It's the season for family, hot chocolate, and year-in-review lists. Guess which one this is! Roots of Unity has been around for two years now, and I'm so glad I have a place to share some of the weird and wonderful math I think about. In chronological order, here are 12 of my favorite posts from 2014.

Divergent series Lucille says, "1+2+3...=-1/12." Video from Fox, gif from

Does 1+2+3... Really Equal -1/12? In January, the Numberphile gang released a controversial video that claims that the sum of all the positive integers is -1/12. This drew some ire from some math bloggers, myself included. I had a lot of fun making Lucille Bluth gifs to explain why I think their statement requires a few asterisks.

Hyperbolic Quotes about Hyperbolic Geometry. People sometimes go a little over the top when it comes to hyperbolic geometry. George Bruce Halsted described one of the first treatises on hyperbolic geometry as "the most extraordinary two dozen pages in the whole of human thought!" I like hyperbolic geometry way more than the next person, but I don't know if I'd go that far. This was the first of a few posts I wrote this year on the history of geometry. The others, about chasing the parallel postulate, Euclid's fourth postulate, and that time Lewis Carroll called someone Hitler Nero because they wanted to use a different geometry textbook, were fun too. Oh yeah, and that grumpy geometer Omar Khayyam.

A knitted (5,15) torus link. Image: sarah-marie belcastro.
Knotted Needles Make Knitted Knots. In which sarah-marie belcastro makes gorgeous mathematics out of yarn.

Graham's Number is Too Big for Me to Tell You How Big it Is. News flash: big numbers are big. And up arrow notation lets you make numbers that get big fast!

The Slowest Way to Draw a Lute. A sixteenth century painting manual by Albrecht Dürer contained instructions for a purely theoretical painting method, and that makes me smile.

Measure Yourself by the Standard of the Capybara. "Unit of Measure" by Sandra Beasley was my poetry find of the year. Just go read it.

More Fun than a Hypercube of Monkeys, a sculpture by Henry Segerman and Will Segerman.

Nothing Is More Fun than A Hypercube of Monkeys. The quaternion group. Monkeys. What more do you need?

How to Talk about the Fields Medal at Your Next Cocktail Party. 2014 is a number that gives a remainder of 2 when divided by 4, so the Fields Medals International Medals for Outstanding Discoveries in Mathematics were awarded in August this year. I compiled a list of tips that undoubtedly helped many of you through social situations that required a working knowledge of one of the most prestigious awards in mathematics. This year, the four winners included the first Brazilian, the first Brazilian whom the French are proudly reminding us is also a French citizen, the first Canadian, the first Canadian of Indian heritage, the first Austrian, the first Austrian creator of award-winning sound editing software, the first Iranian, and the first Iranian woman working in California, to win the prize. Quanta Magazine had excellent profiles of all the winners.

A Proof of the Math Fact of Rolle in Short Words. I wrote some math in words with just one sound.

The Saddest Thing I Know about the Integers. Why prime numbers mean pianos are all out of tune. This post was followed by two more math and music posts.

Online Game Crowd-Sources Theorems. Help digital topologists prove theorems about digital topology! All you have to do is drag points around until lines aren't red.

What We Talk about When We Talk About Holes. It's surprisingly hard to say what a hole is. I had fun trying. (Inspired by an earlier post on higher homotopy groups, which I think are spooky.)

Happy Mathing! See you next year.