by Dru Alexander Horne, Mathematics

Most people would see writing and mathematics as diametrically opposed, but I see them as two sides of the same coin. I’ve been doing both of them for most of my life: honing the fundamentals, learning new techniques, and exploring new directions. After all, both mathematics and writing are about capturing and explaining the world in a way that can be communicated to others.

I find writing similar to solving a good math problem. You spend a lot of time figuring out how to get started and thinking about different ways to approach the problem. Occasionally, one approach seems more promising, so you continue down that path until you hit a roadblock. You then zoom back out, revisit some of your previous ideas, and try to brainstorm new ones. Over time, you amass a collection of symbols, ideas, and direction until eventually you find a solution. At which point, you begin thinking about how to communicate your solution. Writing has the same process. You begin with your initial thoughts and ideas and slowly turn them into sentences and paragraphs. Occasionally, you’re at a loss for words, so you revisit what you’ve already written and revisit your outline for inspiration. Sometimes this is sufficient to make progress and other times, you realize the structure isn’t quite working and it needs to be tweaked. Eventually with enough time and effort, you’ve amassed a collection of words, sentences, and paragraphs and have a complete first draft. At this point, you begin thinking about how to best communicate what you’ve written. See mathematics and writing have basically the same process!

Once you have a mathematical solution or a complete first draft, what happens then? With the first draft, it’s time to edit, and with the mathematical solution, it’s time to write it up. How do you do this? Believe it or not, for both things, you can ask yourself the same set of questions! Do the ideas fit together logically? Can I follow the structure of the argument? Is the argument concise and succinct? Are the words (or symbols) chosen unambiguous? Are there any (mathematical or grammatical) errors? Who is the audience? Armed with these questions, you begin editing and editing. Slowly polishing your ideas until they are intelligible and understandable by someone else.

In the editing phase for mathematics and for writing is where I find myself doing most of my thinking and understanding. Sure, I’ve had to think to solve the problem or create a first draft, but that thinking is minimal compared to editing. It’s in the grappling with ideas to make them understandable that I am able to step back and see the bigger picture. It’s in the wrangling of words and mathematical symbols to share my thinking that I’m forced to clearly explain my inner thoughts. It’s in trying to communicate that I need to untangle my own thoughts and put them in a reasonable order. It’s the act of editing my writing and my mathematics that I come to better understand and make sense of the world around me.

I write because I do mathematics, and I do mathematics because I write.

I don’t do math or write because I want to but rather, I need to. I am driven by my own experiences of the world. I am driven by a curiosity to understand the world. I am driven to share my insights of the world. I need to do mathematics and to write in order to share all of the awe-inspiring aspects of the world. I write because I do mathematics, and I do mathematics because I write. After all, writing and mathematics are just two sides of the same coin.