• ### The Cantor Function: Angel or Devil?

| March 31, 2015 |

When you're looking at it, it just stays there, constant and still. But if you turn your back for just an instant at a point in the Cantor set, the function grows impossibly quickly.
• ### A Few of My Favorite Spaces: The Cantor Set

| March 26, 2015 |

Last month, I wrote about the -Base, a website that serves a similar function to the book Counterexamples in Topology. I'm teaching a topology class this semester, and it's been fun to revisit some good counterexamples.
• ### What’s so Great about Continued Fractions?

| March 17, 2015 |

The more I learn about continued fractions, the more enamored I am with them. Last week, when I wrote about how much better continued fractions are than the arbitrary decimal digits we usually use to describe numbers, I mentioned that continued fractions tell us the "best approximations" of irrational numbers.
• ### Don’t Recite Digits to Celebrate Pi. Recite Its Continued Fraction Instead.

| March 11, 2015 |

The digits of pi reciting contest is an all-too-common Pi Day event. And as this year is a once-in-a-century confluence of month/day/year with the first few decimal digits of pi, we might be in for more of those than usual.
• ### Uber, but for Topological Spaces

| February 28, 2015 |

So it's cold and rainy, and you're up a little too late trying to figure out why that one pesky assumption is necessary in a theorem. Wouldn't it be nice if you could just order up a space that was path connected but not locally connected?
• ### Things to Make and Do in the Fourth Dimension (Book Review)

| February 26, 2015 |

Sometimes you want to learn a “new” multiplication algorithm from a general interest math book, sometimes you want to learn why voting systems are doomed to imperfection, and sometimes you just want to play with numbers, patterns, and pictures.
• ### Gauss and Germain on Pleasure and Passion

| February 13, 2015 |

Sophie German, who was not allowed to attend university, was the first woman to make significant original contributions to mathematical research.
• ### The Media and the Genius Myth

| February 5, 2015 |

I’ve been thinking a lot about the genius myth, the notion that in order to be a successful in certain disciplines, you need to have a special innate talent that can’t be learned.
• ### Understand the Measles Outbreak with this One Weird Number

| January 31, 2015 |

15. That’s all you need to know about the measles. OK, that’s not true at all. There's no one weird trick that will give you a flat belly (besides lying face-down on something flat), and there's no one weird number that explains measles epidemiology.
• ### Learn to Count like an Egyptian

| January 26, 2015 |

Last semester, I began my math history class with some Babylonian arithmetic. The mathematics we were doing was easy—multiplying and adding numbers, solving quadratic equations by completing the square—but the base 60 system and the lack of a true zero made those basic operations challenging for my students.
• ### Mathematics, Live: A Conversation with Amal Fahad and Rasha Osman, Part II

| January 19, 2015 |

I had the pleasure of attending the 2nd annual Heidelberg Laureate Forum in September. Modeled after the Lindau Nobel Laureate Meetings, it brings together recipients of prestigious awards in mathematics and computer science and young researchers in those areas.
• ### Mathematics, Live: A Conversation with Amal Fahad and Rasha Osman, Part I

| January 12, 2015 |

I had the pleasure of attending the 2nd annual Heidelberg Laureate Forum in September. Modeled after the Lindau Nobel Laureate Meetings, it brings together recipients of prestigious awards in mathematics and computer science and young researchers in those areas.
• ### 12 Things I Had Way Too Much Fun Writing This Year

| December 31, 2014 |

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.

| December 25, 2014 |

For Halloween, I wrote about a very scary topic: higher homotopy groups. Homotopy is an idea in topology, the field of math concerned with properties of shapes that stay the same no matter how you squish or stretch them, as long as you don’t tear them or glue things together.
• ### Online Game Crowd-Sources Theorems

| December 23, 2014 |

Now is your chance to prove some theorems without knowing what they mean! Chris Staecker, a mathematician at Fairfield University, created the game Nice Neighbors to get crowd-sourced solutions to problems from a field called digital topology.
• ### Seeing Music: What Does the Missing Fundamental Look Like?

| December 10, 2014 |

I wrote a post yesterday about the missing fundamental effect. It’s a startling auditory illusion in which your brain hears a note that is lower than any of the notes that are actually playing.

| December 9, 2014 |

Telephones lie about sounds because odd numbers aren't even. Once again with those integers and sound perception! Telephones can only pick up frequencies above 300 or 400 Hertz (cycles per second, also called Hz), but most adults’ speaking voices are lower than 300 Hz (approximately the D above middle C).

| November 30, 2014 |

The integers are a unique factorization domain, so we can't tune pianos. That is the saddest thing I know about the integers. I talked to a Girl Scout troop about math earlier this month, and one of our topics was the intersection of math and music.
• ### The Math Geek Holiday Gift Guide

| November 23, 2014 |

Looking for a gift that says, "Hey, I know you like math"? Look no further. There is an embarrassment of riches when it comes to wonderful mathematical things to give to people, but here are some of the coolest items I've seen this year.
• ### A Proof of the Math Fact of Rolle in Short Words

| November 17, 2014 |

This proof of the math fact of Rolle, I wrote it down; here was my goal: Use just words with one part. (So it won’t sound too smart.) Please tell me if you find a hole.
• ### Higher Homotopy Groups Are Spooky

| October 31, 2014 |

When I tell people I'm a mathematician, I get a lot of different reactions. Perhaps surprisingly, I mostly get positive responses. Many of them are of the "You go, girl" variety.
• ### In Which Omar Khayyam Is Grumpy with Euclid

| October 28, 2014 |

My math history class is currently studying non-Euclidean geometry, which means we've studied quite a few "proofs" of Euclid's fifth postulate, also known as the parallel postulate.
• ### Beyond Emmy and Sophie: Resources for Learning about Women in Math

| October 14, 2014 |

Today is Ada Lovelace Day, an international celebration of women in science, technology, engineering, and math. If you’d like to read about women in math for the occasion, you're in serious danger of coming across an article about Hypatia, Emmy Noether, Sophie Germain, or Sofia Kovalevskaya.
• ### Build Your Own Fractal with MegaMenger!

| October 9, 2014 |

Later this month, people will be gathering at museums and schools around the world to build giant Menger sponges as part of a global fractal extravaganza called MegaMenger.
• ### Another Reason to Love the Number Seven

| September 29, 2014 |

The world's favorite number is seven, at least if the result of a poll conducted by Alex Bellos is to be believed. Some people like it because it is prime, some because they have a lot of sevens in their birthdates.