Groupprops:What makes us special

Okay, you've probably come here wondering what is so special about having a wiki on group theory, and what exciting things this wiki can offer which aren't already there in the textbooks and the world-wide-web. I'm not sure a dull and dry purpose statement, or a list of contents, or a description of an organizational paradigm, can quite capture the flavor and excitement that Groupprops holds. So in this rather loosely written article, I try to outline what really got Groupprops started, and why I think it's going to be something of great use and value both to you as an individual and to the overall community.

Why use anything other than Wikipedia?
Wikipedia, which calls itself the free encyclopedia, is increasingly being touted as the first reference point for everything. The day is probably not far when people, looking for some new information, go, not to the Google search bar, but to the Wikipedia page. In fact, Wikipedia is drawing people not just to read its articles, but also to write them.

So that's good, say some people. There's one canonical reference point, or source place, where we can get all information, and where we put all information. Let's cooperate on Wikipedia.

But it doesn't work that way. Wikipedia may have the most impressive-looking articles on film-stars and on topics of general interest but the way its science and mathematics articles are designed is very poor -- and the rate at which those are going to improve (if at all) is too slow.

But then why not go and contribute there?
That's what I thought &mdash; to begin with. I spent quite a bit of effort on various aspects of articles in group theory, including the articles on characteristic subgroups, pronormal subgroups, abnormal subgroups, and what not. But there are or were lots of problems:


 * There was absolutely no rule-book about how a group theory article, or how an article on a group property or a subgroup property should like. So here, I write one article like this, somebody else writes another article like that, and there's no way to compare across articles. Some articles could even omit the basic definition of the term!
 * There was no way of knowing who the community of editors and people working on group theory was, and of trying to hash out a common policy/strategy with them. Probably there are all sorts of WikiProjects and Portals but it would be hard to find one where quick decisions and discussions are possible.
 * Since Wikipedia is this one huge big thing, there are people from all over putting pressure on the appearance of articles. So there's the person concerned that the language is accessible to people across the world. There'll be another person who wants that the stuff should be technically correct, another person will want to put adequate references, another person will try to put in more explanatory text. Often the people editing, or wanting to edit, may know nothing of the subject matter.

So the question was: why contribute to Wikipedia when I had little control over the way the final outcome would be? When all the content could get mixed up with stuff different people put in different ways? When individually laudable efforts by people resulted in a collective mess?

The only attraction of Wikipedia was its inertia, the fact that it was already there, the fact that many things were laid out. But it took me only a while to figure out that this inertia was also a big factor against it &mdash; a lot of poorly written, or mixed-up, material, couldn't be changed because it was already there.

But aren't there any better alternatives?
As of now, there's only one large-scale effort that claims to work towards being a big wiki-encyclopedia: the Citizendium. The Citizendium lacks a lot of the chaos that's inherent in Wikipedia, at least as of now, and it has this greater sense of community and workgroup with the people having discussions on what to put up and how. However, in so far as a group theory reference is concerned, the Citizendium suffers from quite a few problems similar to Wikipedia:


 * It has too many people, all with conflicting ambitions. There may be some who want to focus on what schoolchildren most need, some who want to focus on giving information to research-oriented groups, some who want to cater to college students.
 * It is an encyclopedia of everything. Which means that the policies and organizational principles are designed for everything. So group theory will probably have to bow down to policy decisions that are suited for some other things.

Okay then what? Reinvent the wheel?
Read on.

What we want to do here
This wiki is for people like you who don't want to wade through all the wrong books, or go barking up links, to look for one simple definition, statement or proof. People who do like to explore, but who also want to get somewhere, and get there fast. People who may enjoy detailed reading and want to know the correct and reliable references.

Which means, for instance, that if you deal in some particular area of group theory, then you should be able to quickly locate articles in that area, That if you want to look up some definition, you should get the article which has that definition stated clearly and precisely. That if you wantto know more about why something is important, you should be able to locate an article that explains the importance.

You should be able to search and locate stuff by category and type, by analogy, by contrast, by variation, by proximity. And you should be able to choose precisely what tool you want to use in your search.

Why its needed in research and study
Research and study is a very different ballgame from surfing the net. And finding information, particularly small and simple bits of information, is far from easy. Mathematicians often come up with small and simple questions and problems in their work which they don't have any idea where to look for solutions to. So they wade through the big books on the subject, have extensive consultations and discussions with colleagues, and try doing a lot of general reading to figure out the answer (alternatively, and more likely, they postpone or give up thinking on the matter).

In fact, even people with doctoral degrees and full tenure may forget simple facts and not have easy ways to look them up -- something which slows down research tremendously.

Some might argue that this is actually good for research -- that getting stuck leads one to read, and explore, more. Yes, true! But one can choose to explore in a more positive sense, by first locating what one is searching for and then exploring around that. And for that we need a method of organizing knowledge and ideas that is interactive, reliable and deep.

Textbooks may be very reliable and very deep but it's often hard to get exact answers to specific questions from them, particularly if one doesn't know the correct textbooks. On the other hand, general encyclopedias may be written in too vague and general a manner, may lack the precise definitions, and may lack both reliability and depth.

Why its needed in group theory
A lot of research has been done in group theory. One of the largest theorems of mathematics, the classification of finite simple groups, has a proof that's 15,000 pages long, spread across hundreds of journal publications. There were very few people who understood the proof and even now, there are very few who have the big picture.

And there are lots of efforts going on currently for bigger theorems involving classification, duality, correspondence, invariants and what not.

If we want that the mathematicians of today can grasp these things, and can look up both the general ideas and the particular definitions, we should put them up in a way that's easily accessible to all.

So what alternatives do we seek?
We seek a solution that is:


 * highly interactive and allows people to jump around in exactly the way they want
 * highly structured and organized in as many different ways as possible so that people can search and locate along any parameter
 * easy to edit, modify and improve iteratively, by many people (it may not be strongly collaborative but should possess collaborative capacities)

The wiki model struck me as the best and most natural one for all these requirements, which is why I chose it.

What has been achieved so far?
So far, it has been fairly good, but it's nothing compared to what/where we finally plan to go. In fact, there has been only one contributing person so far, and that's me. A few others have started reading and referring to the wiki, but it doesn't have a community of its own &mdash; as yet.

However, even in its current, highly fledgling state, the wiki already displays the high interactivity and high organization principles. And it is already becoming a nice place to navigate for quick and easy information. In fact, I personally use the wiki a lot to:


 * Look up definitions that I've forgotten
 * Find references and external links
 * Hunt for related terms

Which means that the wiki, though so far written by me, has already gone beyond me. And I foresee that it will go way beyond anything we can imagine.

THE group theory wiki
Yes, Groupprops aspires to be a wiki in group theory, one as comprehensive as possible, one which helps people at all levels of group theory. However, we have no intentions of being the wiki in group theory, or THE place where everybody edits and everybodyreads. In particular, we have a lot of policies and organizational paradigms which are not likely to be compromised and are not open to debate and public decision. These principles form the backbone of the wiki and are not meant to be edited out.

On the other hand, our hope is that this will not be the only wiki in group theory, and that others will be inspired by the idea and will choose to implement their own knowledge source (which may or may not be a wiki). Content may be freely borrowed from Groupprops. After all, competition never does or did any harm.