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Massive Open Collaboration In Math Declared a Success

Posted by timothy on from the you-count-the-feet-we'll-count-the-toes dept.

nanopolitan writes "In late January, Tim Gowers, a Fields Medal winner at Cambridge University, used his blog for an experiment in massive online collaboration for solving a significant problem in math — combinatorial proof of the density Hales-Jewett theorem. Some six weeks (and nearly 1000 comments) later, Gowers has declared the project a success, and some of the ideas have already been written up as a preprint."

5 of 60 comments (clear)

  1. Massive open collaboration in math by morgan_greywolf · · Score: 5, Funny

    I wonder if you could do massive open collaboration for software? You could probably write an OS kernel, maybe even an entire operating system!

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  2. List of authors by pimpimpim · · Score: 4, Insightful

    I am all in favor of this, as it allows people outside scientific communities to join in with a low barrier (that is, if you happen to be a math wizard). But is, and if so, how is he going to ensure that the right people will be mentioned as co-authors in the paper?

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    1. Re:List of authors by Sheafification · · Score: 4, Informative

      Gowers mentioned this in one of his early posts about the project. Publishing will probably be under some sort of pseudonym (think Bourbaki), with a link given to the blog entries. If you're curious about how much someone contributed, you can go check it out exactly.

  3. It's about n-dimensional tic-tac-toe. by bcrowell · · Score: 4, Informative

    What you won't be able to figure out from the slashdot summary, or from either of the links (unless you're a specialist) is that this is a theorem about n-dimensional tic-tac-toe. The idea is that you make an n×n×n×...×n in some number of dimensions, and then you fill in some fraction of the boxes with x's and o's (or possibly some set of more than 2 symbols). The theorem says that if the dimension is high enough, and the fraction of the boxes that get filled in is high enough, you're guaranteed to have a line of symbols (possibly diagonal) that wins the tic-tac-toe game. In other words, a tic-tac-toe game in a high-dimensional space can't end in a draw, and can't even go on for very long before someone wins. The definition of "high enough" is what they're trying to pin down. They apparently proved it (or just made some progress toward proving it?) in a particular special case.

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  4. Re:halp! by Anonymous Coward · · Score: 5, Informative

    A good way to think about it is a very abstract and sophisticated version of the "Pigeonhole principle" :

    Lets say you have k + 1 balls and only k bins. If you want to put all the bills into those bins then you are going to have to put at least 2 balls into one of the bin.

    Ramsey theory deals with general problems of this type where if you have too much of one thing (balls) then something else is bound to happen (two balls forced to share a bin).

    e.g if you have at least six friends at a party then they are bound to be a subset of 3 friends who either all know each other or all don't know each other.

    The idea is that once you get a certain density or to a certain quantity of something, some other structure is bound to appear.

    This Density Hales-Jewett theorem specifically deals with playing tic-tac-toe in high dimensional cubes

    i.e if you have a D dimensional hyper cube or whatever and the dimension D is sufficiently large then there is guaranteed to be a win for one player (unlike the regular version which can end in a draw).

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