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

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.


Continue reading

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.

Continue reading

21 Essential Quotes from Sir Michael Atiyah

a dispatch from the fourth annual Heidelberg Laureate Forum

The joke among bloggers over breakfast: What award hasn’t Atiyah won?

(My suggestion: the gold glove? But maybe he’s won that, too.)

A Fields Medalist and Abel Prize recipient, he is a living legend: his index theorem (developed with Singer) revolutionized both mathematics and quantum physics.

In a sweeping talk on Monday morning, he leapt so nimbly from the upper echelons of abstraction to the gritty details of reality that you began to realize that they are one and the same. The purity of mathematics, the practicality of computer science—they’re interwoven.

Here are 21 quotes that capture the experience of hearing this knighted mathematician, a thinker of extraordinary depth and curiosity.


First, he introduced himself as our tour guide through the last century of theory in mathematics and computer science:

  1. I’m as new as the hall.
    on lecturing in the so-called New University Building, built in 1929—the same year as Atiyah’s birth


  1. I’m going to be your tour guide of the last century. But don’t believe everything the tour guide says. They exaggerate.
    a self-effacing introduction to his far-ranging talk

   Continue reading

The Universal Language (in Translation)

a dispatch from the fourth annual Heidelberg Laureate Forum

A combinatorist working in India, Manjil Saikia is soft-spoken and super-knowledgeable: we chatted about Isaac Asimov and the history of the Fields Medal before getting into his passion project, which (like mine!) is a blog.

It’s called Gonit Sora.

That’s Assamese for “Gateway to Math.”


As a monolingual American, it’s easy to forget just how easy I have it. My native tongue happens to be the global language. Case in point: I blundered into Germany yesterday not speaking a word of German. No problem! For me, provincialism carries no penalty.

But for Manjil, growing up in northeast India, he had to fight for access to knowledge in a world that catered far better to folks like me. When the internet arrived in his home at age 18, it was a revelation—but even online, he had to leap linguistic hurdles. There were almost no sources on math and science in his native Assamese.

It was English or bust.

Continue reading

In a Quaint German Town, Mathematicians Converge

You’d like Heidelberg.

I mean, maybe you wouldn’t. Do woodland landscapes enrage you? Are you repulsed by chocolatiers and scenic castles? Do you shudder at the thought of nibbling on a handmade sphere of marzipan and nougat cream?

If so, Heidelberg is not for you.


As for me, it’s pretty heavenly.

I’m here as an invited blogger to cover the fourth annual Heidelberg Laureate Forum. Huge thanks to the HLF team for inviting me—and to the year 2016 for making “invited blogger” my bizarre unearned reality.

The HLF is a meeting of minds. Those minds include:

  • 22 Laureates from the highest echelons mathematics and computer science, ranging from the “father of the internet” (Vincent Cerf) to the man who solved Fermat’s Last Theorem (Sir Andrew Wiles)


  • 200 Young Researchers, whose work spans every area of math and computer science, and who hail from 56 countries including Switzerland, Spain, Sweden, Sudan, Sri Lanka, South Korea, Slovakia, Singapore, South Africa, Serbia, and Saint Kitts & Nevis—and that’s just the S’s.


I’m here to watch, to listen—and to eat handmade spheres of marzipan and nougat cream.

The conference’s goal is a simple one: to build community. Today’s grand masters will share meals, conversations, and offhand wisdom with tomorrow’s research leaders.

Continue reading