Want to see the real secrets of set theory in YouTube format?

tl;dr Set theorist Asaf Karagila is looking for YouTubers to collaborate.

My colleague and sometime rival Asaf is a top notch young set theorist who works a lot on pushing the frontier of the method of forcing. At one point we were in competition to construct, without using large cardinal assumptions, the first model of set theory where the axiom WISC failed. Asaf won, but as I was working in a different formalism, I still had the satisfaction of arriving at my own solution. This was right at the start of his academic career, and he’s only gone from strength to strength, recently being awarded a prestigious UK Future Leaders Fellowship.

The upshot is, he included explicitly in his Fellowship application that he would produce outreach videos about set theory, and is looking to collaborate with YouTubers with wide reach to achieve this. As he writes:

“There is a clear lack of good videos addressing set theoretic ideas, which I honestly believe that I can make at least somewhat accessible. And hopefully this will make set theory more accessible to the public, or at the very least, to other people interested in mathematics.”

He has set up a contact email if you are a YouTuber:

At the moment I’ve set up an email address, youtube2020@karagila.org, where you can email me. Let me know about your channel, what kind of content you want to make, etc. I cannot make any promises about money, but I’m always happy to advise with regards to content, should the need ever arise.

And if you are not a YouTuber, but want to see some more nitty gritty about what it is that set theorists do nowadays, point them to Asaf’s blog post! Asaf tells me that Numberphile and Tibees have already made contact, but if you are super keen to support the idea, it would help if viewers promoted the idea.

Now, if YouTubers want to make videos about category theory, on the other hand, then, ahem, I don’t mind having a chat 🙂 But they should talk to Asaf first, I don’t want to intercept his efforts!

5 thoughts on “Want to see the real secrets of set theory in YouTube format?

  1. Is a ‘set theorist’ simply a model theorist who specialises in models of set theories? Because to me it seems the vast majority of modern ‘set theory’ such as forcing methods and testing axiom strength/consistency/independence of set theoretic models such as ZFC and extensions thereof are really model theoretic concepts that could apply to other mathematical theories as well, such as models of type theory or category theory.


    1. Is a “group theorist” simply a model theorist who specialises in models of group theory?

      No. And the same is true about set theorists. Set theorists are mathematicians who are interested in set theory. The techniques in set theory are not model theoretic in nature, not any more than the wreath product of two groups is model theoretic, or that “free group” is a model theoretic construction.

      But unlike other subfields of mathematics, e.g. group theory, in set theory we simply use the term “model of set theory” in a more explicit way.


      1. The objects that group theorists study are groups. The object that ring theorists study are rings. The objects that measure theorists study are sets equipped with a measure. And so on. On the other hand, the objects that most modern set theorists study seem to be models of set theories, especially models and extensions of ZFC, as well as the consistency, strength, and independence of said axioms, rather than actual sets themselves. So the situation between group theory and set theory is different.

        Actually, perhaps a better example against my original point would be string theory from mathematical physics. Modern string theorists, especially with the string landscape and the swampland program, study models of string theory, rather than strings themselves, yet aren’t considered model theorists.


      2. I was under the impression that groups are models of group theory; and rings are models of the theory of rings.

        Also, “model” outside of pure mathematics is not the same as “model” in pure mathematics. In pure mathematics, model usually means a structure satisfying a certain theory. Outside of it, a model is normally some collection of mathematical equations which seem to approximate a certain behaviour, or so. I’m sure someone can find the connection, but it is certainly not immediate and the same.

        You can also make the claim that a model is showing new cloths and designer shoes, but is not a model theorist, that is also true.


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