A remarkable on-line collaboration in mathematics happened recently. Tim Gowers initiated a fairly modest program some 6 weeks ago, trying to get a heuristic justification (or refutation) on how one should go about obtaining a combinatorial proof for the density Hales-Jewett problem. He intended it to be a on-line collaboration between many, with lively discussion that goes somewhere, not necessarily to a mathematically rigorous proof of the theorem, but at least (what I interpret as) a sufficiently convincing outline or heuristics that the problem can be thrown at a PhD candidate to finish.

It appears that the participants far exceeded the expectation (granted, they had some real high-powered minds in that discussion). It is hard for me to tell what they actually achieved, since there are way too many posts for me to sit here and read (especially considering I am supposed to be working on my dissertation), and that the subject is combintorics and ergodic theory, two things with which I am rather unfamiliar. But if Tim Gowers says that the problem is basically solved (not "we have a good idea on how to go about approaching the problem"), I am inclined to believe him.

Anyway, this experiment is rather exciting for me for two reasons.

Firstly, I have been rather a fan of the internet as a facilitator for communications. I have always imagined a possibility of collarborative work in mathematics using some sort of Wiki format. But Gowers's experiment shows that even the linear-flow of just comments-on-a-weblog may even serve better. For one thing, it gives an indication of the thought process behind the formulation of the strategy, something very useful for historical and pedagogical purposes. Secondly, the exploratory debate means that it may be easier for a new participant to grasp what has been tried and what has not. Overall, I think this is a much better method of preserving the progress and opening up the discourse than just my limited imagination of a Wiki.

Secondly, I just found out (rather belatedly, so it seems), that WordPress has built-in support for LaTeX. This put me at a quandary. While I am busy right now with my dissertation, I have always intended to go back and revisit the code for blogOhm (especially now that bash-4.0 was released). One thing I'd liked to work on is improved LaTeX support. I had planned to devote some portion of this summer (before migrating to my post-doc) on it. Furthermore I have never gotten the commenting system to work properly. Now I am wondering whether I should just give-up on blogOhm altogether and migrate to WordPress. Decisions, decisions.