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.


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

The Professor with a Billion Students


This September in Germany, between talks at the Heidelberg Laureate Forum, I managed to catch a few minutes with Cornell professor John Hopcroft.

He’s a guy with bigger things on his mind.

“I’m at a stage in my life,” he says, “where I’d like to do something which makes the world better for a large number of people.”

Skimming Hopcroft’s C.V., you start to wonder: Um… hasn’t he done that already?


Born to a janitor and a bookkeeper, he grew up to become a foundational figure in computer science. Exhibit A: His textbooks on automata, algorithms, and discrete math have been adopted across the world. (His most recent one—on data science—is free online.) Exhibit B: He has a distinguished research record, highlighted in 1986 with a Turing Award— the closest thing to a Nobel for computer science. And finally, Exhibit C: During a decorated teaching career, he was twice named Cornell’s “most inspiring” professor.

With all this, you’ve got to figure he’s done at least a little good for a few people, right?

Well, Hopcroft has a larger number in mind: 1.3 billion.


Hopcroft has become an advisor to Li Keqiang, the Premier of China. He describes this as “the opportunity of a lifetime”: to transform Chinese education for the better.

“They have one quarter of the world’s talent,” Hopcroft says, “but their university educational system is really very poor.”

What makes Hopcroft—working-class Seattle-ite turned Ivy League professor—think he can leave his mark on a country as vast, distant, and internally diverse as China? Isn’t this like a swimmer trying to steer an aircraft carrier?


“A couple of things are going in my favor,” he says. First, he is apolitical. “I don’t have any special agenda to push in China,” Hopcroft explains. “I’m pushing education.”

The second is subtler, and carries echoes of Hopcroft’s engineering background.

“I understand the scale of the problem,” Hopcroft says.

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Who Subsumes the Subsumers?

a final dispatch from the fourth annual Heidelberg Laureate Forum

At a conference like the HLF—bringing together researchers from across diverse fields—you’re bound to run into a few turf wars.

Mathematician vs. computer scientist.

Mathematician vs. physicist.

Even—in one delicious exchange on Tuesday—mathematician vs. mathematician.

In his morning talk, Sir Andrew Wiles emphasized a fundamental change in his field of number theory over the last half-century: its move from abelian to non-abelian realms.


Afterwards, Michael Atiyah—fellow mathematician and fellow Sir—rose to comment. After praising a “brilliant talk,” he started to redraw the intellectual boundaries.

“The whole idea of doing non-abelian theory permeates not just number theory,” Atiyah said, “but physics and geometry and vast parts of mathematics. What we’re really looking for is an overall unification in some distant future.”

Wiles mostly agreed, then laughed: “We’ve had this discussion before.”

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When You Learn a New Language to Read a Single Book

a dispatch from the fourth annual Heidelberg Laureate Forum

In 1984, the legendary Alexander Grothendieck released one of the greatest mathematical texts of the century: “Esquisse d’un Programme.”

It became a viral hit. Like an epic novel, it painted a sweeping vision of the blossoming field of algebraic geometry. The topic would soon come to dominate research mathematics, and Grothendieck pointed the way.


The young Vladimir Voevodsky was desperate to read it. There was just one problem: it was in French, and Vladimir didn’t speak French. So he did what any ordinary person would do.

He waited for the translation.


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Sometimes the Noise is Signals, Too

a dispatch from the fourth annual Heidelberg Laureate Forum

Early in his talk, computer scientist John Hopcroft noted a funny fact about clustering algorithms: they work better on synthetic data than real data. But this is more than an odd tidbit about software.

It’s an insight into the nature of our world.

When we invent our own synthetic data, we try to mimic real data by mixing true information with random distraction–combining “signal” with “noise.” But in real data, the divide isn’t so clear. What often looks like noise turns out to be the deep structure we haven’t grasped yet.


The noise is just signals you can’t yet hear.


Hopcroft’s insight: data doesn’t just have one structure. It has many. If I scanned notebooks from a hundred people, and made a database of all the individual letters, I could sort them lots of ways. Alphabetically. Capital/lowercase. Size. Darkness. Handwriting. Each of these is a different layer of structure.

And to understand data–and the world–you’ve got to reckon with all those layers.

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Collaboration (in Cartoons)

a dispatch from the fourth annual Heidelberg Laureate Forum

Mathematics is lonely work. Or so the romantic stereotype has it: the lone genius in an empty library. The sage on the mountaintop. Andrew Wiles in the attic.

But most mathematical work is profoundly collaborative.

I caught four young researchers between events, and gave them the prompt: On one piece of paper, show me the essence of good collaboration.

Their drawings? Four different flavors of brilliant.

First, from Ana Djurdjevac, born in Serbia and now studying partial differential equations:


In pursuing PDEs, Ana perhaps missed her other calling: as a painter specializing in stark symbolism.

“First, you need different types of people,” she explained. “Men and women. Standing and sitting.”

“Gray and purple,” I added. Continue reading

The Essence of the HLF, in One Story

a dispatch from the fourth annual Heidelberg Laureate Forum

At most scientific conferences, you find a cross-section of ages: elder statesmen, rising stars, mid-career workhorses, maturing postdocs, and fresh-faced PhD candidates. The HLF brings together the two extremes: the most legendary of the legends, and the most bright-eyed of the youngsters.

What do such disparate groups have to talk about?

A lot, it turns out.


During the opening ceremony, Jean-Pierre Bourguignon—the president of the European Research Council—told a story from his own days as a young mathematician.

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