The polymath blog

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 {P} of two variables with rational coefficients, such that the map P: \mathbb Q \times \mathbb Q \to \mathbb Q  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 P: \mathbb Q \to \mathbb Q \times \mathbb Q  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.)


  1. Hi, its nice article about media print, we all know media is a great source of information.

    Comment by blog — July 19, 2019 @ 1:27 am | Reply

  2. Estimated Gil Kalai. Exists Collatz Conjecture polymath? How can be created? If I am not a professional, can I participate?I am looking a place to discus about the conjecture and share ideas,but I can not find it.may be I am too much crank but exist a 0.01% possibly that a not professional,with help ,could participate on solving the conjecture.Thanks.

    Comment by Alberto Ibañez — August 16, 2019 @ 9:33 pm | Reply

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