Tricki

Yes. If you (as others) would like to present a mathematical trick/method either on a blog or on the tricki (or in both places), then it is worth the time doing it. There is considerable chance that good posts on the tricki (and similar posts in mathemaical blogs) will be useful even if the tricki will not pass the critical point of comprehensive and comprehansable collection of tricks.

and (ii) whether there is any chance that if I did so then eventually it would continue to grow without substantial input from me.

I think it is unrealistic to believe that it is possible for one or few people to push the tricki beyond the critical point where it contains a large amount of “tricks/methods” in mathematics.

So I think a useful working assumption for (ii) is “no”.

Maybe, even without restricting the scope of the entire tricki, it will be useful to examine to what extend it covers a large amount of tricks in extremal combinatorics.

• gowers Says:

A related thought that occurred to me is this. Perhaps MO can help the Tricki in the following way. One of the difficulties in writing a Tricki article is that it can be hard to think of examples. For example (!) I know that the trick of making something easier by generalizing it is frequently useful. But if I try to think of a good example my mind goes a bit blank, which is part of the reason I have not written such an article.

However, the job has just got easier: if I post a big-list question on MO asking for good examples of this technique, I can be pretty sure of getting some excellent ones. Then I can base an article on people’s answers and include a link to the MO discussion (partly to credit people with their help, and partly because the discussion will be different and will therefore offer more than the Tricki article on its own). In fact, I think I’m actually going to do this, just to see how it goes.

• gowers Says:

Well, not a very auspicious start to the new era of Tricki/MO symbiosis. I asked the question here and almost immediately it was pointed out that my question was a near duplicate of this question.

• Thomas Sauvaget Says:

Wouldn’t it be worthwhile to then perhaps redo your experiment by asking another question that was really never asked on MO before?

E.g. you might wish to focus on a topic known to be popular enough on MO (along the lines “what tricks and thought processes do you wish to have known earlier when working on X (or: with a Y)”, this to allow not using only the ‘big-list’ tag on MO, which some people filter out, I think).

• palibacsi Says:

I remember a very elementary statement which one can prove by generalization. I think I have seen it in Arthur Engel’s Problem Solving Strategies: For all natural numbers n larger or equal to two, the following inequality holds:
sqrt(2xsqrt(3x…xsqrt(n)…)<3.
One way to prove this is by proving the following stronger statement:
For all natural numbers m, n satisfying 1<m<n+1 the inequality
sqrt(mxsqrt((m+1)x…xsqrt(n)…)<m+2 holds.
Proof by induction: The statement holds for all natural numbers n, if m=n since sqrt(n)<n+2. Now, suppose sqrt(mxsqrt((m+1)x…xsqrt(n)…)<m+2 for some natural numbers m, n satisfying 2<m<n+1. Then,
sqrt((m-1)xsqrt(mx…xsqrt(n)…)<sqrt((m-1)(m+2))<sqrt((m+1)^2)=m+1. Now, we have the general statement and get the original one for m=2.
I am sorry if somebody elso posted this before or if it is considered a boring example.

• palibacsi Says:

Sorry, there is a flaw in my above reply. I hope, now it is correct:
For all natural numbers m, n satisfying 1<m<n+1 the inequality
sqrt(mxsqrt((m+1)x…xsqrt(n)…)<m+1 holds.
Proof by induction: The statement holds for all natural numbers n, if m=n since sqrt(n)<n+1. Now, suppose sqrt(mxsqrt((m+1)x…xsqrt(n)…)<m+1 for some natural numbers m, n satisfying 2<m<n+1. Then,
sqrt((m-1)xsqrt(mx…xsqrt(n)…)<sqrt((m-1)(m+1))<sqrt(m^2)=m. Now, we have the general statement and get the original one for m=2.

15. Omer Says:

Just a thought: A glimpse into the cognitive process of “doing math”, presented structurally and in details, could be priceless for researchers and programmers working on automated theorem proving. I think that alone makes it very valuable.

• gowers Says:

As a matter of fact, that was one of my strongest motivations for the Tricki: the thought that one day the ATP programmers would be able to do all the low-level stuff and the Tricki would be able to tell them how to do the higher-level stuff.

16. Ricardo Sandoval Says:

One idea that I have is to make a book (initially basic to medium level) that motivates the reader to explore different ways of thinking about the problems, the “tricks” and the techniques involved something like:

First: Give a problem, set the basics, make the student curious and interested in it (hard but possible) and maybe give him some initial ideas.

