L’idée de dimension -- Topologie und Algebra -- Complex-analytic manifolds -- Homotopie et dualité -- Groupes d’homotopie et dualité -- Homotopy and cohomology theory -- Simple homotopy type and categories of fractions -- Some recent developments in the homology theory of groups -- Poincaré duality groups of dimension two are surface groups -- Continuous solutions of linear equations — An old problem, its history, and its solution -- Mathematics: Questions and Answers -- Hurwitz-Radon matrices revisited: From effective solution of the Hurwitz matrix equations to Bott periodicity -- Birth of fibre spaces, and homotopy -- 4-Manifolds, group invariants, and ? 2-Betti numbers -- The Euler characteristic — a few highlights in its long history -- Topology, algebra, analysis — relations and missing links -- to ?2-methods in topology: Reduced ?2-homology, harmonic chains, ?2-Betti numbers -- Die Zukunft der Mathematik Ein Rückblick auf Hilberts programmatischen Vortrag vor 100 Jahren -- Kolmogorov and contemporary mathematics -- Is algebraic topology a respectable field? -- Social choice and topology. A case of pure and applied mathematics.