Massively collaborative mathematical projects
A post over Combinatorics and More describes Nissan Hajaj s proposal to combine AI with polymath projects. Together with Nissan Hajaj and Ido Kaminer we plan to run some projects (possibly also here on the Polymath Blog) and at a later stage to consider resources and tools that can advance such projects. Tim Gowers recently proposed [ ]
After 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 post mentioned 9 possible projects. (Four of them later turned to polymath projects.) Following the post and separate posts describing some of [ ]
Is there any polynomials of two variables with rational coefficients, such that the map is a bijection? This is a famous 9-years old open question on MathOverflow. Terry Tao initiated a sort of polymath attempt to solve this problem conditioned on some conjectures from arithmetic algebraic geometry. This project is based on an plan [ ]
Ten years ago on January 27, 2009, Polymath1 was proposed by Tim Gowers and was launched on February 1, 2009. The first project was successful and it followed by 15 other formal polymath projects and a few other projects of similar nature.
Three short items: Progress on Rota s conjecture (polymath12) by Bucić, Kwan, Pokrovskiy, and Sudakov First, there is a remarkable development on Rota s basis conjecture (Polymath12) described in the paper Halfway to Rota’s basis conjecture, by Matija Bucić, Matthew Kwan, Alexey Pokrovskiy, and Benny Sudakov Abstract: In 1989, Rota made the following conjecture. Given $n$ bases $B_{1},\dots,B_{n}$…
The Hadwiger-Nelson problem is that of determining the chromatic number of the plane (), defined as the minimum number of colours that can be assigned to the points of the plane so as to prevent any two points unit distance apart from being the same colour. It was first posed in 1950 and the bounds [ ]
(From a post the music of the primes by Marcus du Sautoy.) A new polymath proposal over Terry Tao s blog who wrote: Building on the interest expressed in the comments to this previous post, I am now formally proposing to initiate a “Polymath project” on the topic of obtaining new upper bounds on the de Bruijn-Newman constant . [ ]
This post is to report an unplanned polymath project, now called polymath 14 that took place over Terry Tao s blog. A problem was posed by Apoorva Khare was presented and discussed and openly and collectively solved. (And the paper arxived.)
This post is to note that the polymath13 project has successfully settled one of the major objective. Reports on it can be found on Gower s blog especially in this post Intransitive dice IV: first problem more or less solved? and this post Intransitive dice VI: sketch proof of the main conjecture for the balanced-sequences model.
A polymath-style project on non transitive dice (Wikipedea) is now running over Gowers blog. (Here is the link to the first post.)