The proof by Harnack is in Mathematische Annalen 25 (1885) pp. 241 - 250. It can indeed be viewed as a measure theory proof that the reals are uncountable, but Harnack misunderstood what he had proved. For a discussion of Harnack's mistake, see David Bressoud's A Radical Approach To Lebesgue's Theory of Integration, p. 63.

A less technical version by Robson may be viewed at jmhammond.github.io/history/Robson2002.pdf

Indeed, MacLane said so himself, on p. 17 of Categories for the Working Mathematician: 'As Eilenberg-Mac Lane first observed, "category" has been defined in order to define “functor” and “functor” has been defined in order to define "natural transformation" .'

There is a more recent (2022) annotated version of Gödel's paper: The Annotated Gödel, by Hal Prince.

I think the expression is "cylinder seal" rather than "seal cylinder"; see en.wikipedia.org/wiki/Cylinder_seal

@TimothyChow There is a painting by Tintoretto, "Triumph of Venice," which IMHO looks like a view of the 3-sphere with earth and Venice at opposite poles. (It is on Wikimedia but I can't seem to paste the URL correctly.)