The Goose Girl
"Are you here to find a husband?"
"I'm here to study. Like you."
Truda Baum leaned away from Oswald Teichmuller's pink eyelids and thin lips. She was not like him. Truda had moved in a straight line, from her home and from her early mathematical studies, towards the most famous female theorem maker in the world. But by the time she had arrived at Georgia Augusta University in Göttingen to study with Professor Emmy Noether, it was too late.
Like a girl in a fairy tale, Emmy Noether had begun by sweeping ashes, then risen from them. As she stepped from the gray ash, she outlined differentiable symmetry. She had cleaned classrooms and remained silent in the back, absorbing ideas that later transformed into the questions she would ask of Albert Einstein. Noether became the backbone of the university's Mathematics Institute in Göttingen.
Then the Nazis intervened. They made any Jew who hadn't fought in the previous war leave the university. Before Truda Baum arrived for her wartime education, Emmy Noether had escaped to a far-away place called Pennsylvania.
Oswald-with-pink-eyelids leaned in closer. "Let me know if you need any help."
"I'm engaged," Truda said.
Truda was one of only two female students in the math department, and the other one had been at Göttingen for six years. Despite his thoughts about the incompatibility of women and mathematics, her father had given permission for Truda to attend Georgia Augusta University's lauded Mathematics Institute when her fiancé took a job at the hospital, As long as Truda was pursuing her young doctor, the advanced studies made a kind of sense to him.
In one of her classes, Professor Landau was not allowed to stand in front of the class and teach. Instead, he listened from his office as an Aryan graduate student who worked under him taught the classes using the professor's notes.
Truda wrote down the equations and pondered. Did Professor Landau listen to the graduate student stumble over the complexity of the equations? Why did he stay in Göttingen when the Nazis refused him? Even Emmy Noether had gone to America when the Nazis told Jews they couldn't work at the university, and she had worked for free when they wouldn't let a woman be an expert mathematician.
Filing out of the classroom one gray afternoon, a newer student from Berlin asked, "Why can't Professor Landau teach his class? He served in the war, yes?" The Reich made exceptions for Jews who had fought for Germany in the previous war, so Professor Landau's veteran status should have preserved his job.
Oswald Teichmuller lifted his chin and narrowed his eyes into pink slits. "We want Aryan mathematics and not Jewish mathematics."
"What is the difference?" Truda realized she had spoken the words. Her male counterparts turned to her. They didn't like having a girl in their classes, so usually Truda kept her head down and hid her scores, which far surpassed theirs.
The blond boy pressed his lips together now. "If you don't know the difference between a pure Aryan and a dirty Jew, perhaps you are not a true German." Oswald leaned in far too closely. "Or perhaps your delicate constitution struggles to understand."
Truda escaped through the arch of the Mathematics Institute into the square, walking quickly towards the fountain where the Gänseliesel statue stood surrounded by geese and carrying a basket of flowers. She made a promise to herself to find a flower to tuck beneath the dark Gänseliesel's arm, a spot of color in this winter war. When she finished her degree, Truda Baum would also be able to kiss the Goose Girl statue, the tradition of all advanced students.
A girl stood in the courtyard, in front of Weender Gate framing the once illustrious, now Jew-less, Mathematics Institute. She was small, with wispy curls and homemade shoes. She looked very young to be a student at university. Still, the sight of a girl in front of the imposing Mathematics Institute prompted Truda to speak. "Do you need help?"
"Where has Professor Noether gone?" the girl said. From a distance, the girl seemed a child of ten, but when the girl spoke it was clear she was older.
"She's left Germany."
"When will she come back? I need to find her." The girl rubbed her hands together and let her eyes travel up the side of the institute towards the tallest windows.
"I'm sorry," Truda said. "She won't be returning."
A small, cold hand touched Truda's arm. "Can you help me?"
"What? I don't know you. Professor Noether is no longer at this university. She has gone to the U.S." Had this ragged girl travelled to Göttingen in hopes of studying with Professor Noether?
The small girl nodded. No one was surprised anymore when people escaped Germany.
"Does she have any friends?"
"Friends?" This conversation about friends could be incredibly dangerous in Göttingen, in a mathematics institute with all of its most brilliant pieces subtracted, and in the middle of a historic town with all its safeties gone.
The girl's tiny features and battered basket reminded Truda of the statue behind her, the Gänseliesel with her flowers and geese. She took a deep breath. "We were sent for Emmy Noether. I waited and watched for a woman professor by the Mathematics Institute. You were the only one. Can you help us?"
"I'm not a professor, just a student."
