Celebratio Mathematica — Freedman

Topology in dImension 4

Works connected to Felix E. Browder

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incollection M. H. Freedman: “Working and playing with the 2-disk,” pp. 37–47 in Mathematics into the twenty-first century: Proceedings of the 1988 Centennial Symposium (Providence, RI, August 8–12, 1988). Edited by F. E. Browder. American Mathematical Society Centennial Publications II. American Mathematical Society (Providence, RI), 1992. MR 1184613 Zbl 0924.57026

This article is simply a written lecture and what philosophy it contains should not necessarily be taken seriously. However, it is much easier to learn a whole story than a single theorem, so many of the latter are woven into the former. Our hero, for fun, is the two-dimensional disk which seems to intrude at many important junctures of geometric topology. Also, there is the theme that ideas of great importance can be enormously simple. As the Centennial recalls to each of us our small mortal places and seems to threaten even mathematics with a certain loss of youth — computer proofs, proofs too long to write (or think), the joint power and vacuity of abstraction — I enjoy recalling a few forceful but simple ideas in the subject I know best. I have no prediction for the next century but am content to express the hope that mathematics will still, from time to time, be extraordinarily easy — that the last simple idea is still far off.