*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 triples^{1}, 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 topics*^{2}. 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 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 math^{3}, 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

- 3Blue1Brown,
*All possible pythagorean triples, visualized* - See their videos on the Navier-Stokes equation or darts in higher dimensions, for instance.
- 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).

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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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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