Resources

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.

By MrHonner, ago

NCTM 2023

I’ll be in Washington, DC later this week for the National Council of Teachers of Mathematics (NCTM) Annual Meeting, where I will be giving two talks.

On Thursday, Gary Rubinstein and I will be presenting “So, You’re Teaching Precalculus”.

With the College Board’s new Advanced Placement Precalculus course on the horizon, a lot of math teachers will be teaching a brand new course in 2023. What are the big ideas in AP Precalculus? And how might AP Precalculus differ from the courses already taught at your school? In this session we’ll look at the themes that define the AP Precalculus framework and how they link important ideas in algebra, geometry, and trigonometry to what lies ahead in a calculus course.

And on Friday, I’ll be making “A Case for Linear Algebra”.

Students need as many pathways to mathematical success as we can give them, and linear algebra offers a flexible and versatile course option that can fit alongside an established sequence or help define a new one. Come learn about the whys and the hows of teaching linear algebra, and see where the core ideas pop up in the classes you already teach.

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By MrHonner, ago

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.

By MrHonner, ago

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.

By MrHonner, ago

Math Patterns That Go On Forever but Never Repeat — Quanta Magazine

I wrote a column for Quanta Magazine on the recently discovered “hat tile”, the first ever aperiodic monotile!

Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, arrangements of shapes that fit snugly together while filling up space. Two-dimensional tilings are admired all around the world, both for their beauty — as seen in the artistry of mosaics in cathedrals and mosques around the world — and for their utility, in walls and floors everywhere.

In math, tilings are often appreciated for their regular patterns. But mathematicians also find beauty in irregularity. It’s this kind of beauty that a retired print technician was seeking when he recently discovered the first “aperiodic monotile”— a single tile that fills up the plane in a non-repeating pattern. To get a handle on this big discovery, let’s start by thinking about a simpler problem: how to tile a line.

You can read the full article for free here.

By MrHonner, ago
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