2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67230If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are not Turing-computable.v2; introduced standardised ACI compliant notation for citations; 13 pages; an HTML version is available at http://alixcomsi.com/Can_Turing_machines.htmGeneral Mathematics03B10text