The “polymath project” is a blog where serious unsolved problems in math are attacked in a massively collaborative way. A problem is posted and hundreds of users suggest lines of attack. Of course, a lot of the progress is made by a few superstars, but it is still a cool idea. The cynical economist in me must point out that while the supposed m.o. of the project is to harness the beauty of collaboration and cooperation in the age of the web, surely the fuel behind the engine is the competitive instincts of the participants. Nothing wrong with that, though; if not for the competitive drive we might still all live in the jungle.
Also, once a year they run a “mini-polymath” project where they attack a problem from the International Math Olympiad. Of course this is very different from an unsolved problem; everyone knows there is a solution that can reasonably be found by a single person in an hour or two. Still a fun idea. This year’s problem, posted yesterday, is phrased as a game. I’ve played with it for a few minutes and I suspect that knowledge of specific theorems or concepts in game theory will not be useful, though of course the habit of thinking strategically will. (Rubinstein would say that this is true of most real-life applications of game theory as well.) Try your hand, or look at the comments, which surely have spoilers by now as it has been up for about a day.