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When the Association of German Scientists and Physicians last met in Düsseldorf exactly twenty-eight years ago on September 24, a debate took place following lectures by Felix Klein and Alfred Pringsheim on roughly the same topic to which I would like to direct your attention today. The printed report of the Düsseldorf debate only remarked that, “It is not possible to go into details here,” so one can only guess how two of the most powerful teacher personalities among German mathematicians of that time had confronted one another with their diametrically opposed views on this topic and how they did so with their characteristically lively spirit. [ABSTRACT FROM PUBLISHER]