Gowers had ideas for an elementary approach, and his ideas are described in this later post. Famously, Einsiedler, Katok and Lindenstrauss proved that the Hausdorff dimension of the set of counterexamples to the conjecture is zero. The conjecture states that if and are any two real numbers, and, then there exists a positive integer such that. Littlewood’s conjecture and related problems. The proposed projects in Gowers’s 2009 post and updates regarding these projects.ġ. For various proposals, see also the polymath blog administered by Tim Gowers, Michael Nielsen, Terry Tao, and me, and this MO question. There are so far three very interesting proposals there, and the first proposal is the Friedgut-Kalai Entropy/Influence conjecture.
Let me also mention The PolyTCS Project aimed for proposing projects in theoretical computer science. (At the end of the post I also mention a few “meta” questions.) (A quick rather vague and tentative preview can be found at the end of this post.) Today we go back to Tim’s 2009 post and the problems posed there.Ĭomments on the 2009 proposed projects, the new proposed projects, other proposed projects, and on the polymath endeavor, are most welcome. I will describe several possibilities for my next polymath project. One of our next posts will have the same title and similar purpose as Tim’s 2009 post. (Three of them later turned to polymath projects, and one turned into a project of a different nature.) Following the post and separate posts describing some of the proposed projects, a few polls were taken and a problem – the Erdős discrepancy problem, was selected for the next project polymath5. This experiment resulted in a new answer to a difficult problem, and since then the Polymath Project has grown to describe a particular process of using an online collaboration to solve any math problem.Īfter the success of Polymath1 and the launching of Polymath3 and Polymath4, Tim Gowers wrote a blog post “Possible future Polymath projects” for planning the next polymath project on his blog. The project began in January 2009 on Timothy Gowers’s blog when he posted a problem and asked his readers to post partial ideas and partial progress toward a solution. A polymath project ( Wikipedia) is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution.