OpenAI, the Partition Principle, and mathematics

By the time I got out of bed yesterday, I had three people ask me if I'd seen the OpenAI announcement that the Partition Principle does not imply the Axiom of Choice. The number kept increasing during the day, and I can see why. I am famously interested in this problem. Indeed, at least two people asked if I plan on sending Sam Altman a bottle of whisky, as promised in my Problems page. The answer to that is no. And let me explain to you why, and why you should be very angry at OpenAI. Continue reading...