Second: Present options to him: Ex:
a) If you prefer to divide the figure go here.
b) If you prefer using a more algebraic method go here.
c) If you like/know such theorem go here.

With options that would feel natural or possible to most people.

Perhaps going to the extreme of presenting some option that is a natural one but that in this particular problem isn’t helpful. Explaining that the technique is really useful in others types of problems but because of some particular obstacle in this case (probably not clear in the first look) it doesn’t work. The student should be in some way rewarded for thinking an initially good idea. And that also prepares him for the inevitable small setbacks in problem solving.

For the whole process the two objectives being: Obviously to solve the problem in case but mainly to instigate/teach useful ways of thinking preferably in line with what the student finds easier to grasp or what fells more natural to him (so that the student is a more active part of the learning process). Maybe if he is curious he can look the other ways and see if they improve his understanding of the subject.

17. Ricardo Sandoval Says:

To better justify the need for different options, I can start by stating the obvious: People have different ways of thinking. But less obviously, I don’t see a way of teaching that works really well to everybody, but I can see trends of thinking. Teachers get used to answer more or less the same questions every class because there is many times a student that thinks in a particular way.

Most interesting ideas have different ways of being explored, some solutions work faster and/or work more generally (and so are generally established in the traditional textbooks) but other solutions that are also valid get many times pushed aside because they are longer/harder or not entirely general. These methods can give different, insightful, useful, or simply give more thinking tools to the student and so should be instigated for the students that like these ways of thinking.

Other thing that happens is that with experience teachers/mathematicians often see that some techniques are equivalent (give the same results). Eventually they (or the educational system) will make a choice that goes generally smother or faster.

But the first time student will not see this. The students should be given some liberty here so they can devise their own way (that will feel better to him) or learn latter on by himself the equivalency (that will also make him happy). To me the bad choice here is to generally force some type of solution saying “trust me this way works better” that clearly undermines the more creative students.

Many teachers generally stabilize in some way of teaching that gives to them the least amount of problems. And that many times is not the way that gives the students the best results. I am not proposing a revolution in teaching just giving a more interactive book that can appreciate the student’s strengths and abilities and conduct him in a lighter and more interesting process of learning.

Different books already give different proposals about how some topic can be understood, and mathematicians naturally tend to try to find the best way (most efficient way) to understand something (according to their personal evolving criteria). I would like to collect that general knowledge that is already out there of some simple problems in an evolving book form.

Resuming: What I would like to see in some form is “books” in traditional topics that shows problems/theory and the existing thinking culture that naturally surrounds them emphasizing the different viewpoints and the different cognitive tools that can be used.

18. Emmanuel Kowalski Says:

I still like the idea of the Tricki a lot. For me, the difficulty in writing more articles is that I feel that a Tricki article should be well-written, in a way which is different from either a blog post, or a MathOverflow question or answer. And this means it involves more time — I typically write blog posts in one sitting, and would dash off an answer to a MO question as I would a comment to a blog post, but when I wrote the only Tricki article I have done, it was more like writing a short survey paper. Unfortunately, time is difficult to find for such contributions, at least for me…

I think one should allow more time to judge whether the Tricki works. I have written a few blog posts which, I think, would make good additions or complements to the Tricki, after some rewriting and editing, and hopefully I will do this one day.

(On the other hand, I am certainly against reputation systems, like the one in MO, which I find distinctly unhelpful.)

19. dmoskovich Says:

I must admit not to being entirely convinced of the usefulness of Tricki. It’s a lot of effort to write a good Tricki article, and there isn’t enough motivation. It’s not so easy to figure out a practical way to provide that motivation.

20. David Roberts Says:

Some thoughts I hope will be constructive:

Here are some numbers related to activity on the Tricki.

About 770 users have registered on the site since it opened to users about a year and a half ago. Of these, something like 30 users have created articles and something like 70 users have edited articles.

There are about 300 articles on the site in total. Of these, only two were created in 2010.

Over the past six months about 100 users have registered, which averages out at roughly 3.8 registrations per week. These ‘new’ users have created one article and edited eight.

During September the site has had 7651 ‘unique visitors’, though I can’t tell how many of these correspond to genuine users and how many are from spam bots, and about 40000 pages have been served. (I think search engine bots are specifically excluded from these numbers where it has been possible to identify them.) So far September looks to be fairly typical.

