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John Baez (May 14 2020 at 20:41): John Baez (May 14 2020 at 20:43):So, you spent the academic year 1963-64 as an assistant professor at Reed College.
At Reed I was instructed that the first year of calculus should concentrate on foundations, formulas there being taught in the second year. Therefore, in spite of already having decided that the category of categories is the appropriate framework for mathematics in general, I spent several preparatory weeks trying to devise a calculus course based on Zermelo-Fraenkel set theory. However, a sober assessment showed that there are far too many layers of definitions, concealing differentiation and integration from the cumulative hierarchy, to be able to get through those layers in a year. The category structure of Cantor's structureless sets seemed both simpler and closer. Thus, the Elementary Theory of the Category of Sets arose from a purely practical educational need, in a sort of experience that Saunders also noted: the need to explain daily for students is often the source of new mathematical
discoveries.
John Baez (May 14 2020 at 20:44):No details on how the students reacted to this.
Morgan Rogers (he/him) (May 15 2020 at 15:52):I honestly wish I had been taught some categorical foundations during my undergrad; it's not like they could be any dryer than ZF foundations!