2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80167The Neumann system on the 2-dimensional sphere is used as a tool to convey some ideas on the bi-Hamiltonian point of view on separation of variables. It is shown that, from this standpoint, its separation coordinates and its integrals of motion can be found in a systematic way.LaTeX file, 12 pages. Talk given at the NEEDS2001 ConferenceExactly Solvable and Integrable SystemsMathematical Physicstext