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.)

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