2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129054In this paper, we complete the proof of an equivalence given by Nye and Singer of the equivalence between calorons (instantons on $S^1\times R^3$) and solutions to Nahm's equations over the circle, both satisfying appropriate boundary conditions. Many of the key ingredients are provided by a third way of encoding the same data which involves twistors and complex geometry.Dedicated to Nigel Hitchin on the occasion of his sixtieth birthdayDifferential Geometry53C07; 53C28text