On the Problems of Topology
Samuel Eilenberg · Annals of Mathematics · 1949
In December 1946, as part of the Bicentennial Celebration of Princeton University, a conference was held on Problems of Mathematics. The participants of the Topology Session of this Conference have submitted a large number of unsolved problems, and it is the purpose of this article to present these problems to the mathematical public. In order to make the presentation more understandable and palatable it is necessary to include a birds-eye view of some of the trends of present day Topology. An effort is made to include opinions expressed during the Session and in the subsequent informal discussions. Very little effort towards objectivity has been made in writing this report; in a field that moves as rapidly and in as many directions as Topology today, it is impossible to remain an impartial observer. The classical unsolved problems in Topology (e.g. the Hauptvermutung, Poincares hypothesis, triangulability of manifolds, Dehn's lemma) have not been restated.