It’s been over a month since I put my last post on wikis, and at that time, I had just started on my group properties wiki. Much content has flown into the wiki since then, and with the passage of time, I have become more and more convinced that wikis could be a powerful aid to learning and sharing knowledge of mathematics — perhaps even a tool for the active creation of mathematics.
When I first started out in CMI, I was full of a lot of curiosity regarding groups, and I would try to satisfy this curiosity in different ways. I read the Wikipedia articles on the subject, I would surf arbitrarily for terms related to group theory, locate some papers and try reading a few pages and gathering a few definitions from the papers. This was all really exciting and I got a number of ideas and organizational principles on group theory.
ideas were a mesh of complicated stuff. I had this idea here, that idea there. I had some frameworks for my ideas, and I tried writing up the ideas here and there, but it was way too much effort — developing an idea in a full article required a whole lot of effort, and further, there was so much constant changing and updating that was needed that it tended to become a pain.
As a result, many of the ideas and organizational principles that I had remained undocumented. Even the ones that did get documented were usually hard to retrieve/read from the documentation because they were split across multiple files, some of their definitions got duplicated, some lemmas got re-referenced and kept changing in their wording, and so on. So it was a mess. I didn’t know of any way in which I could put the entire web of thoughts I had, somewhere down in writing.
Given the lack of a medium, I shelved aside my work on this front, and tried working on other fronts. In most cases, though, whether I was working with original ideas or trying to grasp existing ones, the structure of the ideas was highly interwoven and nonlinear and articles/write-ups didn’t seem to capture the understanding properly. Still, I used these to whatever extent possible so that at least whatever was covered in the lectures, got properly documented.
Some time in June 2006, I started on an ambitious project of putting up important group theory definitions on Wikipedia. I in fact did put up a whole lot of new articles; however, I soon realized that much of my effort was poorly directed and poorly organized, and moreover, that a lot of it may be undone because there were many other people who felt the articles and material should be organized differently.
It was towards the end of 2006 that I seriously started considering the possibility of starting my own wiki in group theory, and by early December 2006, I had gotten started.
Now for the experience with making the wiki so far.
My initial goal was to use the wiki as a Pensieve (one with easy retrieval) for all the various ideas and facts that were literally taking up too much space in my head. Thus, to begin with, I just kept introducing/writing random articles in nearly random formats. However, as I went along, a certain format/pattern started emerging (in fact I had been subconsciously following this pattern earlier). I also realized that this pattern could be significantly improved upon and thus I designed some generic layouts and formats for various kinds of articles. (I have documented some of these at Groupprops:Article)
Initially, I would manually insert the categories for each article. But then I realized that a more efficient and nicer way would be to create a ”template” for the article type (refer Groupprops:Templates). The advantage of this is that apart from including in a category, it could also print a nice message on screen telling us something about the term (which causes it to be included in the relevant category).
I have also tried to keep a few of the articles always in tune with the latest style. For instance, I have tried to make sure that the articles on normal subgroup, characteristic subgroup, and some others, have the latest format so that they can be used as reference points.
During the month of December and part of January, I was focussing on putting in definitions. Probably that’s because definitions are the thing that fascinate me the most. In January, i started experimenting with articles describing facts and their proofs — I prepared a format for these and started churning out proofs of important statements.
Currently, I am trying to work on improving the depth of the wiki in various themes, for instance, the Classification of finite simple groups, the Extensible Automorphisms problem, combinatorial/geometric gorup theory, and linear representation theory. I am also working on writing more survey articles and expository articles (like the ones on conjugacy class-representation duality, varying on the subgroup property of normality, and varying on the subgroup property of simplicity. These help tie in a lot of definitions and proofs, thus leading the wiki to offer more value than just an organized set of definitions and proofs.
Somehow, though I have put up a lot of content on the wiki and am rapidly adding more, I am still not clear about where this wiki will finally be headed. For instance, I am not clear about the question: do I currently want other people to join into the collaborative effort, or would I prefer to make the wiki fairly robust before I get started on that? Also, do I want other people to come and read it — if so, how and where should I publicize the wiki?
I’ve already circulated the link among a few of my friends here in CMI and a few people outside, but so far I don’t think it has picked up.
(On the other hand, how much can a wiki in group theory pick up?)
Another question I want to answer is: how much effort am I willing to sustainedly put into the group theory wiki? As in, will I continue working on it once I join Graduate School? If the wiki does indeed grow bigger with more people participating and getting involved, am I willing to take on the additional responsibility of coordinating and maintaining it? What end will that serve?
In answer to that, I think I can use the wiki very effectively to document and clarify my ideas in group theory, if only to myself. Hence if I choose group theory as my dissertation subject, the wiki should be very useful in helping me formulate and refine my ideas.
I’ve also been thinking beyond the group theory wiki, towards a general culture of having a wiki per topic (or rather, a huge mass of wikis such that every subject is covered by at least one) — possibly each with different organizational principles or paradigms. For instance, others who don’t like the style or organization of my group theory wiki, but like the idea of a wiki, can start another wiki of their own. Multiple wikis means more competition and more pressure to produce quality material. It also means greater variety for the end-user, each user can choose the wiki whose style more suits his/her personal learning style.
Of course, wikis would not replace the traditional tools of learning, but they could supplement, and provide new inputs. I definitely find learning in front of a computer, with the freedom to click on whatever links I want, and the freedom to search for any term, far more exciting than reading from a textbook. And it often points me to interesting texts to read that I wouldn’t have heard of otherwise.
So for now, I guess, it’s: keep working at the wiki till I get an idea of where it’s headed.