"I need help."
"I don't know how to get in touch with her."
"My friend is in trouble. We need help."
Truda led the girl to the alley adjacent to the square. "Shh. You know, speaking of being in trouble is enough to actually get you in trouble during this war."
"Will you help us? My friend is in trouble," the girl said again.
"I don't even know you." Truda felt too much saliva in her mouth and wanted only to go to her room to read mathematical theorems.
"You do know Emmy Noether. My friend Helka's father, whose name is Eligius Balaban, told us that Emmy Noether would help us here in Göttingen and now we really need help." The hope in Olga's eyes made Truda turn away.
A pair of soldiers leaned against the east side of the gate.
"I cannot help you."
Truda hurried away from the birdlike girl.
In her differential equations class the next day, Viktor Strauss took the seat next to Truda. "What made you choose the Mathematics Institute?" he asked.
"I wanted to work with Emmy Noether," she said.
"I as well," Viktor said, shaking his thinning hair in a frustrated nod.
"I wonder what the Nazis know of mathematics." As soon as the words were said, Truda looked behind her. These were not things to be said.
"Professor Noether was more forgiving than the Nazis," Viktor said. He told Truda a story about Emmy Noether. In the days when Emmy Noether wasn't allowed to use the lecture halls, she had gathered students in her own home.
A student had arrived one night wearing a Nazi uniform.
A classmate told Truda that everyone froze, expecting Professor Noether to expel the student with his swastika-ed arm. But she didn't. "Even those in their brown shirts are welcome," Professor Noether said and led everyone through the conservation laws.
Truda reread Emmy Noether's paper which explained the theory of ideals as the left and right ideals in a ring. Truda read the paper over and over, hoping to understand the Noetherian ring. If she could understand Emmy Noether's theorems, then the physics of the universe would fall into logical place.
When Nazis purged Göttingen's Jews, the university lost one-third of the math professors and three-fourths of the heads of the math and physics institutes.
The only professor still teaching his own classes after Nazis gutted the Mathematics Institute was Gustav Herglotz, and he stuck to numbers, refusing to comment on the excessive rains or on the shortage of chalk. He pressed his palms to the chalkboard when the chalk was nothing more than a tiny white stone.
But as mathematics asserts, nothing is ever truly gone.
When his pressed palms created only sound and not lines, Professor Herglotz spoke the numbers into the air while Truda, Viktor and the other students tried to capture their configuration on the paper.
When class was over, Truda rushed out of the room before one of her classmates trapped her in a conversation in which she might mistakenly talk of Nazis. She must only speak mathematics.
Across the square, beneath the tall spire of St. James, a man with red hair waved at Truda. If not for the wave, she might have pretended not to see him. Instead, she sighed and walked towards the man she had promised her father she would marry.
Her fiancé put his arm across her shoulders. "My Truda," he said. "You look lovely as always. All those equations agree with you."
"If only they would agree with each other," she said, smiling while slipping away from his arm.
"Your jacket is stained," she said. Truda hated to think what it might be, considering the work he did at the hospital.
"This is why I need a wife. What are you working on?" He pointed at the papers in her hand.
"Noetherian rings. Descending chain conditions are key." Truda knew that despite his architectural knowledge of every bone in the body, he didn't push mathematics beyond the measurements necessary for precise surgeries.
"Can you join me for a walk?" her fiancé said. "I've had a thought." Her red-haired doctor put his hand on her upper arm. Truda sighed. Was this marriage? Waiting for him to reveal his next thought? She wanted him to release her arm and perhaps step back a pace.
"What is your thought? Tell me now."
"We shouldn't hesitate to get married," he said. "No need to wait."
"It's bad luck to marry in the middle of a war. Plus, we can't get butter for the cake."
He smiled at her adorable love for butter. Now she sounded like a proper German girl, without her obsession with balancing equations and calculating linear momentum.
"I might have some connections," he said with a wink.
As Truda strolled Göttingen's streets on her fiancé's arm, a small gray figure carrying a basket of coal passed, reminding her of Olga. If she helped a girl who was "in trouble," then Truda might end up in the university prison, if not in one of the camps that no one liked to discuss.
Trouble took mathematically improbable forms during this war, increasing exponentially as it continued. Truda must focus on her studies, to figure out the complex calculations of linear momentum and energy within a system.
Truda walked back to her room through the square, stopping as always by the Gänseliesel. In that story, written by professors at this very university, girls change places and become someone else. These types of transformations are possible: a princess becomes a goose girl, and the most brilliant professor at Göttingen, who just happens to be female, becomes a refugee.
