This blog will have manifold uses, so the format will not be consistent by any measure.
Part of the use of this blog will be to post notes from classes as well as homework solutions. In that instance I will mostly post PDFs of handwritten (on OneNote) notes every day of class to the “hot takes” section, which (as the Wikipedia page for hot takes states) will be “usually written on tight deadlines with little research or reporting, and even less thought.” Ideally I will then flesh those out weekly into more full and typed up (i.e LaTeXed) notes and solutions.
The blog posts outside of the class notes genre will have more varied format (and the rough drafts of those will often be posted to “hot takes” as well). Ideally a lot of the time they will follow the following format, so as to avoid going down the mathematical rabbit hole:
"Motivating Example Definitions Lemmas and Theorems Applications"
Nevertheless, when the subject matter or happenstance encourages deviation from that format, then I will write those posts otherwise.
The purpose of this blog (which is a dangerous thing to philosophize about before having actually done anything with it) is mostly to have a repository of things I have learned, and to have an outlet which lets me flesh out a lot ideas in the way that writing can only facilitate. It has a secondary purpose, also, to encourage me to overcome, as David Foster Wallace calls it, the “tragedy of perfectionism” meaning letting me sacrifice how perfect an idea is in my mind to how imperfect it must be when I try to write it materially (perfectionism is a tragedy because it is only in sacrificing that mental perfection that a work can ever really come to be).
Although these will not take the form of epistles to myself, I will (again quoting DFW) be writing as if speaking to someone who is suspiciously like myself. Ideally this will make this project useful to me, and if I ever condescend my readers, it is because I myself am too dense, and not because I underestimate my currently non-existent readership.