Groupprops:Mission statement

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This article is about the mission, goals and values of Groupprops

This is a first-person article written by: Vipul
First-person articles give opinions of their authors, as long as these opinions are broadly endorsed by the wiki

This article describes where groupprops, or its successors or offshoots, may be placed ten years from now. I have let my imagination run free, and wild.

To understand and place in context this mission statement, I'll review to some extent the important recent developments, and the current big work in group theory, as I go along.

A tool for cutting-edge research and understanding existing research work

The big classification programmes

One of the biggest theorems proved so far in mathematics is the classification of finite simple groups, whose proof runs to 15,000 pages over several journals. Even the newer, more sophisticated, proofs of the result come to 2,000 or more pages. Understanding the proof completely is a daunting task.

Ten years from now, it'll still be a daunting task -- but it'll be achievable. It will be achievable because an interactive web interface can be organized in a way suitable to understanding a huge, many-pronged, result such as the Classification. People can see, and focus on, just the parts they want. In other words, the wiki will allow you to enter the huge mass of the Classification from anywhere, and understand any part whenever you want.

For instance, you can get specific information, whatever, information you want, on each of the sporadic simple groups. Further, the Classification splits results into various cases and sub-cases, and you can see the proof ideas relevant to each case or sub-case.

One of the problems with following such a proof on paper, is that one constantly needs to keep referring forward and back for references to definitions and proofs. But an interactive web interface can allow one to, with the ease of a click, recall definitions, terms and proofs that are referenced in a given exposition without getting distracted.

But I think the groupprops wiki can go a lot further. It, or its successors will, a few years from now, be used as tools for the next big developments in group theory. Currently, there are two big classification programmes in the offing -- the classification of non-simple finite groups (which reduces to the group extension problem) and, at a somewhat simpler level, the classification of groups of prime power order. Apart from these, there are classification programmes for infinite groups with various additional structures, particularly classifications that seek to relate one level of structure with another. (Cherlin conjecture and bad groups are an example).

Small steps

Much of research is done in small steps, and Groupprops or its offshoots could be really helpful there. The great thing about something like Groupprops is that unlike a research paper, which gets published somewhere and joins a huge rack, a Groupprops article remains forever "live". It can easily be accessed and viewed by any other researcher in the subject.