Throughout the month of July 2023, I participated in a PD experience that was unique to me. Justin Lanier, a former math teacher turned professional mathematician, held a PD he developed called “21st Century Mathematics” and the ultimate goal was “To grow as mathematicians, both for our own enjoyment and for the benefit of our students.”

Each week in July, he provided problem sets for us to work on. Justin kindly allowed me to share these: week 1 problems, week 2 problems, and week 3 problems. Each week’s problems were related to a chapter in the book that formed the backbone of the course: Theorems of the 21st Century by Bogdan Grechuk.

This book’s author went through articles published in 2000-2010 in the prestigious Annals of Mathematics and found (at least to his opinion) the most important results, and wrote a section trying to explain to ____ precisely what that result was and if possible, the general argument used to get that result. The reason I used the blank in the previous sentence is because I am a little confused who the intended audience of the book was. What was great is that I — a math teacher who majored in math two decades ago — could follow along some of the sections. And we had a number of participants who were middle school math teachers who were playing along too.

Justin picked interesting and accessible sections of the book for us to read (one per week) and built his problem sets around those sections.

• Week 1: Section 3.2, Representing 1 as a Sum of Reciprocals of Selected Integers.
• Week 2: Section 2.13, Transforming Convex Bodies into Balls.
• Week 3: Section 10.2, On Divisibility Properties of Dyson’s Rank Partition Function.

I got really hooked on the problems. They reminded me of doing super fun “morning math” at PCMI, where we got to discover new things, think in different ways, and remember the frustrations and elations of learning new math. I did hit some walls, but also had some insights I was really proud of. Since I wanted to take my hand at practicing LaTeX after many years, I typed up my work each week.

For personal archival purposes, I’m uploading my writeups for each problem set here:

We had a choice of reading the section from the book the problem sets were based on before or after working on the problems. Mostly, I chose to work on the problems first, and then after finishing the problem set to the best of my ability, work on understanding the section from the book.

In addition to working on these independently, all the participants had a Discord that we were invited to to chat. I had never used Discord before, but it was pretty neat. We introduced ourselves there, and not all people used it to talk, but some of us were sharing insights and asking questions about the problems there.

Each week, we had a Zoom. Justin offered it twice each week because everyone has such different schedules in the summer. The first part of each Zoom was Justin talking to us about what it means to do research, and be a mathematician, in the 21st century. It was interesting to see some of the charts and data he collected about number of publications, number of PhDs, and gender and minority representation (or underrepresentation, as the case it, obviously). Then we broke up into breakout rooms and discussed the problem set questions.

Additionally, we were invited to read and summarize a different section in the book — whatever section felt accessible and interesting to us. I really enjoyed this part! The first week, I chose a section and then got into a long discussion of something I didn’t understand on the Discord with a few others. I honestly think I found an error in the book — not in the math, I’m sure, but in how the theorem was described in the book.

The three sections I chose to read and try to understand were:

• Section 8.7: ”A Negative Answer to Littlewood’s Question about Zeros of Cosine Polynomials.
• Section 10.2: ”On divisibility properties of Dyson’s rank partition function.”
• Section 2.5: ”The Optimality of the Standard Double Bubble”

(You can read my summaries of what I understood from each section at the bottom of each problem set I turned in.)

Additionally, Justin invited mathematicians to talk to us on a Zoom each week. The truth is, this is one thing I didn’t participate in. I’m so mad at myself. I talked myself out of it, because I secretly was so nervous of being the only person in the Zoom and then having nothing to say. An irrational fear, but it won out.

Lastly, in the fourth week, Justin didn’t have problems and readings. We each were asked to create a 2-5 minute presentation on anything related to the course. Some wrote up what they learned. Others created activities for their classroom based on something they discovered mathematically or pedagogically. Some delved more into the readings. I did that.

Again, for archival purposes, here’s my presentation on “partitions” and “rank”. However just note that it’s designed for someone who read the reading.

The structure was sort of a choose-your-own adventure. You could choose to do the problems or not. You could choose to engage in the Discord or not. You could choose to the Week 4 presentation or not. I was curious how I’d feel about this being a remote PD. I’m so over Zoom that I almost didn’t sign up because of that. But it turned out that for someone like me, who wanted to do (almost) all the things, this all threaded together to make a really wonderful mathematics-filled July.

Justin didn’t charge for the course, which was great because I signed up after my school year ended so I probably couldn’t have gotten funding from my school. But in line with his values, he instead requested if we could, to donate $25 to one of these organizations.
African Institute for Mathematical Sciences (AIMS) – donate
Bridge to Enter Advanced Mathematics (BEAM) – donate
Enhancing Diversity in Graduate Education (EDGE) – donate
Julia Robinson Mathematics Festival (JRMF) – donate
Latinx and Hispanics in the Mathematical Sciences (Lathisms) – donate
Mathematically Gifted and Black (MGB) – donate

I chose two :)

I loved doing math over the summer, and having some light structure to guide me! And learn a bit about what has been happening in mathematics more recently in a different way than reading Quanta articles.