Open Source Mathematics

Maths is a famously lonely discipline - I should know, having spent three years of my life grappling with a single equation (the equation won). Mathematicians meet, and collaborate, it's true; but what would a truly open source approach to the process of solving mathematical problems look like? Maybe something like this:

Suppose one had a forum (in the non-technical sense, but quite possibly in the technical sense as well) for the online discussion of a particular problem. The idea would be that anybody who had anything whatsoever to say about the problem could chip in. And the ethos of the forum — in whatever form it took — would be that comments would mostly be kept short. In other words, what you would not tend to do, at least if you wanted to keep within the spirit of things, is spend a month thinking hard about the problem and then come back and write ten pages about it. Rather, you would contribute ideas even if they were undeveloped and/or likely to be wrong.

Do read the rest of the post if you can: (a) because it's thought provoking and (b) it's written by the Trinity man and Fields medallist Timothy Gowers.