(Kevin Buzzard is partly to blame for my participation; his sci.math.research posting first made me aware of the MathOverflow forum.)
In celebration of MathOverflow’s fifth anniversary, I have a post on meta.mathoverflow.net which answers the question “How is MathOverflow useful to me?”, and I would expand on both the answer and the question now.
A brief recap of my posted answer: MathOverflow allows me to express that part of me which enjoys mathematics and sharing mathematics. It gives me the benefits of academia that I enjoyed as a graduate student, which I see as access to the thoughts and opinions of a select and like-minded group of people as well as the ability to contribute, while avoiding the major disadvantages of academia, which for me appear to involve politics and the pressures to perform associated and distracting administrative tasks.
I would expand the question to ask how MathOverflow can be useful to me and to others. Here are some of my ideas and observations.
MathOverflow serves as an online forum where (often) specific questions are asked and specific and relevant answers to these questions are given. Other things also happen on this forum and associated fora (chat and meta versions), some of which are useful side effects:
- collaboration on existing research questions,
- hyperlinked references to useful material,
- some discussion,
- some automated cross-referencing,
- some crowdsourcing requests,
- some new research questions are asked,
- some insights and suggestions for understanding arise.
I think the following are related to and can be derived from the current efforts at MathOverflow:
- making an archive version of some of the database
- creating a public directory of those wishing an online presence that reflects and enhances their real-life interests in mathematics
- allowing the creation of several templates for collaborative efforts, such as proof-wikis, tackling research problems, documenting the current and future historical development of disciplines of mathematics as well as past development.
I also think that certain efforts outside of MathOverflow can benefit from the work being done on the forum. In particular, encouraging and influencing the development of the WDML (World Digital Mathematics Library), helping people in developing countries with their mathematical efforts by showing them how to create localized (language-specific) versions of MathOverflow, and development of applications to facilitate various kinds of computation on low and intermediate levels and make them available to many. Further, I believe MathOverflow heralds the development of online resources to accompany and perhaps surpass upon current graduate level textbooks, improving their breadth and accessibility.
It is presently beyond the basic mission of MathOverflow to attempt any of the above efforts under its umbrella. I would instead suggest various project proposals for public consideration and I shall create some “Internet space” for development and small-scale implementation of some of these proposals. Serious inquiries can be directed to an email address found on my MathOverflow user page; a link to this page is at the meta post above.