The next day in class, one of the more complex linear equations confused the graduate student instructing Professor Landau's lesson. He stood at the blackboard sweating and stammering until a door squeaked, and a small bespectacled man emerged.
Professor Landau. He cleared his throat and proceeded to clarify, writing notations on the chalkboard.
Oswald Teichmuller shook his white hair and slipped from the classroom.
Only minutes after Ernst Landau stood to teach his own lesson, the door slammed open. Two men with guns entered the room and pointed them at Professor Landau. Both men had red faces, and behind them Oswald's pinkness stood in the doorway.
"What's happening?" Truda asked Viktor.
"The professor isn't allowed to teach the class." Viktor's voice was small and tight.
"But it is his class. He fought for Germany," Truda whispered.
Viktor shook his head with a small movement.
Truda stayed quiet.
They peered from the windows as the Nazis led the esteemed professor by his upper arms away from the Mathematics Institute. For several minutes the students sat silently looking from the retreating figures out the window to the numbers trailing off on the blackboard.
In the doorway, Oswald grinned. Truda wanted to kick in his teeth, but she only folded up her notes.
Once outside the classroom, the students buzzed with the news that the professor had been removed.
In mathematics, nothing ever really disappears.
She wondered where they'd taken Professor Landau. At this university, professors like the Grimm Brothers had a history of resisting tyranny. But resistance got them exiled or worse. If Truda resisted in some way, where would she go and what would she do in the face of the exodus from the Mathematics Institute?
Without the life of the mind, Truda felt she had no life at all. Her father had protested her studies. "A girl in mathematics. You are a silly goose," he'd said. He wanted her to be more like her two older siblings, Liesel and Britta. She shared her blond hair but little else with those two. They loved to talk and to dance and to sing in Heidelberg. Truda loved only numbers and books.
An important-looking man in a robe walked through the Mathematics Institute talking to five other men. "The Jews are roaches. We are creating a more pure area for study."
Truda closed her eyes.
Numbers were pure and non-political. She would focus there.
Integral over Time
Truda sat on the lip of the fountain around the Gänseliesel. This goose girl had beat out men of science. When they had chosen the statue for the square, town officials had two other options, both statues of taller, more intimidating men of science. But the unassuming girl had won out.
"Are you heading for a dance, to the music hall?" Oswald Teichmuller put his hand on her shoulder, making Truda jump. He pulled his lips across his teeth in what was and was not a smile.
She would rather herd geese or feed pigs than dance with Oswald Teichmuller, the Nazi mathematician. And he was not even a good mathematician.
Oswald Teichmuller was a danger, with his blond mustache that twitched when he wasn't speaking, and his moist, red-rimmed eyes.
"I do not dance," she replied. Over by the gate, she saw a small gray figure who might be Olga.
She hoped Olga would not approach with Oswald nearby.
Oswald sat beside her and asked questions about her studies. Truda knew what Oswald wanted was her commendation on him on removing a Jewish professor.
"Our Institute can be proud now," he said. "Don't you think?"
Truda stared at the dark metal of the Gänseliesel. She wanted to picture herself with a wreath of flowers, kissing the girl's cold cheek. She wanted to graduate from an institute renowned for its Jewish mathematicians.
She wanted to be far away from the pink twitch of Oswald Teichmuller's eyelids.
"How long do you sit at this fountain?"
"This is where I come to think at length about mathematics," Truda said.
"Do you need me to explain any concepts?" Oswald leaned in and she could smell a fermentation like sauerkraut on his warm breath.
She tried not to breathe. "No."
Principle of Least Action
After a too-long amount of time, Oswald Teichmuller patted her knee and walked away.
Just a moment later, the girl Olga appeared. "I was waiting," she said.
"Don't go near that man. He is not one of the good ones."
"No, I didn't think so."
"What do you need help with, Olga?" Something about Olga's eyes, something about Oswald's repellent touch, something about Professor Landau's final lesson made Truda speak.
"They are now looking for my friend Helka. If they find her, everything is lost," she said. The girl had delicate bones and a sweetness that made Truda's eyes burn.
"Who is looking?" Truda already knew this answer.
Olga stared out at the metal-gray sky. They both knew that in Göttingen, the ones being sought needed help.
"I stood in this square when they chose us for work." Olga nodded towards the open area in front of the Gänseliesel.
"Who chose you?"
"No one. I am too small."
"Do you work now?"
"The restaurant woman, she lets me work there. She is kind. But she cannot help Helka escape. Can you help?"
Truda let her thoughts blink as the girl stood in silence, unwilling to speak but also unwilling to leave. How could she help a girl escape Nazis? She was a mathematics student.
