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.
The conjecture 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.
The proof depends on a theorem due to Stanis%C5%82aw %C5%81ojasiewicz.