Most visitors (by far) arrive at the site from Google.

• vipulnaik Says:

These numbers look pretty good. Another revealing metric that would be worth reporting is the number of “large depth” visitors, i.e., the visitors who visit more than, say, five pages in a single visit. A good number there indicates that people are actually getting value from the website and not just reaching a page through a web search and then realising it isn’t the place they need to be.

Your crude ratio of pageviews to unique visitors indicates that a pretty large fraction of visits comes from large depth visits, but this statistic can be measured separately. If you’re using Google Analytics, it allows you to filter and segregate visits by depth. Other analytics tools should offer similar features.

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23. Américo Tavares Says:

This is a suggestion trying to deal with the lack of time and the need to have well written articles.

I would suggest to create a label such as “to-be-polished” (or similar) to indicate that an Tricki article not so well written due to lack of time of the contributor is intended to be improved by the same author and/or “polished” by others.

Another possibility would be to create a section for the articles not yet in the final form.

• gowers Says:

If you look at the Tricki you will see that the to-be-polished label basically already exists, although perhaps not in the exact form you were imagining.

Well, perhaps that’s not quite true. There’s a label for incomplete articles (roughly corresponding to what Wikipedia would call a “stub”) and there are plenty of paragraphs in articles saying things like “This article needs more examples.” But this doesn’t seem to have encouraged people to supply those examples.

24. Américo Tavares Says:

You are right!

My idea was to make it even more visible.

But the utility of such a feature depends very much, I think, on how much one wants to post something that has not yet the final quality one is used to display in her/his writings.

25. Joseph Malkevitch Says:

Unfortunately, for those contributors to Tricki who are academic mathematicians (employees of mathematics departments) there is little career incentive to writing or developing materials of this kind.

Perhaps there might be a group of people who would volunteer to be “editors” for certain pieces of Tricki and when these individuals saw a post to MO, journal article, or web article, with content related to the area they “supervise,” they could contact the author of that item to modify if for posting on Tricki. The fact that there is less work in adapting something nice that has been done already compared with creating something new from scratch may encourage more contributions.

26. vipulnaik Says:

I think there’s a general perception here that what needs to be done is get a large number of contributors. But I think that at this stage, if the Tricki needs to grow, it needs just 2-5 very passionate contributors, who agitate day and night about continually improving the organisation, adding new articles, etc. Large numbers of diffused contributions could take over at a later stage, but they won’t do the trick at this stage.

For instance, the psychology wiki here:

http://psychology.wikia.com/wiki/Psychology_Wiki

was written almost completely by one person at least for the first few years — now there are contributions from large numbers of people.

The story is a little different with something like Math Overflow, because it is not primarily an information corpus as a place to ask and answer questions. But even there, it is the dedicated few who monitor the site who made sure that it took off. The need for that “dedicated few” in the case of the Tricki would be substantially more.

27. Probable trickipedian Says:

One likely source of Tricki contributors – not for deep mathematics, but useful applied math “tricks” – would be people who use mathematics for our research, but are not necessarily academic mathematicians. For instance, I have (over the years) built a collection of definite integrals not found in standard “tables of integrals”; because they occur in (my) somewhat obscure research area, they are generally unknown outside it.

I (obviously) cannot publish such work in the journals of my discipline, and the techniques are too classical and elementary to constitute modern mathematics research, but it would be nice if I could post them on a well-trafficked public venue and someone else found it useful. I could supply (weak) proofs or justifications for them and have verified them to the best of my abilities, though the proofs would certainly not meet the standards of rigor required by pure mathematicians. If a mathematician could ‘vet’ them, I would be pleased to get a login and contribute.

28. math_enthusiastic Says:

I don’t think so that tricki deserves to be eliminated. The quality and presentation of the `tricks’ presented on the tricki is faboulous. I think, it would be like underestimating the significance of tricki articles if one measures their importance via their usefulness in pure maths regieme only. For example, I found the following article pretty relavent to a question in my mind that I posted as a comment on 18th of this month nearly after a year since the last comment was posted. The url of the article is:

http://www.tricki.org/article/How_to_use_the_method_of_stationary_phase_to_control_oscillatory_integrals

So, I hope that tricki stays alive not for the sake of pure mathematicians only but also for those who are in a bit applied stuff. Cheers!

