I’m still hoping to get a new version of Introducing Category Theory out in January. I want to rewrite the chapter on power objects which is a bit dense, and also carefully read through Part II once more for reader-friendliness: but changes should be minor. Meanwhile, I have more substantially revised what was the short last chapter on the Elementary Theory of the Category of Sets – it is now two short chapters. The somewhat deflationary message, however, remains much the same. You can download a draft of the new chapters here, and needless to say, comments are most welcome as always.

I used to contribute quite often to MSE (math.stackexchange.com), mostly responding to relatively elementary logic questions, of the kind worth answering if you can give hints as how to find a natural deduction proof, clear up a confusion about Gödelian incompleteness, explain a sticky passage in a well-regarded text book, etc. (At any rate, that’s a harmless enough way of procrastinating on the internet!)

But the number of such elementary questions seems to have plummeted over the last two or three years. Why so? I bet it is because students have found ChatGPT and the like seem to give them what they want. After all, if ChatGPT (or an alternative) has become the first port of call for so many students for help with coursework of one kind or another, then surely we’ll expect it to have become the first port of call for answering many of the more elementary kinds of question we used to encounter more at MSE.

It is of course quite another matter whether the answers provided by such AI tools will be reliable. (Just yesterday, as an experiment, I asked both ChatGPT and Claude the same question, whether there was a second-order quasi-categorical version of first-order ETCS. One confidently said yes, and “explained” why so at some length: the other confidently said no, and “explained” why so at equal length. You pays your money and you makes your choice …)

For the moment, MSE still gets a decent number of interesting, more advanced questions. But if the number of sensible but elementary questions there continues to decline, the rationale for having a resource separate from the higher-level MO (mathoverflow.net) will begin to fall away.

Two wonderful concerts this week. At Kettle’s Yard in Cambridge, Cordelia Williams played, inter alia, late Beethoven, the Six Bagatelles, Op. 126. This isn’t music I know at all well, but I was much impressed. But for me the high point of the evening was a performance of Schubert’s D. 959. I have never heard the nervous breakdown of the middle section of the Andantino played with such intensity. (Kettle’s Yard — a tiled floor, bare walls — has a harsh acoustic for a piano recital: I can’t wait to Cordelia Williams to make, as she surely plans, a CD including D. 959 in a more sympathetic acoustic, to follow up her extraordinarily fine recording of D. 958.)

A couple of days earlier, more late Beethoven, this time from Elisabeth Brauss at Wigmore Hall. She began by playing — almost as one continues piece — a selection (mixing the dramatic with the poetic) of Grieg’s Lyric Pieces, imaginatively interwoven with four short pieces from Hans Abrahamsen’s Ten Studies. Then, after the Interval, and following Liszt’s Variationen über das Motiv von Bach S180, we had a truly fine performance of Beethoven’s penultimate sonata, Op. 110. The concert was video recorded and I was about to give you the link (and say, Watch This!) only to find that it has been taken offline after three days. I do very much hope this isn’t because Elisabeth wasn’t happy with some element of her performance — her audience as always was so very warmly appreciative of her playing, and she ended wreathed in smiles as she took her prolonged applause. Fortunately, I had already downloaded the recording …