The Three Phases of the Mathematical Life

This autumn, I got the chance to ask a few questions of Ngô Bảu Châu.

If your jaw is not on the floor, it’s because (A) you’ve spent shockingly little time browsing the list of Fields Medal winners, and (B) you’re not Vietnamese.

A helpful Vietnamese journalist I met explained to be that Châu is “the biggest celebrity in Vietnam.” Châu won his Fields Medal in 2010 for proving—hands inside the vehicle, please, because this is a wild ride—a key relationship between “orbital integrals on a reductive group over a local field” and “stable orbital integrals on its endoscopic groups.”

In Vietnam, that relationship is apparently the one sizzling on tabloid covers.

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Châu is not your prototypical superstar. Even in Vietnam, apparently, he is a cryptic figure; not a chatty TV celebrity, but a silent legend. At the press conference where I met him, at the Heidelberg Laureate Forum, he gave some journalists terse one-sentence answers. Not because he was being standoffish, but because a mathematician like Châu never proves in ten lines what he can prove in just one.

I didn’t know what to ask him. I’m not a research algebraist and have never been mistaken for one. So I asked about his education, his youth in Vietnam, his mathematical coming of age.

How does Ngô Bảu Châu get to be Ngô Bảu Châu? Continue reading

Why Are Mathematicians So Bad at Arithmetic?

Thomas Mann once said, “A writer is someone for whom writing is more difficult than it is for other people.”

I believe the same applies to mathematicians doing arithmetic.

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It’s a running joke among mathematicians that they’re bad with numbers. This confuses outsiders, like hearing surgeons plead clumsiness, or poets claim illiteracy, or Rick Astley confess that actually he is going to give you up and let you down, maybe even run around and desert you.

Does it come from some false modesty? A skewed sense of humor?

No, some mathematicians insist: it’s really true, we’re bad at arithmetic.

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Continue reading

Other Ways to Carve Up the Math Curriculum

If the Food Network has taught me one thing, it’s that how you plate a meal matters almost as much as what you’re serving.

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So here are some ideas of other ways to slice, dice, and rearrange the mathematics currently taught in high schools. (And hey, maybe we’ll want to switch out an ingredient here or there, too.)

I’ll lay out four proposals.

First up…

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This is an approach with a simple goal: Make Math Useful. Continue reading

The Student-to-Teacher Dictionary

Sometimes students say precisely what they meant. “I don’t understand the question” means they don’t understand the question. “This is too hard” means it’s really too hard.

But sometimes, it takes a little translating…20161024085458_00043

Half of my classroom conversations go like this.

Student: “I don’t get the question.”
Me: [longwinded, exhaustive explanation of what the question is asking]
Student: “Yeah, I knew that. But I don’t get the question.
Me: “Oh. This is one of those conversations.”

Continue reading

A Quadratic of Solace (or, Maybe Math Class Has a Purpose, Question Mark?)

I find that lots of students are really good at how.

Like, how do you factorize a quadratic? How to you differentiate a cubic? How do you solve a system of simultaneous linear equations? How do you poach an egg?

(Apparently you need a gentle whirlpool to get the egg moving. Whirlpools: the unsung hero of the breakfast table.)

Why are they so skilled at how? It’s because students like procedures. They like certainty, clarity, the feeling that you know exactly what to do at every moment.

But they struggle with why. And – even more basically – they struggle with what.

For example…

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I find that questions like this elicit one of two responses from students. Either this:

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Or this:

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These aren’t questions students are accustomed to answering in math class. In history, perhaps, where they have to write IDs of historical figures and events; or even in science, where they have to understand each component’s role in a theory.

But not in math. We math teachers tend to ask lots of how questions, and not so many what questions.

If you ask me, that’s sort of sad. They’re experts in how, and they can’t even tell you what the how is for.

And in this case, it turns out, there’s a pretty satisfying answer. Continue reading