Online study groups for individual mathematical texts

Question

This has been one of my earlier academic dreams. I have pitched the idea to Prof Ravi Vakil, among others. Recently, because of participation in the mathematical competition hosted by Alibaba, I have decided to revive my decade-old enthusiasm. The basic idea is as follows. Many mathematical texts are difficult to penetrate on one's own, be it due to typos, vagueness, or prerequisite assumptions. Thus it is helpful to study with friends or mentors. People outside of the academic circle, or even graduate students, may find it difficult to meet people with similar interests, let alone reading the same chapter of the same graduate text in mathematics (GTM) book.

Given the success of numerous online Q & A fora, including this one, and the ridiculous level of specialization, it seems plausible that with the right timing, we can now dedicate one group/site to each textbook. Even though it is often advised that one should not read a technical treatise sequentially, there is something satisfying about being able to finish a single math text from cover to cover, that a cursory scan or occasional reference lookup does not conjure. To be honest I have not managed to finish a single book this way during grad school. Note taking on a single text is also a great mnemonic tool in the long term, as I am sure many people still practice.

So my question is simple, are there existing platforms that offer such a service already? I am aware of something tangentially related, such as Fermat's Library. But I don't see a way to expand it into a full-blown book-based service. My recent encounter with Slack suggests that the latter may be a more suitable style than stack exchange, since it encourages multi-threaded conversations around a single topic. The level of specialization there is naturally more fine-grained than MO, down to a specific piece of software for instance. Not all books need to get the same amount of attention, but just having a few books being annotated and Q&A'ed frequently can really facilitate self-paced learning.

Any thoughts or suggestions? Would this be helpful to many students/researchers in math?

Answer 1

This question was asked a long time ago but remains on the unanswered queue, so I will try to answer.

The OP correctly identifies that the biggest obstacle to a community working through a book together is timing. Historically, the best way to generate such a community and keep it running on the same timetable is to organize a seminar. Nowadays that can also be an electronic seminar, and there are plenty of examples of successful electronic seminars:

https://s.wayne.edu/echt/echt-reading-seminars/echt-kan-seminar-fall-2023/

https://www.math.uwo.ca/faculty/kapulkin/seminars/hottest.html

https://researchseminars.org/seminar/eCHT

The Kan seminar is famous: homotopy theorists in Boston would work through the classic results the field builds on, each person reading in depth, and one person (rotating) presenting the results of the week and answering questions on those results from the group. I've also organized a number of seminars and reading groups at my university where a bunch of professors got together to work through a book and internalize its content.

Slack is a relatively new innovation, and is not really necessary for this functionality. The point of slack is to get someone's immediate attention. Many academics prefer not to allow their attention to be grabbed so easily. I had a co-author once who communicated with me via slack and I feel somewhat traumatized by that (I have a physiological reaction to the Slack three-tap "knock brush" sound, as it meant I had to drop everything to work on something urgent in the moment whenever I heard the sound). Much better than Slack, for academics, is a Trello board. With Trello, whenever you have something you don't understand, you can put a post-it note about that up on the board. And others can answer it in their own time, or can prepare an answer to give you at the seminar meeting. In theory a MathOverflow-esque site could be used for such a Q & A interface, or MO chat, but the comments make it clear that in practice this hasn't worked very well. It's important to keep the size of the group manageable and make sure everyone is invested.