I gave the talk “A unified view towards diagonal arguments” at Archimedeans yesterday and the transcript is now available here.

The talk is on Lawvere fixed point theorem, beginning with cartesian closed categories, proceeding to state and prove the theorem in that context (although in the version I delivered most formal treatment of categories was skipped for brevity and better intuition), and going on to give classical applications, culminating in Gödel incompleteness theorem.

As I said in the acknowledgement, I want to thank Archimedeans for organising this event, which I found a great way to know what my friends on the other side are doing in their own time. I am also extremely grateful to those who have, in one way or another, helped me in the preparation, delivery and feedback of the talk.

Finally I would like to wrap up with a feedback I got from a friend, who asked me if I had some kind of superpower IA mathmo in mind when I was writing prerequisite for the talk. Yes and no: you are an extremely strong IA mathmo if you went to the talk and understood everything on the spot. But even if you did not, there is some part of the talk (I hope) that makes sense to you, and more importantly, I hope this has made a dent somewhere in your repertoire of maths knowledge so that later on when you learned, for example, Gödel incompleteness theorem along the way, the idea will click with you. Perhaps with no coincidence, this is also the opinion I had towards category theory: learn it formally at some point and let time sink in.

So long!