It was a pleasure to review Ben Orlin’s wonderful book Math Games with Bad Drawings in the American Mathematical Monthly. The review is available online, with subscriber access, here, and will appear in the next print edition of the Monthly.
And in case you’re still shopping, Math Games would make a fabulous holiday gift for the math enthusiastic, math teacher, math student, or math parent in your life!
In my latest column for Quanta Magazine I combine my love of geometric dissections with my appreciation of The Great British Bake Off.
Gina the geometry student stayed up too late last night doing her homework while watching The Great British Bake Off, so when she finally went to bed her sleepy mind was still full of cupcakes and compasses. This led to a most unusual dream.
There’s a remarkable result in geometry that any two polygons of equal area are “scissors congruent”. In my column I explain what this means, why it’s true, and how it connects to some recent research about a famous impossible problem!
You can read the full article here.
My latest column for Quanta Magazine explores one of my favorite topics: infinity!
At the end of the Marvel blockbuster Avengers: Endgame, a pre-recorded hologram of Tony Stark bids farewell to his young daughter by saying, “I love you 3,000.” The touching moment echoes an earlier scene in which the two are engaged in the playful bedtime ritual of quantifying their love for each other. According to Robert Downey Jr., the actor who plays Stark, the line was inspired by similar exchanges with his own children.
The game can be a fun way to explore large numbers:
“I love you 10.”
“But I love you 100.”
“Well, I love you 101!”
This is precisely how “googolplex” became a popular word in my home. But we all know where this argument ultimately leads:
“I love you infinity!” “
Oh yeah? I love you infinity plus 1!”
Learn how a staple of high school math — functions — can help mathematicians understand infinity and even describe the different kinds of infinities there are! The full column is available here and includes a few challenging exercises at the end.
My latest column for Quanta Magazine ties recent news about “digitally delicate” primes to some simple but fascinating results about prime numbers.
You may have noticed that mathematicians are obsessed with prime numbers. What draws them in? Maybe it’s the fact that prime numbers embody some of math’s most fundamental structures and mysteries. The primes map out the universe of multiplication by allowing us to classify and categorize every number with a unique factorization. But even though humans have been playing with primes since the dawn of multiplication, we still aren’t exactly sure where primes will pop up, how spread out they are, or how close they must be. As far as we know, prime numbers follow no simple pattern.
There’s a tension among the infinitude of prime numbers — that there will always be primes close together and primes far apart — that can also be seen among digitally delicate primes, primes that become composite if any digit is changed. It may come as a surprise that any digitally delicate primes exist at all, but that’s just the beginning of their story. Find out more at by reading the full article here, and be sure to check out the exercises!
My latest column for Quanta Magazine uses the viral word game Wordle to explore the basic ideas of information theory, the branch of mathematics developed by Claude Shannon that revolutionized fields as diverse as digital communication and genetics.
Wordle is a perfect place to discuss the way Shannon defined “information” to posses certain important mathematical properties, like additivity and and inverse relationship with predictability.
For example, how would you proceed if your Wordle guess came back like this?
What you guess next says a lot about you both as a Wordle player and as an information theorist. To learn more, and maybe even level up your Wordle game, read the full article here.