As is its wont, the end of December has me reflecting on what I have done during the past year. I wrote a lot of posts here on Roots of Unity, but I noticed that my favorites fell into a few categories.

Favorite spaces

Back in March, I started a new series on the blog: a few of my favorite spaces. It started as a way to revisit some classic examples in my topology class, but I’ve branched out a little, and I hope to branch out more in the next year. My favorite post from that series is probably the one about Cantor’s leaky tent, if only because I loved sharing my impressive illustration skills, but the house with two rooms led me to discover a cool video made in Minecraft by a former colleague’s kid, so it is a close runner-up.

Pretty things
It is a well-known fact that pretty things are pretty. Pretty mathematical things are pretty and mathematical. This year, I especially enjoyed writing about Emily Grosholz's mathematical poetryBob Bosch’s optimization art and Malin Christersson’s hyperbolic tiling tool

What it feels like to be a mathematician

Mathematics makes people feel things, and some of my favorite posts were about those feelings. I really enjoyed reading correspondence between Carl Friedrich Gauss and Sophie Germain and seeing how Johann Heinrich Lambert got within inches of discovering hyperbolic geometry outright while wrestling with his personal distaste for some of his discoveries.

I also enjoyed writing about the media and the genius myth, where I wondered how we could get beyond the idea that only people with an innate math brain can be successful in and enjoy mathematics. (See also my genius myth post on the Blog on Math Blogs.) Somewhat related is the post I wrote earlier this week about contrasts in number theory: Shinichi Mochizuki's work on the abc conjecture and Piper Harron's funny, "laysplained" thesis offered an interesting juxtaposition of different approaches to explanation in mathematics.

Although my post about running pace and the intermediate value theorem was on its face about mathematics itself, it was also about how mathematicians might approach the question and the dangers of relying too much on intuition.

Goofy quizzes

One of the things I love about being a mathematician is the way it helps me see the world differently. Even when it doesn’t have a practical impact on my life, it enriches my experience. Case in point: when I visited the architectural masterpiece La Pedrera in Barcelona this summer, I saw tons of different shapes in the parquet floor there. The logical conclusion was to create a highly scientific personality quiz based on which shapes jump out at you.

The other quiz I made this year is about mathematics and poetry. Inspired by JoAnne Growney, I found some quotations that sound like they could be about either poetry or mathematics and made you try to figure out which ones were which. No matter your score, in this quiz, everyone’s a winner.