Jacobian conjecture

The Jacobian Conjecture is a mathematical hypothesis concerning polynomial functions. It suggests that if you have a system of polynomial equations that changes variables, specifically if the determinant of the Jacobian matrix (which measures how these variables change) is a constant, then it can be "inverted." In simpler terms, if you can transform your original variables into new ones through these polynomial equations, the conjecture claims you should be able to revert back to the original variables without losing information. Despite its simple formulation, proving or disproving it remains an open challenge in mathematics.