2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166704We prove two conjectures of C. Gordon. We show that the maximal number of exceptional Dehn surgeries on a 1-cusped hyperbolic 3-manifold is 10, and that the maximal intersection number between exceptional slopes is 8. The proof uses a combination of new geometric techniques and a rigorous computer-assisted calculation.33 pages, 10 figuresGeometric Topology57N10; 57M50text