Olga's braid made a crooked line across her head. Her part was also crooked.
The girl would sit without moving for decades.
Truda stood. "I will think. Come here tomorrow morning."
A group of students gathered in the central hall of the Mathematics Institute. Truda looked for uniformed soldiers and breathed out when she saw only students gathering around a fellow student, Ludwig Fischer.
Ludwig cleared his throat for attention. "So today, we received news. Our institute received a letter from Pennsylvania, in the United States." He hesitated there in the center of the Mathematics Institute, beneath the ceiling's sweeping curve. Truda realized that perhaps he wasn't authorized to share this information.
"Emmy Noether has died," he announced. He went on to explain she hadn't survived surgery to remove a tumor.
"The non-Aryans have a less than perfect constitution," Oswald Teichmuller said in a voice meant for all the students in the room. "That's why they end up dying."
Truda wanted to drive a knife into his constitution. Her rage blurred her vision and she repeated Pascal's triangles in her head to calm herself. Now she knew. She had to help the girl Olga. She had to help her because of what the Nazis did to the Mathematical Institute at Göttingen. She had to help the girl escape because of Emmy Noether. She had to help the girl escape because she didn't want to get married. She had to help the girl escape because, if she did not, she was no better than this Nazi Oswald with pink eyelids and a shaky grasp of linear algebra.
She thought about Emmy Noether, and an answer presented itself.
The next morning the square was crossed with people from the train, carrying bushels and bags to various corners of the city. Truda arranged her face to reveal no expression.
Olga stood by the fountain with her eyes on the ground. With her small stature and faded clothing, she was easy to miss.
"Come, walk with me," Truda said.
"Can you help?" Olga asked. The girl turned her light eyes on Truda, who had to turn away. Her gaze transformed her softness into something else. The words must be careful equations to balance exactly what Truda needed to convey for her plan to work.
"An operation," Truda began. She wanted to tell Olga that Emmy Noether had died and couldn't help either of them. But then Emmy Noether's calculations crossed the Atlantic once again. In her mind, the transformation became complete. "Your friend needs an operation," Truda said instead.
"She is healing from the attack," Olga replied. "I think her health is improving."
"No, she needs an operation to save her. When people need surgery, they can be safe. If she's in the hospital, we can keep her safe from being found." Truda headed across town to where her fiancé treated casualty after casualty in the Göttingen University Hospital. Olga stayed beside her. "I need to see Doctor Hertz," Truda said to the woman in the hospital lobby. The place was packed, and groans floated down the broad stairs in front of them.
"He is very busy." The woman shook her braids at Truda's cloak, then Olga's shabby dress. Despite the woman's Red Cross uniform, Truda knew in a moment this nurse lacked generosity. Truda stood straighter.
"He is my fiancé, and he is expecting us."
The nurse put down her papers, blinked, and disappeared behind the curtain.
Soon the red-haired doctor appeared, and Truda left Olga in the hospital lobby. In the alley behind the hospital, she used each of her feminine wiles to get the man who loved her to agree to endanger everything.
That evening, it was ready. A boy lugging a large canvas rectangle approached the restaurant where Olga lived behind the kitchen. Truda stood waiting for him. "Truda Baum? The doctor sent me. I have the stretcher, but I cannot carry a patient alone." Acne ravaged this boy's skin, and he couldn't have been more than thirteen.
"She is this way. Be careful. She is very ill." Truda spoke in the voice she might someday use to explain complex mathematical functions to students. She led the boy to where Olga and Helka waited.
"I can walk," Helka whispered.
"No!" Truda said. She leaned away from the boy and spoke in a hiss. "This is not possible. Anyone can stop us anytime after we cross this threshold. You must be in such pain that this is a medical emergency, even if they know who you are. If they find you, they will take you away, and you will never come back here, to this spot."
Helka's face paled. She could look ill after all and gave small gasps as they lifted her onto the canvas. If the Nazis caught Helka walking through the square, they would kill her. But as a patient on the dark canvas lifted by the two poles, Helka might not be recognized. The boy carried one end while Olga and Truda lifted the other.
The trip to the hospital took almost an hour since they had to stop and rest. Olga's arms were strong from stirring soup, but Truda hadn't lifted much except for her calculations and books for the past year. The boy with the angry skin sighed when they had to stop and lower Helka to the ground, who moaned when they did so in mock pain and real frustration.
They carried Helka towards the hospital, through the square, brushing past the spiraled metal pergola curving above the Gänseliesel, the most kissed girl in the world.