Montesinos Amilibia, José María2023-06-202023-06-2019970214-316Xhttps://hdl.handle.net/20.500.14352/58641Versió catalana del discurs inaugural de l’any acadèmic 1996–1997 a la Real Academia de Ciencias Exactas, Físicas y Naturales.The author describes such things as the Poincaré conjecture, Waldhausen's generalization of it, and the dimension 4 Poincaré conjecture. Then he turns to the finite-infinite and discrete-continuous dichotomies. For the former he gives examples in number theory (the computation of decimal and septimal digits of e and π, and the continued fraction continuants for π) and for the latter he gives examples from combinatorial topology (triangulations and homology) and knot theory (homotopy and Whitehead's example). The paper is a written version of a talk given to a general scientific (in contrast to a general mathematical) audience.frajournal articlehttp://www.raco.cat/index.php/ButlletiSCM/article/view/149235/201136http://publicacions.iec.cat/PopulaFitxa.do?moduleName=revistes_cientifiques&subModuleName=&idColleccio=173restricted access511Teoría de números1205 Teoría de Números