5 Ways to Troll Your Neural Network

Alexei Efros, a laureate of computer science, opens his lecture here in Heidelberg with a striking fact: 74% of web traffic is visual.

Foto: Bernhard Kreutzer für HLFF

“Everybody’s talking about big data, the data deluge—all this data being rained down on us,” Efros says. “But I think a lot of people don’t appreciate that most of the data is actually visual…. YouTube claims to have 500 hours of data uploaded every single minute. The earth has something like 3.5 trillion images, and half of that has been captured in the last year or so.”

Today, teams of computer scientists like Efros are working to understand that data via “deep learning” algorithms. First, you prepare a network of connections. Then, as a training regimen, you show it vast quantities of photographs. With time, it learns to accomplish extraordinary tasks—writing captions, colorizing black-and-white photos, recognizing animal species.

Unless, of course, you troll it. Continue reading


The Professor vs. the NSA

Today, Martin Hellman stands before a crowd of hundreds, narrating the history of his research in public key encryption. It’s foundational: internet security is built on mathematics, and Hellman (along with collaborator Whitfield Diffie) helped to fashion that math. Throughout the talk, you can see their adorable bromance: Diffie heckles from the front row, and Hellman banters right back.

Back in the 1970s, Hellman and Diffie couldn’t have known that their work would lead to this stage. In fact, there was a likelier destination.

Federal prison.

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“It’s July 1977,” Hellman tells the audience. “Whit and I are involved in a major fight with NSA over the data encryption standard.” Continue reading

No, There’s No Nobel in Math

It’s the very first on the Nobel Prize’s list of frequently asked questions: Is there a Nobel Prize in Mathematics?

Alas; it turns out that Alfred Nobel didn’t much appreciate the icy abstractions of mathematics. And before you ask, there’s no prize for computer science, either.

Faced with this emphatic snub, what’s the best response for the math/CS community? Should we pout? Throw tantrums? Pen angry, tear-stained letters to the King of Sweden? Gossip that Nobel was just jealous because his fiancée slept with a mathematician (fact-check: probably false)?

Though not above juicy gossip, the math/CS world has mostly pursued a different solution: Give fancy prizes of our own. Today, these five prizes rank among the highest in math and computer science: Continue reading

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.

Continue reading

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 me 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.

Continue reading

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.”

Continue reading