By Ulla-Maija Kulonen
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2 Technical interests and applied mathematics There are numerous documents evidencing Zermelo’s involvement with technical problems during his time in Göttingen and in Zurich. The same is also true for Freiburg. He became interested there in monorail trains and steam and gas turbines. In March 1931 he submitted an—unsuccessful—application to the national German Patent Oﬃce, asking for a patent on a construction which used a gyroscope to stabilize bicycles and motorcycles during a stop, at the same time providing energy for a new start.
5 Defence of the well-ordering theorem In May 1905, during his spring cure in Italy, Zermelo was working on the theory of ﬁnite sets. In June he observed that Richard Dedekind’s theorem 160 from the Zahlen treatise Dedekind 1888 can be elegantly proved by use of the well-ordering theorem. , not equivalent to a proper subset. For the direction from right to left he makes tacit use of the axiom of choice. Zermelo notes that the argument becomes trivial if one starts with a well-ordered Dedekind ﬁnite set.
Thus he was fully integrated into the teaching programme of the Mathematical Institute to an extent quite unusual for an unpaid honorary professor. ” The appointment to the honorary professorship coincides with a remarkable increase in Zermelo’s scientiﬁc activity. It launched his second period of intensive research, about twenty years after his time in Göttingen. One might therefore be tempted to view the professorship as a stimulant. On the other hand, his improved health might also be taken into consideration.