The polymath project
Tim Gower’s experiment in massively collaborative mathematics is now underway. He’s dubbed it the “polymath project” – if you want to see posts related to the project, I suggest looking here.
The problem to be attacked can be understood (though probably not solved) with only a little undergraduate mathematics. It concerns a result known as the Density Hales-Jewett theorem. This theorem asks us to consider the set
of all length
strings over the alphabet
. So, for example,
is in
. The theorem concerns the existence of combinatorial lines in subsets of
. A combinatorial line is a set of three points in
, formed by taking a string with one or more wildcards in it, e.g.,
, and replacing those wildcards by
,
and
, respectively. In the example I’ve given, the resulting combinatorial line is:

The Density Hales-Jewett theorem asserts that for any
, for sufficiently large
, all subsets of
of size at least
contain a combinatorial line,
Apparently, the original proof of the Density Hales-Jewett theorem used ergodic theory; Gowers’ challenge is to find a purely combinatorial proof of the theorem. More background can be found here. Serious discussion of the problem starts here.
Polymath = user innovation « Jon Udell said,
July 31, 2009 @ 1:11 pm
[...] mathematics possible? Since then, as reported by observer/participant Michael Nielsen (1, 2), Tim Gowers, Terence Tao, and a bunch of their peers have been pioneering a massively [...]
Matt O’ Rama » Blog Archive » The Coefficient of User Innovation Friction said,
August 3, 2009 @ 7:31 pm
[...] then, as reported by observer/participant Michael Nielsen (1, 2), Tim Gowers, Terence Tao, and a bunch of their peers have been pioneering a massively [...]