2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123165We give a short proof of the fundamental result that the critical probability for bond percolation in the planar square lattice is equal to 1/2. The lower bound was proved by Harris, who showed in 1960 that percolation does not occur at $p=1/2$. The other, more difficult, bound was proved by Kesten, who showed in 1980 that percolation does occur for any $p>1/2$.17 pages, 9 figures; typos corrected. To appear in the Bulletin of the London Mathematical SocietyProbabilityCombinatorics60K35; 82B43text