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the polymath blog massively collaborative mathematical projects the polymath blog april 3 2026 polymath news and ai filed under discussion polymath proposals gil kalai 7 48 am 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 a polymath project about the word problem in the artin tits group it also has some ai component leave a comment february 20 2021 polymath projects 2021 filed under polymath proposals gil kalai 4 11 pm 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 the proposed projects a few polls were taken and a problem the erdős discrepancy problem was selected for the next project polymath5 in combinatorics and more i reviewed some of the proposed projects from 2009 and in the same post i briefly and sometimes vaguely discussed the 2021 list that i plan to present and discuss in detail in the next couple of months comments 9 june 9 2019 a sort of polymath on a famous mathoverflow problem filed under polymath proposals gil kalai 6 09 pm 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 by tao for a solution similar to a 2009 result by bjorn poonen who showed that conditioned on the bombieri lang conjecture there is a polynomial so that the map is injective poonen s result answered a question by harvey friedman from the late 20th century and is related also to a question by don zagier comments 11 february 3 2019 ten years of polymath filed under discussion gil kalai 3 14 pm tags polymath projects polymath1 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 comments 3 october 19 2018 updates and pictures filed under discussion gil kalai 9 10 am tags polymath pictures polymath12 polymath16 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 in an n dimensional vector space v one can always find n disjoint bases of v each containing exactly one element from each b_ i we call such bases transversal bases rota s basis conjecture remains wide open despite its apparent simplicity and the efforts of many researchers for example the conjecture was recently the subject of the collaborative polymath project in this paper we prove that one can always find left 1 2 o left 1 right right n disjoint transversal bases improving on the previous best bound of omega left n log n right our results also apply to the more general setting of matroids http front math ucdavis edu 1810 07462 earlier the best result was giving disjoint transversal bases h ere is a subsequent paper about the more general kahn s conjecture https arxiv org abs 1810 07464 polymath 16 is alive and kicking polymath 16 of the chromatic number of the plane is in its eleventh post a lot of interesting developments and ideas in various directions the polymath picture i took some pictures which are a little similar to our logo picture last picture below more leave a comment april 10 2018 polymath proposal finding simpler unit distance graphs of chromatic number 5 filed under polymath proposals ag24ag24 5 56 am 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 were rapidly demonstrated but no further progress has since been made in a recent preprint i have now excluded the case by identifying a family of non colourable finite unit distance graphs i e graphs that can be embedded in the plane with all edges being straight lines of length however the smallest such graph that i have so far discovered has edit after correction vertices and its lack of a colouring requires checking for the nonexistence of a particular category of colourings of subgraphs of it that have edit after correction and vertices which obviously requires a computer search i m therefore wondering whether a search for simpler examples might work as a polymath project an example might be defined as simpler if it has fewer vertices or if it has a smaller largest subgraph whose colourability must be checked directly etc i feel that a number of features make this nice for polymath being graph theory it s nicely accessible seductive to non specialists it entails a rich interaction between theory and computation simpler graphs may lead to insights into what properties such graphs will always usually have which might inspire strategies for seeking 6 chromatic examples improved bounds to the analogous problem in higher dimensions etc i welcome comments aubrey de grey comments 115 january 26 2018 a new polymath proposal related to the riemann hypothesis over tao s blog filed under polymath proposals gil kalai 7 17 am tags polymath proposals riemann hypothesis 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 the purpose of this post is to describe the proposal and discuss the scope and parameters of the project briefly showing that is the rieman hypothesis and it is known that brad rodgers and terry tao proved an old conjecture that the purpose of the project is to push down this upper bound the rh is not considered a realistic outcome comments 6 spontaneous polymath 14 a success filed under polymath proposals gil kalai 6 27 am tags apoorva khare polymath14 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 comments 2 august 22 2017 polymath 13 a success filed under polymath proposals gil kalai 2 09 pm 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 comments 2 may 15 2017 non transitive dice over gowers s blog filed under polymath proposals gil kalai 7 36 am a polymath style project on non transitive dice wikipedea is now running over gowers blog here is the link to the first post comments 10 next page recent comments polymath plus ai c on two polymath of a sort propo ten recent questions on two polymath of a sort propo anonymous on rota s basis conjecture anonymous on rota s basis conjecture anonymous on polymath projects 2021 richard montgomery a on rota s basis conjecture anonymous on crowdmath projec anonymous on rota s basis conjecture anonymous on a sort of polymath on a famous anonymous on a new polymath proposal relat anonymous on polymath projects 2021 anonymous on polymath proposal bounded gap anonymous on research thread v determinst anonymous on a new polymath proposal relat anonymous on polymath8 a success polymath wiki most recent changes an error has occurred the feed is probably down try again later blogroll gil kalai michael nielsen terence tao the polymath wiki tim gowers projects mini polymath1 imo q6 2009 polymath1 density hales jewett polymath2 embedded c_0 or l p in explicit banach spaces polymath4 finding primes deterministically polymath5 erdos discrepancy problem proposals boshernitzan s problem cap sets other proposals polynomial hirsch conjecture proposals on wordpress pages about general discussion general polymath rules how to use latex in comments categories discussion 9 finding primes 8 hot spots 7 improving roth bounds 1 mock up 2 news 9 planning 7 polymath proposals 33 polymath5 1 research 13 search for top posts polymath projects 2021 polymath news and ai updates and pictures ten years of polymath a sort of polymath on a famous mathoverflow problem general discussion minipolymath4 project imo 2012 q3 rota s basis conjecture polymath 12 post 3 explaining polynomials identities success rota s basis conjecture polymath 12 blog at wordpress com subscribe subscribed the polymath blog join 571 other subscribers sign me up already have a wordpress com account log in now privacy the polymath blog subscribe subscribed sign up log in report this content view site in reader manage subscriptions collapse this bar loading comments write a comment email name website