Montesinos Amilibia, José María2023-06-202023-06-201996https://hdl.handle.net/20.500.14352/61115The 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.spaconference paperhttp://www.rac.es/ficheros/Discursos/DI_20080825_069.pdfhttp://www.rac.es/0/0_1.phprestricted access511Number theoryTeoría de números1205 Teoría de Números