In 1904, at the Third International Congress of Mathematicians in Heidelberg, Julius König held a lecture which caused a sensation. In the case his conclusions were correct, they would not coincide with the conviction of G. Cantor, according to which each set could be well ordered. There are two different reports of G. Kowalewski and A. Schoenflies about the lecture, the events and discussions in the following days. For W. Purkert the report of A. Schoenflies seems more trustworthy: The lecture of J. König was one of the key points discussed in a meeting at Wengen some days later. Particularly D. Hilbert, K. Hensel, F. Hausdorff and G. Cantor took part in the discussions. One morning G. Cantor detected, that a proposition of F. Bernstein, on which J. König’s findings were based, could not be correct in general. Still in 1904, F. Hausdorff found an exact proof of F. Bernstein’s error.
The spectacular events are in the centre of the article of W. Purkert. In the first chapter he describes the ideas of G. Cantor concerning the continuum problem and well ordering. In the second chapter the approach of F. Hausdorff to set theory is illustrated. A view about the further developments regarding the continuum hypothesis and well ordering is given in the end.
The controversies and discussions are reflected in contemporary reviews and original texts which can be found in the databases ZMATH or Jahrbuch: Zbl 0037.00203 (G. Kowalewsky), JFM 48.0019.02 (A. Schoenflies), JFM 36.0096.01 (J. König), JFM 36.0097.01 (J. König) JFM 32.0073.02 (F. Bernstein), JFM 35.0089.03 (F. Hausdorff), JFM 36.0097.03 (F. Bernstein).
For the entire collection see [Zbl 1060.01001].