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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It’s Obvious Why Students Cheat; We Just Can’t Agree on the Reason

If you love cringes – and hey, who doesn’t? – then walk into a school and try to start a conversation about cheating.

Depending on the school, I suspect you’ll find a superficial consensus (cheating is terrible! and, thankfully, our students do it very rarely!) masking deep rifts. Is the problem with cheating that it undercuts your own learning? That it steals glory from classmates in the zero-sum competition for grades? That it betrays the teacher’s trust? Are all acts of cheating equally terrible, and if not, what does that mean for “zero tolerance” policies?

We all know cheating is bad. But we seem unable to talk honestly about why.

So, I offer up these dialogue-starting cartoons, a few badly drawn meditations on the most basic question: Why do students cheat?


Is cheating a crime of character, or of opportunity? Continue reading

250 Posts, Still Can’t Draw

This is the 250th post on Math with Bad Drawings.

That’s a quarter-thousand! It’s double five-cubed! It’s 1/4000 of the way to a million! If posts were days in a pregnancy, this blog is… kinda almost birth-ready! If posts were meters, I’d have walked… to the corner store! If posts were nickels, I’d have… uh, $12.50!

Okay, now that you’re duly impressed, I have a confession: I’ve been hiding comics from you.

Since late 2016, I’ve been posting one-off cartoons to the Math with Bad Drawings Facebook page. I encourage you to “Like” the page so you can see them all. But in case you’re some kind of conscientious objector to social media (if true: thanks for exempting WordPress from your boycott!) here’s a (partial) retrospective collection.20160718093148_00012

I find it funny when people claim that “percentages over 100% are impossible.” They’re not just possible – they’re easy! For example, the United States National Debt is currently 105% of the United States GDP.

Now, how hard is it to rack up a little debt? A trillion here, a trillion there, and it adds up surprisingly fast. Easy.


Not depicted: the graffiti itself, which is also a feeble statistics pun.

(That’s what the purple parent is really mad about, obviously. Puns aren’t even jokes, really; they’re just a lazy mind eating its own language. That’s the real deviancy here.)


And the Sigma’s Greek glare!
The terms added in air!
Gave proof through the night
that our sum was still there…

Oh, say does that star-indexed banner yet wave…

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Lines Beyond y = mx + b

What are my professional goals? Many days, I’ve got precisely three: I want kids to feel curious, then frustrated, then ohhhhhhhh.


Math is pretty great for this. It’s full of puzzles and mysteries. Why do the angles in a triangle always sum to the same thing? How many moons would fill the sun? Why is it so hard to roll double sixes? There’s plenty here to excite curiosity, to elicit frustration, and to satisfy the intellectual itch for ohhhhhhh.

But there’s a common problem: too often, kids can beat the puzzles without feeling any of those things.

I find this, for example, with lines in the coordinate plane.

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