Piet Hein's Problems
His inventions and troubling behavior
In 1966, LIFE published “A Poet With a Slide Rule,” a long, glowing profile of Danish polymath Piet Hein. Amidst all the praise—“He found a shape that had never been used before”; “He was Neils Bohr’s mental ping-pong partner”; “He and his sly whimsy eluded ‘thick’ Nazis”—the reporter focuses, for a few troubling sentences, on Gerd Ericsson, the successful Swedish actress who became Hein’s fourth wife.
“I was accustomed to actors losing their tempers and shouting,” she tells LIFE. “It’s just the way theatrical people behave. But one day I thought, ‘My God, for him it’s real.’”
Two years later, in 1968, Gerd would be found dead in her kitchen, next to the stove, only 36 years old. She left behind two sons, ages 12 and 5, and her husband, age 63.
Hein is known in America mainly to mathematical enthusiasts, but remains prominent in his native Denmark, mainly for his poetry. Those poems, known as “grooks,” have been translated into 20 languages with over a million and a half copies sold. He maintained relationships with Bohr, Einstein, Norbert Wiener, and Charlie Chaplin.
Last year marked the publication of Peter Borberg’s 551-page Danish biography of Hein—and it’s only the first half. Around its release Gerd’s older son, Jotun, now a mathematics professor at Oxford, sat for an interview with Bo Bjørnvig of Weekendavisen to speak about his parents. Most of it is incredibly damning. I wish I didn’t have to rely on Google Translate, but it’s painful either way:
She was often beaten during some of our tantrums. I remember how one night, when I was 8-9, I was woken up by noise and screaming. When I came out into the hallway, mother was driving away in a taxi, and I stayed out in the hallway until she came back with the doctor. Her face was severely swollen and she had had a nosebleed from the blow [Hein] had given her. The doctor was begging to be allowed to go to the police.
This was not an isolated incident. In her autobiography, Tove Ditlevsen (who Hein had an affair with) quotes an earlier lover of Hein’s: “He is a dangerous man, created to make many women unhappy.” Birgit Tengroth, a Swedish friend of Gerd, likewise describes an upsetting visit to the Hein home in her memoir “Jag trodde du var död!” The two boys try to get Tengroth to sleep over, while Gerd tries to reassure her friend that she’s really alright: “Oona (Chaplin) has it ten times worse than me.”
Gerd was hospitalized with what sounds like a major depressive episode just weeks before her death, an apparent suicide. The doctor’s notes, according to Jotun, describe Hein as overbearing, controlling, disliked by his own sons. Jotun was sent to live with a foster family soon after his mother’s death. Hein wouldn’t pay them. He was stingy, abusive, self-obsessed.
None of this, to my knowledge, appears yet in English.
I started looking into all this while researching a shape that brought Hein fame in America. It began with Martin Gardner, who in 1956 parlayed a Scientific American article (on flexagons) into a monthly column on mathematical games. He grew interested in HEX, an out-of-production Parker Brothers game that Hein invented. (Hex is terrific.) Gardner reached out to Hein about the game. Their correspondence and a friendship flourished.1
Gardner revived interest in Hex and would cover other Hein inventions over the years, bringing him a measure of fame. (“I shall never forget that I am your discovery, perhaps even creation” Hein wrote to Gardner in 1966.) But nothing struck a chord with the audience quite like the superellipse, largely thanks to the accompanying origin story.
That story goes like this. In 1959, Stockholm razed a bunch of old homes in the name of urban renewal. They ran traffic arteries through the rubble, creating a rectangular patch of city and an urban-planning problem—what shape to make the public fountain inside the rectangle? They didn’t want to make it circular (or elliptical), since that would waste space in the frame. They wanted the fountain (and underground shopping center) to be shaped somewhere between an ellipse and rectangle. What shape could that possibly be?
The chief architect was an old friend of Hein’s and knew he liked this sort of thing. Hein took the phone call and reportedly said, “I think a curve with the same equation as an ellipse but with an exponent of two and a half would do it.” The graph of that equation does, in fact, look like something halfway between a rectangle and an ellipse. Hein called it the superellipse.
I don’t mean to be a jerk—but couldn’t anyone have thought of this? Maybe not the equation. But who needs the math at all? Go ask literally any artist for something between a circle and a rectangle, I promise you’ll get it. It is not that hard. Whatever. They asked Hein, so he gets the credit.
