pnin

Please don't pretend that you've somehow been deceived. Hasn't everyone heard quips like "theoretical physics is like sex: it has some useful results, but that's not why we do it"? How hard is it to understand that doing something is what gives pleasure, rather than the outcome?

Mathematicians (mostly) accepted that the proof was valid, not that it was the kind of thing mathematics should strive for.

The senior title comes first -- Prof. Dr. Dr. Honorary doctorates are "honoris causa", abbreviated h.c. If you get multiple of these, you write Dr. h.c. mult. So you occasionally find Prof Dr. Dr. h.c. mult. X (would have been the correct way to address Umberto Eco, for instance). After introductions, people generally name only the most senior title, if any.

Thanks for the data.

As far as I can tell, o1 is the best model for anything to do with mathematics, by a solid margin.

Please read it again, carefully. Hamkin is not trying to convince anyone of accepting CH.

I think it's a bit like PG Wodehouse. The world of Bertie Wooster or Clarence Threepwood, 9th Earl of Emsworth is certainly an idyll; at the same time no one would pretend it is a classless idyll.

Tolkien would not refer to that class structure as "economic exploitation" - that is part of his politics. That does not mean he did not understand that society very well, and seek to portray it in an idealized form.

Since you provide a zoological metaphor, let me offer an alternative. Category theory is much more like Goethe's work on the /Urpflanze/ (primeval plant). Linné had developed a way of systematically naming species of plants, but Goethe was not satisfied by this approach.

Goethe wanted to find an underlying pattern common to all plants which would explain how plants grow and develop. Something like a "universal grammar" (to draw an anachronistic parallel to Chomsky) of plants. Goethe called this his "morphological" method and wrote about it in "On the metamorphosis of plants".

One caveat: this paints a slightly too esoteric picture of category theory. Goethe was very idiosyncratic as a scientist, whereas category theory, far from being esoteric, is a common language for all of modern mathematics.

I think if you use gears, it would be well to know some Newtonian mechanics. The material structure might not be relevant, but in mathematics you also don't need to go down to the foundational level for every problem. You don't need to go deep into set theory to understand the proofs in calculus (though it is true that Cantor's investigations into set theory started from the question of convergence of certain infinite series, which is a calculus problem).

Henry Green, Graham Greene, Julian Maclaren-Ross, Anthony Powell.

But the review is from just a week after the atomic bombing of Nagasaki, so Orwell is referring to wartime fiction rather than postwar fiction.