25 Are Here, and 1 Is Not

I’ve soul-searched and thesaurus-ed, but there’s no better word for this opening ceremony at the Heidelberg Laureate Forum than “pomp.” The audience rises. Doors are thrown open. And, with a blast of orchestral music, twenty-five living legends of mathematics and computer science shuffle down the aisle.


© Heidelberg Laureate Forum Foundation / Kreutzer – 2017

Last year, when I asked a few of them about this grand entrance, they shrugged and laughed. Yes, they’re icons of academia, titans of scholarship. But also, they’re human beings, blinking in the megawatt spotlight, frowning as they scan for their reserved seats.

The HLF gathers these 25 laureates alongside 200 young researchers to talk about what comes between those two phases: A career spent solving problems. A lifetime of chasing your curiosities and your demons through those strange borderlands, from the cold realm of mathematical abstraction to the messy world of human reality, and back again.

In short: research.

The crowd rises for a moment of silence, to honor three laureates who died in the past year. Two are legends of computer science, both named Charles: Thacker and Bachman. The third picture breaks my heart.

It’s Maryam Mirzakhani.

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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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The State of Being Stuck

Last year, I got the high school math teacher’s version of a wish on a magic lamp: a chance to ask a question of the world’s most famous mathematician.


Andrew Wiles gained his fame by solving a nearly 400-year-old problem: Fermat’s Last Theorem. The same puzzle had captivated Wiles as a child and inspired him to pursue mathematics. His solution touched off a mathematical craze in a culture where “mathematical craze” is an oxymoron. Wiles found himself the subject of books, radio programs, TV documentaries—the biggest mathematical celebrity of the last half-century.

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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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