Gradient conjecture
In mathematics, the gradient conjecture, due to René Thom, was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka, Tadeusz Mostowski and Adam Parusiński. It states that given a real-valued analytic function f defined on Rn and a trajectory x of the gradient vector field of f having a limit point x0 ∈ Rn, where f has an isolated critical point at x0, there exists a limit for the secant lines from x to x0, as t tends to zero.
