Lately I have been daydreaming about a mathematical monastery. I don't know how coherent the idea is, and would be curious to hear feedback.

A mathematical monastery is a physical space where people gather to do a particular kind of math. The two main activities taking place in a mathematical monastery are meditative math and meditation about one's relationship to math.

• Meditative math: I think a lot of math that people do happens in a fast-paced and unreflective way. What I mean by this is that people solve a bunch of exercises, and then move on quickly to the next thing. There is a rush to finish the problem set or textbook or course and to progress to the main theorems or a more advanced course or the frontier of knowledge so that one might add to it. I think all of this can be good. But sometimes it's nice to slow way down, to focus on the basics, or pay attention to how one's mind is representing the mathematical object, or pay attention to how one just solved a problem. What associations did my mind make? Can I write down a stream-of-consciousness log of how I solved a problem? Did I get a gut sense of how long a problem would take me, and how reliable was that gut sense? Are the pictures I see in my head the same as the ones you see in yours? How did the first person who figured this out do so, and what was going on in their mind? Or how might someone have discovered this, even if it is not historically accurate? If I make an error while working on a problem, can I do a stack trace on that? How does this problem make me feel? What are the different kinds of boredom one can feel while doing math? All of these questions would get explored in meditative math.
• Mediation about one's relationship to math: Here the idea is to think about questions like: Why am I interested in math? What do I want to get out of it? What meaning does it give to my life? Why do I want to spend marginal time on math (rather than on other things)? If I had a lot more money, or a more satisfying social life, would I still be interested in doing math? How can I get better at math? What even does it mean to get better at math? Like, what are the different senses in which one can be "better at math", and which ones do I care about and why? Why do I like certain pieces of math better than others, and why does someone else like some other piece of math better?

As the links above show, some of this already happens in bits and pieces, in a pretty solitary manner. I think it would be nice if there was a place where it could happen in a more concentrated way and where people could get together and talk about it as they are doing it.

Above I focused on how being at a mathematical monastery differs from regular mathematical practice. But it also differs from being at a monastery. For example, I don't think a strict daily schedule will be an emphasis. I also imagine people would be talking to each other all the time, rather than silently meditating on their own.

Besides monasteries and cults, I think Recurse Center is the closest thing I know about. But my understanding is that Recurse Center has a more self-study/unschooling feel to it, rather than a "let's focus on what our minds and emotions are doing with regard to programming" feel to it.

I don't think there is anything too special about math here. There could probably be a "musical monastery" or "drawing monastery" or "video game design monastery" or whatever. Math just happens to be what I am interested in, and that's the context in which these thoughts came to me.