# {01.} \begin{blog}

proposition: a new blog

Not too long ago, I finished my application to be a blogger for MIT, and one of the questions stated: “What is an online/networked community you feel like you belong to, have responsibility for, and/or admire?”. To this question, I said:

I feel like I belong in the math twitter community. I started out small by getting into MITwitter (I hate the name Mitter). It was nice to see nerds being nerds, from licking space rocks to starting a job at NASA. Then, I found an even smaller niche in the math community. Now every Sunday I post the obligatory #MathCoffeeSelfie, and I have amazing conversations with college professors about the pedagogy behind motivating differential equations courses.And because of Math Twitter, I even decided to start a math blog (by which I mean, the URL exists and I got WordPress to stop being a pain in the ass). I love talking to people who simply want to communicate/discuss mathematics, and I want to be able to contribute to that in some non-empty way. I feel some responsibility to the community. If nothing else, I admire it and want to see it thrive, which is more than nothing in a purely online space.Recently I’ve been trying to figure out what I want to do with my life after college (whether that be continuing to explore being a professor or deciding to be more ad hoc and become a mathematics communicator), and I don’t know which I fully want yet. But for now, I can write on a silly little blog with a silly little name, and maybe give something back to the community that inspired this existential/career crisis. I belong here, and I hope by existing on math twitter, others might feel like they belong there too, which is more than nothing in a pure online space.

I meant this: I am creating a math blog. I’ve been thinking about this for nearly four years after watching 3B1B’s video on Pythagorean triples1, and I was able to create a proof of this visualization on my own using trigonometry (which I had just learned that semester). At that age I didn’t believe that my thoughts on math should be read– after all I was still a high schooler and I would’ve hated the thought of putting out work like this then. But I do think there is a usefulness to there being more expository-like writing on mathematics out in the world, trying to answer the questions:

What are mathematicians even researching?
What questions do math people like to think about?
and What culture exists/should exist in math communities?

I don’t think I alone have amazing questions for this. After all, I am still an undergraduate. But I don’t hate the thought of putting my work out like this. And I have friends, colleagues, and math twitter to whom I might talk to about certain blogs, or try interviews with people of different backgrounds. Whatever happens, I will be happy if I just Try to create something in this community.

So, what do I want to create?

One of my initial inspirations to create this blog was Numberphile. I loved how different mathematicians get to just talk about mathematics they are interested in, in a way that is accessible to more of the public (and gets people excited about math!). But sometimes I am left wanting more— something to read about to learn more in-depth, or even just another 30 minutes of some examples or proofs. Now I don’t think Numberphile should change at all– not in the slightest. There are reasons they do what they do, and they still manage to discuss insanely difficult topics2. However, this did help me figure out one of the main principles I want to keep in mind when writing this blog:

1) Write out some more of the details– some more of the mathematics. Furthermore, write what expectations I’m assuming when going into a post.

For instance, if I am going to write about understanding Abstract Algebra a bit better through studying matrices, I might write that “In this post I am assuming some familiarity with linear algebra/matrices.” I don’t want to go Out of my way to be mathematically egregious– I won’t simply write abstract non-sense and hope it makes sense. But I also can’t start from the theory of real numbers every time I want to use $\pi$ in a post.

In preparing to start this blog up, I’ve also figured out how to use LaTeX in WordPress. Unfortunately, it costs nearly 300$to use some of the better packages for LaTeX here (requiring the business plan), so for the time being I’m going to make due with the tools I have. That being said, while I hope I can keep most of this as a blog format, some parts of the math can be simply annoying or straight up impossible to write down. Which leads me to my next two principles: 2) Don’t just post a PDF of a LaTeX file in a post and call it a day– at least try to make the WordPress code work for you. 3) Sometimes, write LaTeX files for the blog! 3) isn’t meant to contradict 2), what I mean here is that sometimes on more expository pieces, or ones that have a lot of notation that can be annoying to view in this format, I might write the post in LaTeX and attach it at the end. If I do so, I will try to remember to post near the top that it has been put into a PDF with a hyperlink to that section of the post. I note here that this style of writing was/is inspired by CJ Quines’s own expository writing on math3, as well as Lydia Krasilnikova’s blogpost on Hilbert’s Third Problem. For now, I think I’m going to stop at these three rules and try to follow them as closely as I can. If necessary I may write a new blog discussing adding new principles to the mix, or writing experiments I want to try for this math blog. I really look forward to seeing how this new blog concept goes! OH and: 4) Start every blog with an axiom/proposition/lemma/etc type statement, like what might be in a textbook/paper. I really love the practice of starting with a tldr on all of my personal blogs, so this is what I plan to do for math ones. Final obligatory note (that I will likely write down in the future when necessary): While I may be interviewing other mathematicians or writing about certain papers/books I have read through for the writing, I claim responsibility for mistakes in the mathematics that I may have misinterpreted/misunderstood from papers, discussions, etc.. If you find any of these, as always please feel free to comment them or reach out to me and I will fix it as soon as possible, as well as note at the bottom of the post that it has been edited/what the edit was. Currently, the next few posts I have lined up/planned/want to do are: • 0. Zero-Indexing: A discussion on why the question of whether 0 is or isn’t a natural number. • 01. An ODE to Algebra: An expository piece in which I try to understand linear differential equations better through more algebraic techniques (like linear algebra). • ??. Algebra –> Analysis (not actual name): Some ways algebra gives a better understanding of some formulas/concepts in analysis, for instance, Cauchy’s integral formula in complex analysis and cotangent spaces. • ??. Analysis –> Algebra (not actual name): Some ways analysis gives a better understanding of some formulas/concepts in algebra, for instance, the fundamental theorem of algebra and algebraic varieties. • ??. Categories (not actual name): In which I begrudgingly accept that some parts of Category seem cool (and useful to me) and I want to learn more about that. (I mostly list these here so I have Extra motivation to Do them at some point.) ## References 1. 3Blue1Brown, All possible pythagorean triples, visualized 2. See their videos on the Navier-Stokes equation or darts in higher dimensions, for instance. 3. Some of my favorites include his post on the Umbral Calculus and the one on Incidence Matrices (which was very useful last year as I tried to understand some small parts of incidence theory). ## Published by Paige Bright Hi- my name is Paige Alexandria Bright. I am a rising junior at MIT interested in mathematics and philosophy. I have been writing this blog since the beginning of COVID. Lets see where this goes. ## 2 thoughts on “{01.} \begin{blog}” 1. even smaller niche in the math community » is math twitter really smaller than mitter? more expository-like writing on mathematics » have you read The Mathematical Experience? it costs nearly 300$ to use some of the better packages for LaTeX here (requiring the business plan) » yeah wordpress the service (https://wordpress.com/) is a business, wordpress the software (https://wordpress.org/) is open-source

CJ Quines’s own expository writing on math » omg i got a shoutout im so FAMOUS

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1. Smaller>> oh definitely not that was a mistake on my end I meant moreso it started out way smaller for me since I was in the intersection of math twitter and MITwitter

The Mathematical Experience>> I haven’t! I need to Read more and this seems like a good starting place

Software>> hmm I wish I knew more about this getting into WordPress/blogging but also I think I would Struggle with the open-ness of open source. But I’m glad there are Similar/better options that are less costly

FAMOUS>> oh absolutely you’re famous now xD

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