So here it is: *The elementary construction of formal anafunctors*, arXiv:1808.04552.

For amusement, two of the new diagrams…

Now I need to write the cospans paper…

]]>…. it makes so much more sense written like this! Why have I never been shown this before?? Link to thread:

]]>It turns out that for special parameter values the third Painlevé transcendant, namely

has an absolutely elementary solution. I really wanted to track this down to its source, and ended up finding this:

To verify is a solution to the given case of Painlevé III above requires no clever tricks, no special knowledge. So I tried to make this a question in my (online, open-book, do-at-home) exam…

It turns out that, at least the way I tried to do it, Wolfram Alpha and Symbolab can’t solve Painlevé transcendents

]]>See the Xy-pic home page for package details.

]]>A new class of philosophically-minded mathematician that I just learned from the logician Paul Levy: *smallist*.*CH is a statement of third-order arithmetic. It doesn’t quantify over the universe of sets. GCH, on the other hand, does. For smallists, who take a platonic view of PPN (powerset of powerset of the naturals) but not of the universe of sets, this is a big difference.* (http://www.cs.nyu.edu/pipermail/fom/2016-October/020149.html)

I guess it means a mathematician who doesn’t necessarily want in their axiomatic system arbitrary powersets, rather just the few that are needed for ‘ordinary’ mathematics (say up to PPPN, which is plenty to deal with differential geometry, differential equations, functional analysis, number theory, algebraic geometry over number fields or rings of integers therein etc). I think he just invented the word but I like it. For a categorically-minded person like me, this means I could work in a pretopos with just a few powersets posited.

(Originally posted to Google+ on **11 November 2016**)

But most importantly,

They pull bacc.

]]>]]>…my hope is to show that the class of cochain theories is connected, assuming one exists, and then exhibit one. This may well be singular cohomology, or it might be something else. In particular I want to remove from the proof of uniqueness the privileged position that any one construction has. The only caveat is that I won’t be able to use any super-sophisticated machinery as this is a first course in algebraic topology. I’m happy to have an outline of how to unwind a sophisticated proof.

More excitingly, I aim to stream the lectures on Twitch. I haven’t set all this up yet, but I will hopefully be practicing streaming some of my own work process, maybe even developing some of the course notes, before January.

]]>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!