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.

Workshop — The Geometry of Statistics

I’m excited to present The Geometry of Statistics tonight, a new workshop for teachers. This workshop is about one of the coolest things I have learned over the past few years teaching linear algebra and writing a book on statistics: Finding the line of best fit for a set of data is really a geometry problem, but not the geometry problem you might think it is!

In this workshop we’ll see how finding the regression line is equivalent to finding the shortest path from a point to a plane in a curious high dimensional space. This geometric context helps make sense of many mysterious things in regression, like mean-centering (thanks, All 1s vector!) and the correlation coefficient. It also ties into advanced applied mathematical ideas like Principal Component Analysis (PCA) and the Singular Value Decomposition (SVD).

As is often the case when I learn mathematics, the turning point occurred when I finally understood why I didn’t understand. I look forward to sharing that understanding with others!

Related Posts

People Tell Me My Job is Easy

People tell me my job is easy.

You get summers off.

You only work nine months of the year.

You’re done at 3 pm.

You get paid to babysit.

Students at that school won’t succeed anyway, so you don’t have to do much.

Students at that school will succeed anyway, so you don’t have to do much.

Teaching advanced courses is easy. My students don’t even know the basics.

It must be easy to teach those students. Mine can’t handle that kind of work.

I wish I got to teach those students. Mine aren’t that engaged.

You just walk around asking questions. Your students are the ones doing everything.

The Surprising Simple Math Behind Puzzling Matchups — Quanta Magazine

My latest column for Quanta Magazine is about one of my all-time favorite mathematical ideas: transitivity. Well, technically it’s about intransitivity, a subtly complex mathematical situation which any sports fan knows all about.

It’s the championship game of the Imaginary Math League, where the Atlanta Algebras will face the Carolina Cross Products. The two teams haven’t played each other this season, but earlier in the year Atlanta defeated the Brooklyn Bisectors by a score of 10 to 5, and Brooklyn defeated Carolina by a score of 7 to 3. Does that give us any insight into who will take the title?

Well, here’s one line of thought. If Atlanta beat Brooklyn, then Atlanta is better than Brooklyn, and if Brooklyn beat Carolina, then Brooklyn is better than Carolina. So, if Atlanta is better than Brooklyn and Brooklyn is better than Carolina, then Atlanta should be better than Carolina and win the championship.

Sports fan knows things are never this simple, and in my column I explore some of the surprising mathematical reasons why it may be the case that A is better than B and B is better than C, but C is better than A. You can read the full column for free here.

Math Photo: A Most Mathematical Building

Here are some images from Harpa, in Reykjavík, Iceland. Harpa is home to the Iceland Symphony Orchestra and the Icelandic Opera, and is one of the most mathematical buildings I have ever seen.

The face of the building is a solid wall of glass prisms whose faces are hexagons and pentagons.

Here’s a look up through the wall from below.

Different perspectives highlight the different polygons.

Whoever designed this beautiful building certainly knew the theory of pentagonal tilings!

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