Hello friends! July was a whirlwind. I traveled to Boston, Chicago, and Denver for a combination of work and fun. In between all that, Kevin Knudson and I launched a project we've been working on for a few months: My Favorite Theorem, a math podcast in which, as the name suggests, we interview mathematicians and ask them what their favorite theorems are. We also ask them to choose a food, beverage, or work of art that they think goes well with the theorem. If you've ever wanted to know what fruit pairs best with the fundamental theorem of calculus, this is the podcast for you. You can find it on iTunes and Google Play, and we're looking at getting it on other podcasting apps too. You can also listen to it at my blog, Roots of Unity, or Kevin's website, kpknudson.com. If it's not available on your preferred site for getting podcasts into your ears, let us know and we'll see what we can do.
I went to MathFest, the summer meeting of the Mathematical Association of America, this month. The hotel that hosted it was a treasure trove of fun geometric patterns.
Solving a Rubik's cube, whether the classic 3×3×3 kind, or a larger n×n×n variety, has a polynomial-time algorithm, but figuring out whether you can solve one in a given number of steps (and therefore determining the optimal solution of a given cube) is NP-hard, so as of yet, there is no known way to solve it quickly. I wrote about that result for New Scientist.
The biggest math news of the month was the death of Maryam Mirzakhani, prominent mathematician and first woman to win the prestigious Fields medal, at age 40. I wrote about her for Scientific American.
Craig Kaplan wrote a neat post about Heesch numbers, which describe how much you can surround a tile with other symmetric tiles following certain rules. I'm looking forward to future installments in this series.
The algebra wars are back!Sort of. They're not so vitriolic this time. This time some people are proposing changing the math requirements for community college graduation away from algebra. I don't have a strong negative reaction to that proposal the way I do to proposals to do away with it in middle school and high school, but I still share concerns that students who don't master algebra will have career options closed to them. On the other hand, if the alternative is leaving college, that closes career options as well. In any case, I'm glad to see schools looking seriously at whether their requirements are serving their students well, and I hope that as many students as possible will have opportunities to succeed in math classes and see themselves as people who can "get" math, whether or not they choose to continue in math careers.
Speaking of community colleges, I enjoyed this interview with Ken Monks, a math professor at a community college in the Boulder area. "I LOVED the fact that at the community college there was really no attitude there whatsoever regarding academic chest-pounding or totem-pole climbing or status or prestige or anything like that. The only thing anybody cared about is student success. If someone with minimal resources or external support walks in the door and says 'I’d like to improve my position in life,' we are all obsessed with how do we collectively help them do that."
A sequence of two-pointers can converge to a three-pointer. Marathon running is an unconstrained optimization problem. Cricket is not well-defined. Mathematicians explain sports to each other. (By Ben Orlin of Math with Bad Drawings.)
Blast from the past
In July 2016, I wrote about what to wear in the ninth dimension, or how clothing can help you think about high-dimensional spaces. Are you having trouble finding jeans or dresses that fit just right? That's probably because we're trying to collapse a set of measurements that live in some high-dimensional space onto a one-dimensional spectrum of sizes.