Doughnut Price is a Topological Invariant (and 13 other math cartoons)

To Prove a Murder

A pal on Twitter read this as “elven witnesses.” I wish. Eyewitness testimony is unreliable, but elf-witness testimony is foolproof.

Those Who Do Not Learn Recursion… Continue reading


A World Without the Number 6

a weekly roundup of links, cartoons, and
profound hypotheticals that only a 5-year-old would imagine

Great piece by Adam Kucharski on the discovery of the monstrous nowhere-differentiable function, and its ripples across history:

Calculus had always been the language of the planets and stars, but how could nature be a reliable inspiration if there were mathematical functions that contradicted the central ideas of the subject?

Somehow, linking to Clickhole makes me feel very square and old-fashioned, like taking out a newspaper ad to endorse a Tweet, but I want to draw your attention to 7 Shapes That Will Be Completely Obsolete After I Introduce My Latest Shape, the Triquandle:

The Trapezoid. A quadrilateral with only one pair of parallel sides? Ha! Pathetic. Try a triquanderlateral with so many pairs of parallel sides that men have died just trying to count them all. How many men died creating the trapezoid? Zero. Zilch. Nada.

2017.10.23 objective tests

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Insatiable for Updates

a weekly roundup of cartoons, links, and the updates you and your computer are both hankering for

2017.10.2 no more problems

I’m awaiting the day when the New York Times becomes a full-time math-only publication. This week brought us a step closer.

First, Manil Suri meditates on the social impact of mathematical discovery, by asking who invented zero.

And second, Jordan Ellenberg describes the state of gerrymandering in Wisconsin, where new computational techniques have elevated the old practice from an art to a science. “As a mathematician, I’m impressed,” writes Ellenberg. “As a Wisconsin voter, I feel a little ill.”

2017.10.5 computer updates

A gem from ArXiV: Marvel Universe Looks Almost Like a Real Social Network, applying graph theory to the Marvel comics universe. Each character is a node; appearing together in a comic book is an arc.

Perhaps unsurprisingly, 99.4% of all characters belong to a single connected component of the graph.

2017.10.6 odd number theorists

Last thought: the Best Mathematics Writing of 2017 looks sharp.

The Fortune of Mathematicians

a weekly roundup of cartoons, links, and breathless summaries

I just got back from the most exciting and undeserved week of my year: the Heidelberg Laureate Forum.


It gathers, in an adorable German city, 25 laureates of math and computer scientists (winners of the Fields Medal, Abel Prize, Turing Award, etc.) along with 200 young researchers (students and postdocs), for a week of lectures, discussions, and fancy dinners at museums like this:


Among my favorite activities of the week is ambushing the young researchers and asking them to draw cartoons for me. You can find three posts on the HLF blog: Continue reading

A Probability Puzzle That You’ll Get Wrong

a weekly roundup of cartoons, links, and nefarious probability brainteasers

Like the rest of the math internet, I recently fell in love with this rascal of a problem:

  1. I roll a die until I get a 6. What is the expected number of throws?
  2. When I tried this, I happened to roll only even numbers prior to getting the 6. Knowing this, what is the expected number of throws now?

I’ll let you think. See the end of the post for a solution.

2017.9.18 bull and bear market

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A Symphony with an Irrational Time Signature

a weekly roundup of cartoons, links, and things to make your eardrums bleed

2017.9.11 zeno's persuasion

This cartoon draws inspiration from the tireless work of Julia Galef, the patron saint of being patient in internet arguments. Recently, she has been compiling lists of “unpopular ideas” (about political systems, social norms,  and criminal justice).

Even better, she offers this list of reasons to engage in internet arguments, even when you know that neither of you is likely to change your mind: Continue reading

There Is No Perfect Teacher (Just a Bunch of Great Ones)

I’ve taught at two schools in my career.

The first, in California, had a dozen teachers in total. I adored my colleagues, but we each had our own domain. I handled Trig, Precalc, Calculus, and Stats. Soon I fell into unquestioned habits, built on assumptions I didn’t know I was making.

My second school, in England, had a dozen *math* teachers. It was as if, after years of playing bass in my empty garage, I had suddenly been recruited into an actual band.

My first winter, I took myself on a tour of the department, observing a lesson from each of my new colleagues. I came away convinced that there’s no one way to teach mathematics, that our methods are necessarily as diverse as our goals.

Take two very different teachers: Simon and Tom.

Whereas I’m always fretting about students who can execute procedures without understanding them, Simon wastes no such worrying; he simply weaves the two together far better than I do. His notes at the board model clear and disciplined thinking, and he gives written comments every bit as careful and analytical as the work he expects. (He is also one of the two most competitive sportsmen I have ever met.)


Tom couldn’t be more different. At the front of the room, he’s less a lecturer than a provocateur: the mischief-maker in chief, whose highest goal is to create space for mathematical exploration.  That means open-ended problems, and multiple days spent wrestling with a single provocative question. He incites debates, sets traps, and shines a spotlight on the students’ own thinking. (He is also one of the two most competitive sportsmen I have ever met.)


But the diversity in math teaching runs deeper than the Simons vs. the Toms, traditionalists vs. progressives.

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