first!
starting a math blog associated to this website!
wait why are you doing this
Two main reasons:
- I have an on/off relationship with structured writing and I’ve wanted to start keeping a blog again for some time
- I really enjoy reading various blogs about things I like (math included) and I hope I can make my own!
Other than the fact that it’s fun, though, I think there are good practical reasons for maintaining a personal math blog:
Sharing math regularly
Most math I’ve written up for a class, if not notes, usually justs consists of problem set writeups. Problem set writeups are nice to be good at but are not really an ideal medium/mode for communicating mathematical ideas. Maybe yours are better than mine, but mine are often unpolished and do just enough work to convince someone with experience that I know what I’m doing. They’re not really meant for full, detailed explanations, nor are they written in a nice pedagogical way.
Also, I think the reason I was drawn to doing talks at my undergraduate math club is because I often prepare for them by doing a lot of expository mathematical writing for the flow/topic I chose. I really like doing this because it forces me to disassemble and reassemble my knowledge into a thread that is digestible by a live audience. It also forces me to develop intuition for a given idea instead of just relying on rigorous definitions for it, which is good in general but difficult to communicate quickly, as I’ve found.
Speaking of which:
Drafts for things
As mentioned, since I often do expository writing in advance of a talk I’m preparing to give, it should go the other way around as well - writing a bunch of expository mathematics should be useful for giving expository talks! I don’t think I expect to give any in the near future, but it’s nice to build a bank of potential talks over time. Also, If I happen to write about something related to research I happen to work on, this will also help with being able to write an introduction/background section for the corresponding paper quickly, or help with preparing the corresponding section for a research talk.
However, I don’t think I want to put pressure on myself to make these blog posts the most polished things in the world. I’m not going to go out of my way to not spread misinformation on the internet, but I will make a good-faith effort to try and be as correct as possible while also being concise. Notably, in blogs that I enjoy reading, I really appreciate detailed writing that avoids being dense, and I’d like to practice this in my own writing.
Space for ideas/details
In math classes, one of the many clichés is to leave details as an “exercise for the reader.” Sometimes I appreciate this if it’s in a topic that I don’t have a ton of investment in, but sometimes I really do want to understand some of the gory details of why something works! Some of my planned ideas for things to write about involve doing deep-dives into specific fun but complicated pieces of math, and I hope this gives me an excuse to learn about them (and also a space to complain about bringing on my own suffering).
I’d also like to provide novel takes on topics/ideas that may not be part of the most prominent lines of thought. I think it’s nice to have alternate perspectives available on a subject, and I hope this can contribute to providing some of those perspectives for other people.
goal-setting
As a graduate student, keeping a personal blog is obviously the most important thing I should be doing with my time. Here are the (hopefully realistic) goals I’m setting for myself so that I don’t go/feel the need to go too overboard and to make this sustainable:
- Every quarter, produce at least 5-17 minutes worth of expository mathematical writing for the blog. Perhaps adjust over time, but no specific length requirement per post as long as it feels substantive.
- Every academic year, produce enough content that can be assembled into a typical-length talk (34 to 51 minutes, perhaps).
Hopefully this is the beginning of a healthy, sustainable writing hobby!