After Gardner’s column came the LIFE profile, then another huge, even more ridiculous profile in Esquire. It was titled “King of the Supershape” and it opened with an overheard photo of Hein splayed out on a huge blue superelliptical table—fully clothed, thank God.2 The whole thing has an Austin Powers vibe. “Civilization's oldest war is that between round and rectangular forms,” Esquire declares. “But now, peace. Behold the super-ellipse.” Give me a break.
Hein was not a research scientist or mathematician. He made money a few different ways: from mathematical toys—like Hex, or his brilliant Soma Cube—from his books of poems, from his patents, and as a designer. He had sleek, minimilistic tastes, some physics training, an obsession with abstract clarity, an interest in curves, and a knack for lamps.
Hein soon created and sold superelliptical dishes, tables, rugs. He spun the superellipse into three dimensions, yielding a toy for your desk—the superegg. The superegg is stable on its ends, though it looks just as goofy and inelegant as the superellipse. It’s not surprising that it’s stable, right? I mean, it’s pretty flat on the ends. I guess it’s supposed to be beautiful.
For the record, I also dislike Hein’s poetry. His “grooks” are tidy and clean like his games, but also self-satisfied and cloying. To be fair, he started publishing them when Denmark was under Nazi occupation and he was head of the anti-Nazi union, trying to sneak anti-Nazi messages past the occupying censors—that’s cool. But, personally, I just don’t get much out of this:
LOSING FACE
The noble art of losing face
may one day save the human race
and turn into eternal merit
what weaker minds would call disgrace.“Undiluted Hocus Pocus” is Martin Gardner’s autobiography, written late in his long life. In it he briefly touches on his relationship with Hein. “Piet Hein visited me twice, and we became good friends. On his second visit he brought along his beautiful wife. A native of Iceland, she had become one of Denmark’s famous actresses.” I don’t know why he said “Iceland,” but that’s all that’s been written in English on Gerd—at least until I sent Jotun’s interview through Google Translate and quoted it here.
In 2015, Numberphile, the popular math YouTube channel, released an episode about the superegg. It tells the familiar Stockholm story first told by Gardner. It mentions nothing about Gerd or Hein’s behavior. Of course not—it’s a mathematics video. It would be weird to jump into all that dark stuff, right?
It’s at least partly a question of context. I’m not about to start talking about Piet Hein’s marital life while chatting up students about funny shapes. I’m not sure how I’d approach it in something like an online video, where the context is fuzzier and out of my control. Maybe Martin Gardner should have said something. I don’t know.
There’s a larger conversation about famous monsters, and this is probably part of that. Anyway, I’m struck by something else—knowing about his personal life makes Hein’s intellectual story make more sense.
Think about it. If you gave me a rectangle and a crayon, I’d get close to what Hein made, though I probably wouldn’t write an equation. But Hein liked precision, structure, a kind of cleanliness. He took an urban planning question and turned it into a puzzle. It’s the same sort of tidiness-in-the-extreme that his poetry exhibits. That’s not what I like in my art—I like big messy feelings and huge dramatic gestures. I don’t like aphorisms very much. But Hein sure did.
In art and life, Hein thrived when the rules of the game conformed to his expectations. “If you were alone with him and discussed something that interested him, you would get a lot of attention.” But step outside those lines, and Hein would fight to fence you back in.
There is a poem by Hein that mathematicians are particularly fond of:
PROBLEMS
Problems worthy
of attack
prove their worth
by hitting back.Along with everyone else, I’ve taken it as neat couplet about problem solving. Given what I know now about Hein I’m inclined to expand it. What happens when people become the problems? Does intellectual rigor have a tendency to make us demanding of others? Do they “hit back”? Isn’t it, quite possibly, a more interesting (if disturbing) poem knowing the harm Hein inflicted on the ones he loved?
I can’t say for sure. But God bless Jotun for surviving and telling his tale.
According to “Hex: The Full Story,” Gardner got caught up in a priority dispute over the invention of Hex. The players were Hein and none other than John Nash, of A Beautiful Mind fame.
And we’re lucky he was clothed. Here’s biographer Peter Borberg: “Piet Hein had a free relationship with the body, nudity, and he turned against conformity, titles and authorities.”