Math That Connects Where We’re Going to Where We’ve Been — Quanta Magazine

My latest column for Quanta Magazine is about the power of creative thinking in mathematics, and how understanding problems from different perspectives can lead us to surprising new conclusions. It starts with one of my all-time favorite problems:

Say you’re at a party with nine other people and everyone shakes everyone else’s hand exactly once. How many handshakes take place?

This is the “handshake problem,” and it’s one of my favorites. As a math teacher, I love it because there are so many different ways you can arrive at the solution, and the diversity and interconnectedness of those strategies beautifully illustrate the power of creative thinking in math.

By connecting different approaches like counting and recursion, we can connect mathematical ideas across disciplines and discover new relationships.

Like all my columns for Quanta, this piece is free to read at QuantaMagazine.org.

Books I Read in 2023

Here’s a selection of books that made an impact on me in 2023.

Superforecasting tells the story of psychologist Philip Tetlock’s project to systematically evaluate the predictions of experts. What exactly does an advisor mean when they tell the President that a military operation has a “good chance” of being successful? It wasn’t so long ago that no one thought to even ask such a question, and as Tetlock shows, the consequences couldn’t be more real. Tetlock’s work led to the development of the Good Judgement project, a forecasting competition designed to identify the characteristics of “superforecasters”, individuals with a quantifiable talent for predicting how world events will unfold. It’s a great book, and one I was partly inspired to read because of my involvement in a student forecasting tournament based on the Good Judgement project (where our students took first and second place overall!)

I finally read The Lady Tasting Tea, by David Salsburg, which had been on my list for a while. It’s an excellent history of the development of statistics, told through fascinating characters and interesting anecdotes. It immediately joined my student lending library, and it also took second place on the list of statistics book I’ve learned the most from (to be fair, it’s first on the list of books I’ve learned from by reading it rather than writing it). It’s full of fun little details, like this quote I shared with my linear algebra class the very day I read it.

Manil Suri’s The Big Bang of Numbers was a highlight of my year, both because it’s a unique book that tells a whimsical origin story of mathematics full of insight, humor, and even spirituality, and also because I had the privilege to interview Manil Suri at the Jaipur Literature Festival this past year (video here).

Made to Stick, by Chip and Dan Heath, is the book that I’ve been thinking most about as a teacher this year. Why do silly ideas go viral while important ideas struggle to take hold? It’s a question every teacher should consider, and Made to Stick offers lots to think about. Months later I’m still pondering the power of generative metaphors, story as simulation, and why people should care about duo piano. Thanks to my (former) student Satvik for the recommendation!

Atomic Habits by James Clear was another book that had been on my list, and it was a worthwhile read even if confirmed many previously held beliefs. A core idea of the book is very mathematical, namely that the impact of habits compound like interest in a bank account, generating exponential (hopefully, positive) personal growth.

I feel a bit funny saying that John Fleischman’s Phineas Gage was probably the best book I read this year, seeing as its target audience is middle school students. But this infamous story of the 19th-century man who blasted a railroad spike through his brain and lived to tell about it is so vivid, engaging, and expertly contextualized in the history of science that it keeps coming up in thoughts and conversations.

In fiction, I enjoyed Susanna Clarke’s Jonathan Strange and Mr. Norrell, a fantastical history of magic in Britain told through the story of the apprenticeship-turned-rivalry of the title characters. Amor Towles’s A Gentleman in Moscow was one of the loveliest books I’ve read in a long time. And I enjoyed every moment of Elmore Leonard’s Get Shorty. Leonard also authored the stickiest advice I read in 2023: don’t write the parts that the reader skips.

In addition to getting back to my year-end lists (sorry, 2022) I’ve been trying to be more active on Bookwyrm, the ActivityPub-based social network dedicated to reading and reviewing. You can find me there at phonner.

And thanks, as always, to the (shamefully underfunded) Brooklyn Public Library for making it so easy to read this year and every year.

Related Posts

Pierre de Fermat’s Link to a High School Student’s Prime Math Proof — Quanta Magazine

My latest column for Quanta Magazine tells the mathematical story of the incredible high school student who proved a result about not-quite prime numbers that had eluded mathematicians for decades.

[Daniel] Larsen was a high school student in 2022 when he proved a result about a certain kind of number that had eluded mathematicians for decades. He proved that Carmichael numbers — a curious kind of not-quite-prime number — could be found more frequently than was previously known, establishing a new theorem that will forever be associated with his work. So, what are Carmichael numbers? To answer that, we need to go back in time.

You can read the full article for free here.

Math that Moves the Needle — Quanta Magazine

My latest column for Quanta Magazine explores a century-old geometry problem that anyone who’s ever performed a three-point turn can appreciate.

Imagine you’re rolling down the street in a driverless car when you see a problem ahead. An Amazon delivery driver got their van halfway past a double-parked UPS truck before realizing they couldn’t make it through. Now they’re stuck. And so are you.

There’s a fun math problem here about how much space you need to turn your car around, and mathematicians have been working on an idealized version of it for over 100 years. It started in 1917 when the Japanese mathematician Sōichi Kakeya posed a problem that sounds a little like our traffic jam. Suppose you’ve got an infinitely thin needle of length 1. What’s the area of the smallest region in which you can turn the needle 180 degrees and return it to its original position? This is known as Kakeya’s needle problem, and mathematicians are still studying variations of it. Let’s take a look at the simple geometry that makes Kakeya’s needle problem so interesting and surprising.

You can read all about the surprising resolution of Kakeya’s needle problem in my full column for Quanta Magazine.

Jaipur Literature Festival New York

I’m thrilled to be a part of the upcoming Jaipur Literature Festival in New York City, where I’ll be in conversation with mathematician and novelist Manil Suri. Manil’s latest book, The Big Bang of Numbers, is a tour of mathematics from the ground up, allowing the reader to the experience of the power of mathematical creation as Manil constructs the universe using only math. It is a fun, friendly, and one-of-a-kind book.

In our JLF session A Universe Built on Math, Manil and I will be talking about math, writing, teaching, and everything in between. The talk is happening on September 13th at 4:30 pm at the Asia Society. All the details can be found here.

Follow

Get every new post delivered to your Inbox

Join other followers: