Born in the Warsaw ghetto and growing up in France during the rise of Hitler, Benoit Mandelbrot found escape from the cruelties of the world around him through mathematics. Logic sometimes makes monsters, and Mandelbrot began hunting monsters at an early age. Drawn into the infinite promulgations of formulae, he sinks into secret dimensions and unknown wonders.
His gifts do not make his life easier, however. As the Nazis give up the pretense of puppet government in Vichy France, the jealousy of Mandelbrot’s classmates leads to denunciation and disaster. The young mathematician must save his family with the secret spaces he’s discovered, or his genius will destroy them.
Liz Ziemska’s Mandelbrot the Magnificent is a stunning, magical pseudo-biography of Benoit Mandelbrot as he flees into deep mathematics to escape the rise of Hitler—available November 14th from Tor.com Publishing.
Aliette is cooking cauliflower once again. My wife favors an old recipe from Brittany. First she blanches it in rapidly boiling water with salt, butter, and clove. Then she fries it in mouton fat with parsley, chervil, and thyme. The curves and angles of her face as she works under the unforgiving light of the kitchen are still beautiful, even after five decades of marriage. I have always been a great lover of geometry. A dash of vinegar and white pepper completes the dish, so much more palatable than the way Mother used to prepare that hateful vegetable. My job was to chop the head into bite-sized pieces (pallid brain leached clean of thought), but it was cauliflower that saved my family that summer in 1944, so over the years I have taught myself to be fond of it.
Aliette sets the plate down next to my laptop, a gift from our children for my eightieth birthday, so I can finally finish my memoirs (or begin them).
“Eat,” she says, “while it’s still hot.”
I take a forkful and admire the curlicues of steam coming off the tiny florets, each part so like the whole, only smaller (an infinite downward repetition). Cauliflower: my madeleine, memento mori, Mandelbulb, the model for the fractal theory of nature that bears my name. I take a bite and the past returns to me with pitiless clarity.
Warsaw
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I was born on November 20, 1924, at Ulica Muranowska 14, a street that would soon become part of the Warsaw Ghetto. My brother, Léon, was born fifteen months later. We lived in a nice fourth-floor apartment filled with dark wood paneling, richly upholstered furniture, and our most precious possessions, books. The front entrance and sitting room were dedicated to Mother’s dental practice. All day long patients would come to our home, everyone from the poorest peddler to the wealthiest diamond merchant. “Teeth, a more effective leveler of society than Bolshevism,” Mother liked to say.
I have many happy memories of my brilliant Uncle Szolem coming over for dinner with his wife. Father would be working late at his wholesale ladies’ hosiery business, Mother and Aunt Gladys would be busy in the kitchen, and Uncle Szolem would entertain us with stories about the many mathematicians he idolized: Euclid and his geometry, Fibonacci and his integers, Poincaré and his unsolvable theorems, Gaston Julia and his rational functions; but it was the story of Kepler’s ellipses that truly captured my imagination.
“Johannes Kepler discovered a brand-new law of nature,” Uncle Szolem held forth from our best armchair, his manicured fingers pulling shapes out of the air like some metaphysical magician. “Kepler borrowed the conical slice from Apollonius of Perga, and produced a curved shape with not one, but two foci.
“Then Kepler applied that shape to Aristotle’s classical theory of planetary motion, whereby all heavenly bodies, including the sun, orbit the earth in perfectly circular paths . . .
“ . . . and instantly all those ‘anomalies’ that had previously bedeviled astronomers—Mercury retrograde, Saturn return—disappeared, just by replacing a circle with an ellipse.
“So simple!” Uncle Szolem snapped his fingers.
Suddenly I found myself astride one of those painted carousel horses at the Warsaw Zoo, the ones that Mother had never allowed me to ride for fear that I might fall off and break my head. Round and round we rode to the plinking sounds of the calliope, until my horse broke free from its circular orbit and began galloping along a tangent line, gaining speed as we shot off into the distance, the wind tossing my hair, tossing the horse’s no-longer-wooden mane into my face, and just as we reached the outer perimeter of the park, we were snapped back by the invisible force of that second focal point. Relentlessly, our path curved inward, centrifugal forces tugging at my belly button, as we were pulled back in the direction of the carousel.
I came to rest once again in our living room. The chandelier above my head tinkled in harmony to the molecules that had been displaced upon my reemergence into this world. Uncle Szolem hadn’t noticed anything; in fact he was still talking, though I was no longer so interested in what he was saying.
“I want to make a discovery just like Kepler’s,” I announced, my life’s purpose suddenly clear to me, “a discovery so simple, so obvious, that no one else has thought of it.”
Uncle Szolem squinted down at me. “Have you been sitting here the entire time?”
I hesitated. “Yes?”
Uncle Szolem shook his head. “What you wish for is nothing but a childish dream,” he said dismissively.
I looked at Léon, who was busy running a toy truck through the interweaving vines of the Persian carpet. He was a child, I was not.
“Why can’t I be like Kepler?” I insisted. No doubt Kepler had also once ridden the carousel horse to the land of curves.
“Mathematics needs men who are willing to dedicate their lives to her without thought of reward,” said Uncle Szolem, selfless mathematician. He stood up and smoothed the creases from his trousers. “Yearning for fame is childish,” he said as he left the room.
At six years of age, I had disappointed my uncle, and he had lost interest in me. But I had learned something about myself that day: opposition made me only more determined. (Also, shapes can have very curious properties.)
* * *
The Depression hit Poland especially hard and awakened ethnic strife. I was only eight years old, but I already knew that the Jewish situation in Warsaw was desperate. Uncle Szolem left Poland for Paris, where he had been offered a teaching position at one of the universities. I was sorry to see him go, even though I was still tender about his dismissal of my Keplerian dreams.
Father joined his brother to see if he could build a better life for us in France. Unfortunately, there were no prestigious academic positions waiting for him. Father had been sixteen years old when Szolem was born. Their mother died soon thereafter, so Father had been forced to leave school to take care of his little brother, doing anything he could to make money. Eventually he settled into the rag trade. He never complained about the work he had to do to support his family, though the Mandelbrots, originally from Vilnius, were descended from a long line of Talmudic scholars. Who knows what Father would have become had he been able to continue his studies?
Not long after Father left Warsaw, Hitler became chancellor of Germany, President Hindenburg died, and the political landscape began to deteriorate. Soon there was talk of another war. Mother had grown up in St. Petersburg and survived the Russian Revolution. She knew what was coming, knew the price of hesitating. In 1936, three full years before Hitler invaded Poland, Mother, Léon, and I left Warsaw, taking nothing with us but some essential clothing, family photographs, and the dental equipment that could be easily packed and carried. (Friends who had been reluctant to leave their park-view apartments, their Meissen china, their illusory dreams of status, did not survive.)
Paris
Father had rented two narrow rooms in the 19th Arrondissement, set end to end, like a railroad compartment. There was no hot running water, no bath. The first time Mother entered the apartment, she sobbed inconsolably. By the second day she had recovered and taken control of the household. From then on we were all forbidden to speak Polish. Mother brushed up on her schoolgirl French. Soon she was able to write flawlessly and speak with almost no accent. Father lugged home an obsolete multivolume Larousse Encyclopedia and I read it cover to cover. (My accent, however, remained atrocious, like French filtered through Cockney.) I was kept back two grades at school, but my good visual memory served me well and I was soon able to master the French spelling and grammar.
In the fall of 1939, Uncle Szolem received a tenured professorship in Clermont-Ferrand, in the Auvergne region of France, and departed Paris with his family for a small town called Tulle. Father and Szolem seemed to be in agreement about this move, but I was surprised—did my uncle not want to live with us in the same city?
The following spring, my parents took Léon and me out of school and sent us to stay with Uncle Szolem, telling us that there was a meningitis epidemic running through Paris and that the fresh country air would do us good. His new house in Tulle was a simple wooden box built on scrubland near the train station, but it seemed like a palace to slum dwellers like us. Aunt Gladys pampered us and taught us French table manners. My brother and I shared a room, which wasn’t ideal, but there was modern indoor plumbing, and out the kitchen door was a small garden. Léon revealed his natural babysitting skills, and he and our new cousin, Jacques, played for hours, which freed me up to pursue my own agenda. I kept hidden my Keplerian dreams and wooed my uncle patiently, incrementally convincing him that I was worth his time. It worked. He became interested in me again and spent many hours talking to me about mathematics and the natural world.
Uncle Szolem began with simple exercises culled from the lycée curriculum: “If Étienne puts a rectangular fence around his cabbage patch, and the patch has a length that’s nine meters less than three times its width, what is the perimeter of Étienne’s fence if the area of his cabbage patch is five thousand six hundred and seventy meters?”
I found this pedagogical exercise almost insulting in its simplicity, as my uncle must have intuited because soon we moved on to more interesting thought experiments adapted from one of Zeno’s paradoxes:
“Étienne tries to walk to the end of his sitting room, but before he can get there, he must walk half the distance, then a quarter, then an eighth, then a sixteenth, and so on. Will he be able to leave this room and join his wife in the kitchen, where the chicken needs plucking for dinner?”
I didn’t have to think about it too long, for the answer seemed obvious to me. “Étienne may never get to the end of his original sitting room, but as he comes incrementally closer to the middle, he kicks up the carpet of our world and creates a space between it and the floor, and as that space grows larger, he will create a parallel farmhouse in which he can live and never have to worry about plucking his wife’s chickens again.”
Uncle Szolem eyed me uneasily and said, “It’s time for you to grow up, Benoît.”
* * *
One morning, a few weeks into our stay, a telegram arrived from my parents. I remember the breakfast Aunt Gladys had served that morning: toasted buckwheat groats with fresh milk and raisins, the aroma so distinct, so warm and nutty. But the look on Uncle Szolem’s face set a frozen stone in the middle of my stomach.
“Germany has invaded France,” Szolem announced. Aunt Gladys pulled little Jacques out of his high chair and cradled him in her lap.
“Your parents sent this from the train station,” Szolem said to me and Léon, a hopeful smile on his normally somber face. “They will arrive in Tulle by nightfall.”
What followed was a week of terror and anguish, during which time my brother and I became convinced that we were orphans. I let Léon climb under the covers with me at night, though he kicked like a mule and sometimes wet his bed. Finally, toward nightfall of the eighth day, my parents arrived. There had been no trains; all roads heading south had been clogged with cars and trucks piled high with household goods. My parents had left everything behind in the Paris apartment, except for Mother’s precious dental equipment, and walked over four hundred kilometers to get to Tulle, crossing unplowed fields, avoiding main roads, sleeping in abandoned farmhouses.
My parents looked tired and bedraggled when they finally arrived, much older than I remembered them. Mother’s lips trembled as she crushed me to her breast. There were crescents of dirt under her fingernails. The stench of her unwashed body brought tears to my eyes, and Father looked like a golem that had risen out of a dried-up riverbank. At that moment there was a tiny shameful part of me that wished I could go on living with Uncle Szolem and Aunt Gladys.
Excerpted from Mandelbrot the Magnificent, copyright © 2017 by Liz Ziemska.
