I make a brief appearance in this NPR story about teaching using the coronavirus. In “Teacher Uses Coronavirus for Math Lessons”, reporter Emily Files profiles a teacher in Wisconsin who is using the coronavirus epidemic to get his middle school math students thinking about data and rates of change. Files interviewed me a about the lesson I wrote for the New York Times Learning Network on “Dangerous Numbers” (available here).
My latest column for Quanta Magazine is about a clever technique for finding rational approximations to irrational numbers. The technique, developed by the German mathematician Gustav Dirichlet, works by covering the number line with tiny intervals centered at certain rational numbers.
But Dirichlet did better. He improved this method by figuring out how to shrink the intervals around their centers while still keeping the entire number line covered. As the intervals shrink, so does the distance to any irrational number we are trying to approximate. This means we’ll get better and better rational approximations, even using relatively small denominators. But we can’t shrink the intervals too quickly: Even though there are infinitely many of them, if the intervals get too small too fast they won’t cover the entire number line. In the battle between the infinitely large and the infinitely small, Dirichlet had to find the right balance to prevent some irrationals from slipping through the cracks.
Dirichlet’s technique explains why we can always find good rational approximations to irrational numbers using small denominators, like 
You can read the full article here.
I’m honored to be featured in Ben Orlin’s post “What Makes a Great Teacher?”
Ben, the author of “Math With Bad Drawings“ and “Change is the Only Constant” (one of the books I read in 2019) asked four teachers to respond to a fan’s inquiry. Here’s what I had to say.
I’m reluctant to use the phrase “Bad Teacher.” Faced with hundreds of interactions and decisions every day, we all have good and bad moments. Those moments accumulate over a semester, a year, a career, and in most cases yield a net positive result I’d say.
But you can tell a lot about a teacher by how they respond when students don’t succeed. Some will say, “What’s wrong with you?” Others will ask, “What’s wrong with me?”
I really enjoyed thinking about the question, and the different and diverse insights of Fawn Nguyen, Jo Morgan, and Marian Dingle were wonderful. As were Ben’s trademark illustrations of our responses! He nailed mine. Be sure to check out the entire post for yourself at Ben’s blog.
Next week I’ll be visiting Rutgers University to give a talk about communicating mathematics. I’ll be presenting “Math Outside the Bubble” to the Graduate Student Chapter of the American Mathematical Society on Monday, 3/2.
I’m excited to share some of what I’ve learned in my career communicating mathematics to students, parents, and educators through my work as a teacher, as well as to the public through my writing and mathematical outreach. It’s wonderful to know that math students at the beginning of their careers are thinking about the role communication plays in the field. It’s an undervalued, but increasingly critical component of the work.
Update: A recap of the event and some pictures are posted on the Rutgers AMS website here.
My latest column for Quanta Magazine is about the search for sums of cubes. While most integers are neither cubes nor the sum of two cubes, it is conjectured that most numbers can be written as the sum of three cubes. Finding those three cubes, however, can be a challenge.
For example, it was only this year we learned that the number 33 could be written as a sum of three cubes:
33 = 8,866,128,975,287,528³ + (−8,778,405,442,862,239)³ + (−2,736,111,468,807,040)³
What’s so hard about expressing numbers as a sum of three cubes?
It’s not hard to see that it combines the limited choices of the sum-of-squares problem with the infinite search space of the sum-of-integers problem. As with the squares, not every number is a cube. We can use numbers like 1 = 1³, 8 = 2³ and 125 = 5³, but we can never use 2, 3, 4, 10, 108 or most other numbers. But unlike squares, perfect cubes can be negative — for example, (-2)³ = -8, and (-4)³ = -64 — which means we can decrease our sum if we need to. This access to negative numbers gives us unlimited options for our sum, meaning that our search space, as in the sum-of-integers problem, is unbounded.
To learn more, read the full article, which is freely available here.
