Drinfeld-Kohno theorem relates the monodromy of KZ equation to the braid group action on a tensor product of $U_q(\mathfrak{g})$-modules by R-matrices. The KZ equation depends on the parameter $\kappa$ such that $q=\exp(\frac{\pi i}{\kappa})$. We describe the limit Drinfeld-Kohno correspondence when $\kappa\to 0$ along the imaginary line. On the KZ side this limit is the Gaudin integrable magnet chain while on the quantum group side the limit is a $\mathfrak{g}$-crystal. Namely, we construct a bijection between the set of solutions of the algebraic Bethe ansatz for the Gaudin model and the corresponding $\mathfrak{g}$-crystal, which preserves the natural cactus group action on these sets. This can be regarded as the $\kappa\to 0$ limit of the Drinfeld-Kohno theorem. If time allows I will also dicuss some conjectural generalizations of this result relating it to works of Losev and Bonnafe on cacti and Kazhdan-Lusztig cells.