The polymath blog

Is taking place on Gowers’s blog!

For a description of Erdos’ discrepancy problem and a large discussion see this blog on Gowers’s blog.

The decision for the next polymath project over Gowers’s blog will be between three projects: The polynomial DHJ problem, Littlewood problem, and the Erdos discrepency problem. To help making the decision four polls are in place!

Tim Gowers described two additional proposed polymath projects. One about the first unknown cases of the polynomial Density Hales Jewett problem. Another about the Littelwood’s conjecture.

I will state one problem from each of these posts:

1) (Related to polynomial DHJ) Suppose you have a family of graphs on n labelled vertices, so that we do not two graphs in the family such that is a subgraph of and the edges of which are not in form a clique. (A complete graph on 2 or more vertices.) can we conclude that =? (In other words, can we conclude that contains only a diminishing fraction of all graphs?)

Define the “distance” between two points in the unit cube as the product of the absolute value of the differences in the three coordinates. (See Tim’s remark below.)

2) (Related to Littlewood) Is it possible to find n points in the unit cube so that the “distance” between any two of them is at least ?

A negative answer to Littlewood’s problem will imply a positive answer to problem 2 (with some constant). So the pessimistic saddle thought would be that the answer to Problem 2 is yes without any bearing on Littlewood’s problem.

A presentation of one possible near future polymath: the mathematics of the origin of life can be found on Gowers’s blog.