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.)

### Like this:

Like Loading...

*Related*

The status of the project is recorded here: https://terrytao.wordpress.com/2019/06/08/ruling-out-polynomial-bijections-over-the-rationals-via-bombieri-lang/#comment-518118

Comment by Gil Kalai — July 5, 2019 @ 5:40 am |

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 |

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 |