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| via Redbooth.com |
January marks the 10-year anniversary of the collaborative “Polymath Project” begun by Fields Medalist Tim Gowers. Let’s celebrate early!
Here is the main page for the Project:
…and here is the Tim Gowers posting that originally proposed such a crowdsourcing effort be attempted:
I find it interesting how little widespread digital collaboration has made a dent in other sciences, but been productive in mathematics — one suspects there’s some sort of whole sociological dissertation that could be written here! (although perhaps the pen-and-paper, and computer-assisted nature of mathematics makes it more suited to such endeavors than other more applied sciences)
Anyway, Vicky Neale in her fabulous volume “Closing the Gap,” writes a lot about Polymath’s contributions to the ongoing work on the Twin Primes conjecture. She includes many wonderful quotes from Gowers along the way. Here he is when first proposing a digital collaboration on significant unsolved math problems:
“The ideal solution would be a solution of the problem with no single individual having to think all that hard. The hard thought would be done by a sort of super-mathematician whose brain is distributed amongst bits of the brais of lots of interlinked people. So try to resist the temptation to go away and think about something and come back with carefully polished thoughts: just give quick reactions to what you read and hope that the conversation will develop in good directions.”
Neale then writes, “Gowers was very keen to encourage participants to share their immediate thoughts, rather than working on ideas independently in private, with an emphasis on expressing their immediate thoughts as clearly as possible so that others could build on them.”
And then she quotes Gowers again:
“When you do research, you are more likely to succeed if you try out lots of stupid ideas. Similarly stupid comments are welcome here. (In the sense to which I am using ’stupid,’ it means something completely different from ‘unintelligent’. It just means not fully thought through.)”
Later on he writes, “…even ‘frivolous’ observations can (and should) be posted on this thread, if there is even a small chance that some other participant may be able to find it helpful for solving the problem.
“Similarly, ‘failed’ attempts at a solution are also worth posting: another participant may be able to salvage the argument, or else the failure can be used as a data point to eliminate some approaches to the problem, and to isolate more promising ones.”
Gowers also foresaw the problem of assigning 'credit’ for such widespread collaborations, and so addressed that ahead of time as well:
“Suppose the experiment actually results in something publishable. Even if only a very small number of people contribute the lion’s share of the ideas, the paper will still be submitted under a collective pseudonym with a link to the entire online discussion.”
Later in the book Neale references how Terry Tao deferred to recent-grad James Maynard to insure he would get the most credit for advances to the Twin Prime conjecture that both had made independently — Tao, absolutely established in his field with no need for acclaim, knowing that credit to Maynard might boost his career greatly — I don’t know that this type of gesture/collegiality would occur very often in any field outside of mathematics!
At this point the Polymath Project has met much success (with fits and starts) and is working on its 16th project. Congratulations to all participants involved, and to Tim Gowers' foresight. As the post-title above suggests, here's to more collaboration in life, and less collusion! ;)
For entertainment purposes only, I’ll end with a completely different take on collaboration in math, in the form of a wonderful short piece of film fiction (on the Goldbach conjecture) that I haven’t re-posted for awhile — for any who have never seen it, “The Calculus of Love”:
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