29. sisn Says:

I really hope that the tricky can be kept alive.
One thought that occured to me that there is a good reason to expect the number of collaborators to increase in the future, because some of the people who “grew up” mathematically with the tricky will reach the level of mathematical maturity to contribute an article.
Because of this I think that the larger number of article with “undergraduate content”, will be an advantage for the long term growth of the tricky.

30. beroal Says:

The prominent feature of mathoverflow is that it is driven by private incentives. Nobody ensures that a question is tempting to wider audience. It is more like a forum. The prominent feature of Wikipedia is strict rules. All articles looks equally dull, like written by the solitary solemn huge brain. 🙂 Wikipedia does not allow an article to mirror individuality of its author. Therefore no feedback.

There are features that are missing on both. Vivid style. Motivation. History of mathematical notions and theorems (this subject usually is connected to motivation). Proofs (I suppose that PlanetMath tries to do this).

31. Phi. Isett Says:

I think that one way to enhance the way the Tricki functions, distinct from synthesising with Math Overflow, would be to one day integrate it with one of the following services:

– Online, publicly written math books.

Should such things eventually exist and gain popularity, they could interact with the Tricki. For example, usually a textbook will use a well-known and common trick at some stage in a proof, but will rarely have the opportunity to give much insight into the trick itself, its origins, its limits, alternative methods, etc. All too often, the first time you see a trick, it is also much more complicated than the most basic example of its use, which makes it harder to digest. Imagine you learned the Fourier transform before you ever diagonalized a matrix… You might not know why it has certain magical properties when it comes to translations and differentiation — in any event, it’s useful to understand that diagonalizing commuting operators is a truly general trick.

Often the trick appears as an ingenious technical detail in a proof. For example: the proof of Sard’s theorem uses this trick you might call “decomposing the total change into small changes”. For instance, writing

$f(1) - f(0) = (f(1/N) - f(0)) + (f(2/N) - f(1/N)) + ... + (f(1) - f(1 - 1/N) )$

helps you bound the size of the image of critical sets which are “almost connected” (you prove an estimate like $|f(x) - f(y)| \leq |x - y|^{1+\epsilon}$) — a similar technique shows the Lipschitz image of a curve in the plane is not surjective (even has measure 0), a fact which can be used to calculate fundamental groups like that of the 2-sphere. You may recognize this trick from a proof of the Fundamental Theorem of Calculus, but maybe you didn’t see it coming. Or you might find it enlightening to see the same trick in other contexts and in a much more general light. If you can link to the Tricki, then the individual techniques can be explored separately and generally without disturbing the flow of the exposition.

This use of the Tricki would be different from the vision of using the Tricki for your research; instead it would be more like using it for people to better/more easily learn a subject. But I do not think it would get in the way of other purposes.

32. beau Says:

I think the Tricki should continue. My recommendation to accelerate its development is not to focus so much about the taxonomy of the articles or the search technology at this stage. The idea is great but it is not clear how to implement it yet. SO, invest more on adding the greatest number of articles that exemplify the type of tricks you want and worry about how to organize the whole thing later. Maybe there could be a scoring system to help identify the most appropriate articles at the beginning.

33. Tricki Math Methods Website | New Math Done Right Says:

[…] Timothy Gowers 2010 on whether the Tricki is dead? […]

34. Making Primes More Random « Gödel’s Lost Letter and P=NP Says:

[…] for collecting and discussing mathematical tricks, along with Alex Frolkin and Olof Sisask. In a followup, Gowers asked whether it needed more examples of research-level tricks compared to […]

35. Mathematics Wiki | Gaurish4Math Says:

[…] (http://www.tricki.org/) : This was started by Tim Gowers in 2008, but now it is […]

36. Making Primes More Random | Gödel's Lost Letter and P=NP Says:

[…] for collecting and discussing mathematical tricks, along with Alex Frolkin and Olof Sisask. In a followup, Gowers asked whether it needed more examples of research-level tricks compared to […]

37. isomorphismes (@isomorphisms) Says:

Another useful category besides “list of techniques” and “list of problems they solve”, would be a mapping between mathematical ideas and where they have been successful. “What can you do with cohomology?” can’t necessarily be answered, but “What has been done with cohomology?” can.

This is not done by MO or wikipedia. The lean theorem prover might be taking a step this direction.

I would prefer for such a project to reach through from mathematical idea to known engineering applications, or at least to PDE.