PCMI 2021

I’m excited to be a part of the Park City Math Institute’s 2021 upcoming summer program!

PCMI provides immersive mathematical experiences for scientists, students, and educators through their summer programs. This year, I’ll be running a week-long session for PCMI’s Teacher Leadership Program titled Complex Geometry Made Simple. Here’s the course description:

The complex numbers are one of the great achievements of algebra, but their geometry may be even more compelling. Join us as we explore the complex connections between elementary geometry, inversion, rotations, functions, and more! The shortest path to real truth may involve a detour through the complex plane, but in this course we’ll be sure to take time to enjoy the journey.

PCMI’s Teacher Leadership program runs July 12 — 30 and includes courses on Fibonacci Recurrences, led by Daryl Yong and Bowen Kerins, and Hands on Combinatorics, led by Brian Hopkins. You can find out more information on the programs, including how to apply, here.

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The Mysterious Math of Perfection — Quanta Magazine

My latest column for Quanta Magazine explores the mathematics of perfect numbers. Humans have been studying perfect numbers for thousands of years, but we still don’t know if an odd perfect number exists!

Euclid laid out the basics of perfect numbers over 2,000 years ago, and he knew that the first four perfect numbers were 6, 28, 496 and 8,128. Since then, many more perfect numbers have been discovered. But, curiously, they’re all even. No one has been able to find an odd perfect number, and after thousands of years of unsuccessful searching, it might be tempting to conclude that odd perfect numbers don’t exist. But mathematicians haven’t been able to prove that either. How is it that we can know so much about even perfect numbers without being able to answer the simplest question about an odd one? 

With some basic number theory and an assist from a famous formula from Algebra class, we can get pretty far into the world of perfect numbers. So read the full article here, and be sure to stick around for the exercises at the end!

Workshop — Bringing Modern Math into the Classroom

This Thursday I’ll be running my workshop “Bringing Modern Math into the Classroom” for teachers at Math for America.

In this webinar participants will engage with mathematics at the edge of our understanding. We’ll look at examples of math that’s being invented and discovered right now, and see how it connects to what is happening in classrooms.

We’ll play games, explore patterns, and make conjectures in arithmetic, algebra, and geometry. The goal is for participants to leave not only with a better understanding of how school math and research math are connected, but how to better communicate that connection to students.

This workshop is based on the work I’ve done in my Quantized Academy column for Quanta Magazine. I’ve run similar workshops in past years, and I recently gave a talk on this topic at the NCTM 2020 Virtual Conference. But this week’s workshop is all new, and I’m looking forward to bringing some new ideas and new math to play around with!

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The Crooked Geometry of Round Trips — Quanta Magazine

My latest column for Quanta Magazine explores what round-the-world trips would look like if we didn’t live on a sphere.

Have you ever wondered what life would be like if Earth weren’t shaped like a sphere? We take for granted the smooth ride through the solar system and the seamless sunsets afforded by the planet’s rotational symmetry. A round Earth also makes it easy to figure out the fastest way to get from point A to point B: Just travel along the circle that goes through those two points and cuts the sphere in half. We use these shortest paths, called geodesics, to plan airplane routes and satellite orbits.

But what if we lived on a cube instead? Our world would wobble more, our horizons would be crooked, and our shortest paths would be harder to find.

Classification of geodesic paths on platonic solids didn’t happen until relatively recently, and the case of the dodecahedron offers quite a surprise! To learn more, read the full article here.

2020 — Year in Review

At the risk of making the understatement of the decade, it has been a challenging year. But 2021 offers promise along multiple dimensions. So with a hopeful eye toward the near future, here’s a review of very busy professional year.

Everything about teaching changed in the past 9 months. In March, COVID-19 sent New York City into Emergency Remote Learning. In September, we returned to schools still adapting to the pandemic. Writing about both experiences has been helpful for me: First, my unprepared reaction to going all remote in the Spring, and later, my adjustment to becoming a fully-remote live teacher in the Fall. It’s all made my second year at a new school seem like Year Five. But we are getting through it.

The biggest professional honor of the year for me came with the publication of “The Best Writing on Mathematics 2020” from Princeton University Press. It’s still a bit shocking to see my article “On Your Mark, Get Set, Multiply” featured alongside the work of incredible mathematical communicators like Steven Strogatz, Erica Klarreich, John Carlos Baez, and others.

The article was originally published in Quanta Magazine, and I explored many fun topics in my column this year, like how social distancing is a geometry problem, the power of assigning impossible problems in math class, and how we still can’t answer simple-sounding questions like “What’s the biggest shape of diameter one?“.

I also continued to write for the New York Times Learning Network in 2020, publishing “Dangerous Numbers” and “7 Ways to Explore the Math of the Coronavirus with the New York Times“. As a result of those pieces, I was interviewed for an NPR piece about teaching about the coronavirus (and received a surprising message from an old friend because of it!)

For obvious reasons, 2020 was the year of the webinar, and I gave talks, ran workshops, and participated in a variety of virtual panels this past year. This summer I participated in NCTM’s 100 Days of Professional Learning with “Coding Math at a Distance“, and ran “A Crash Course in Geogebra” through Math for America to help teachers prepare to teach geometry remotely. This fall I was invited to contribute to NCTM‘s first-ever Virtual Conference, spoke about computer science education at a PAEMST Alumni Webinar, talked Stats in the STEM Classroom as part of joint program between the Museum of Mathematics and Brookhaven National Laboratory, and participated in a panel discussion on math and media literacy during Media Literacy Week. And even though it feels like we’ve been quarantining for years, I actually travelled to Rutgers in February to give my talk “Math Outside the Bubble” in person.

I continued to review books and manuscripts for various publishers, and read a good deal in 2020 as well. I also stayed connected to the mathematical art community, working with organizations like Bridges Math and Art and the Journal for Mathematics and the Arts. I even had some of my photography on display in a exhibit alongside some of my favorite mathematical artists.

I also took advantage of some down time this summer to redesign my personal web page, PatrickHonner.com, and I updated my Speaking and Writing pages. As usual, the new year is already filling up with new and interesting opportunities, but I’m always open to inquiries and can be contacted here.

It was a full and fulfilling professional year, but like much of the world I’ll be glad to put 2020 behind us. Here’s wishing our optimism for 2021 is justified.

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