I've sometimes wondered about creating a collective for math PhD students, partly for support, partly to practice writing and explaining. The problem is that wr

I've sometimes wondered about creating a collective for math PhD students, partly for support, partly to practice writing and explaining. The problem is that writing for non-specialist peers is significantly different from writing for journals, and different again from the kind of writing needed for the PhD. Part of the attitude in PhD thesis writing is the "This is worth a PhD", whereas when you are writing for non-specialist peers you are trying to explain and be understood. There is a difference. I failed my PhD first time round because I didn't understand the nuances. Note: The above is more concerned with the thesis structure than it is with the definition/theorem/proof content. I'd expect the HN crowd to get all snitty about "gate-keeping" and similar "concerns", but you need to work within the system that exists, and the system is as it is for reasons. Having said all that, practising your writing is essential, earlier than you think, and oftener than you think. My contact details can be found in my profile if you're interested in talking more about this. I would ping you directly, but your contact details are absent from your profile.