Already in your book “Mathematics: A Very Short Introduction” you noted the “myth of music and maths”, and recently I stumbled with an extended opinion of yours published in the “The Independent”.

My question is: does the fact that there exists a branch of Mathematics dealing with the abstract (and some concrete) aspects of music alters in some way your perceptions about the issue?

]]>It seems that it will not be realistic to hope that we are going to observe a massive open collaboration even in the modest meaning of the word “massive” from polymath1-5. However, if a larger set of observers can watch (and perhaps even make remarks occasionally) over the polymath blog how a smaller (hopefully non empty) set of researchers openly trying to solve the problem this can be a useful experience as well. (And as mentioned above off-line conventional collaboration by the small group of involved researchers can be useful.)

Of course, it seems perfectly reasonable if other mathematicians will study separately this problem on their owns in a more conventional matter.

One advantage of having such an open research is that it makes it easier for the community to understand the issues, ideas and proofs.

There is a famous example of Ian Agol who openly studied and eventually proved over his blog the famous tameness conjecture. Proofs of the conjecture were reached also by Suhyoung Choi who had a different approach and used some ingredients of Agol’s open ongoing work to complete it, and by Dan Calegari and David Gabai who independently worked on the conjecture and solved it.

(I hope I tell the story right.)

That’s an important point that we’ve discussed. Given that several people are passing through Cambridge in the near future, there are obvious opportunities for that kind of interaction. Indeed, Ben Green, Tom Sanders and I have already had various discussions.

I get the impression that the way of working for this project may be a bit different from how it has been with previous projects. Somehow a rapid throwing out of half-formed ideas seems a bit less helpful: we all have a fairly clear idea of the kind of thing we are trying to do, and the difficulties involve getting to grips with some issues that may be technical and may be more fundamental. It could be that the right way to proceed is for people to do a bit more private thinking, and to write as much expository material as we can, with the aim of all helping each other to understand the two key papers and the other techniques that are around.

]]>It is still an interesting problem, but for me other things have been taking up my time and energy.

A survey paper sounds like a nice idea, and thinking about it might wake some new ideas as well.

]]>Something like that would suit me very well.

]]>Maybe we should have a reunion EDP post a few months from now. (I had planned to write something myself but it goes slowly.)

]]>It just sort of gradually wound down as the participants lost energy. However, I have it on my to-do list to write a survey paper (with the assistance of anyone who wishes to join me) summarizing what we learnt during the project. Also, I don’t rule out returning to it at a future date, as I still feel as though there are some ideas to explore.

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