The value \(\sqrt{2+\sqrt{2}}\) of the connective constant on the hexagonal lattice has been derived non rigorously by B. Nienhuis in 1982, using Coulomb gas approach from theoretical physics. We will discuss the first mathematical proof given by Hugo Duminil-Copin and Stanislav Smirnov that the connective constant of self-avoiding walk on the hexagonal lattice is equal to \(\sqrt{2+\sqrt{2}}\).