About a year ago, as an experiment, I set up on this blog a “mini-polymath” project, in which readers were invited to collaboratively solve the sixth question on the 2009 International Mathematical Olympiad (aka “the grasshopper problem”). After two or three days of somewhat chaotic activity, multiple solutions to this problem were obtained, and have been archived on this page.
In the post-mortem discussion of this experiment, it became clear that the project could have benefited from some more planning and organisation, for instance by setting up a wiki page early on to try to collect strategies, insights, partial results, etc. Also, the project was opened without any advance warning or prior discussion, which led to an interesting but chaotic opening few hours to the project.
About a month from now, the 51st International Mathematical Olympiad will be held in Kazahkstan, with the actual problems being released on July 7 and 8. Traditionally, the sixth problem of the Olympiad (which would thus be made public on July 8) is the hardest, and often the most interesting to solve. So in the interest of getting another data point for the polymath process, I am thinking of setting up another mini-polymath for this question (though I of course do not know in advance what this question will be!). But this time, I would like to try to plan things out well in advance, to see if this makes much of a difference in how the project unfolds.
So I would like to open a discussion among those readers who might be interested in such a project, regarding the logistics of such a project. Some basic issues include:
- Date and time. Clearly, the project cannot start any earlier than July 8. One could either try to fix a specific time (to within an hour, say), to officially start the project, or one could open the thread in advance of the IMO organisers releasing the questions, and just let the first person to find the questions post them to the thread, and start the clock from there. I assume one can rely on the honour code to refrain from privately trying to solve the question before any official starting time.
- Location. In addition to this blog here, there is now also a dedicated polymath blog for these projects, which has some minor advantages over this one (e.g. numbered and threaded comments with wide margins). It has fairly low levels of activity right now (though we are just starting to write up some modest progress from the ongoing Polymath4 “finding primes” project), but this may actually be a plus when running the project, to minimise cross-traffic. Also, another benefit of the other blog is that the project can be co-administered by several people, and not just by myself. This blog here admittedly has significantly higher traffic than the polymath blog at present, but I would certainly post a crosslink to the polymath blog if the project started.
- Ground rules. The rules for the first mini-polymath project can be found here. Basically the spirit of the rules is that the objective is not to be the first to produce an individual solution, but instead to contribute to a collective solution by sharing one’s insights, even if they are small or end up being inconclusive. (See also Tim Gowers’ original post regarding polymath projects.) But perhaps some tweaking to the rules may be needed. (For instance, we may want to have some semi-official role for moderators to organise the discussion. Ideally I would prefer not to be the sole moderator, in part because I want to see the extent to which such projects can flourish independently of one key person.)
- Set up. It seems clear that we should have an official wiki page (probably a subpage from the polymath wiki) well in advance of the project actually starting (which could also be used to advertise the project beyond the usual readership of this blog). Is there anything else which it might be useful to have in place before the project starts?
- Contingency planning. It may happen that for one reason or another, 2010 IMO Q6 will not turn out to be that good of a polymath problem. I suppose it may be sensible to reserve the right to switch to, say, 2010 IMO Q5, if need be. This might be one place where I might exercise some unilateral judgement, as it may be difficult to quickly get consensus on these sorts of issues. I don’t know if it’s worth discussing these sorts of possibilities in advance; it may simply be better to improvise when and if some course corrections need to be made.
Anyway, I hope that this project will be interesting, and am hoping to get some good suggestions as to how make it an instructive and enjoyable experience for all.