Dedication
For the women who light the way forward,
and for David—here, there, and everywhere
Contents
Cover
Title Page
Dedication
An Invocation
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Chapter 25
Chapter 26
Chapter 27
Chapter 28
Chapter 29
Chapter 30
Chapter 31
November 1943
Author’s Note
Acknowledgments
About the Author
Also by Catherine Chung
Copyright
About the Publisher
An Invocation
EVERYONE KNOWS THAT ONCE UPON A TIME THERE were nine muses. They were known as the daughters of Zeus, and wise men loved them, for they bestowed the gift of genius. Sing in me O Muse! cried Homer, and the muses answered: filling his voice and spinning out his mortal talents to make immortal tales.
What not everyone knows is that once there existed another sister, who chose a different path. She was the youngest of them, and the most reckless, and when she came of age and it was time to claim an art, she shook her head, and she refused. She said she did not wish to sing in the voices of men, telling only the stories they wished to tell. She preferred to sing her songs herself.
Her sisters were shocked at this rebellion from their most beloved sister and ordered her to push these dreams aside. “Don’t you know the rule,” they said, “that the price of your dearest wish is always everything you have?” But her dreams were her dreams and she was stubborn, and when she refused to turn from them, her sisters offered her their own gifts to choose from, in the hopes that one of them might tempt her. “You may have the epic poem,” said Calliope, the most powerful among them. “Just put away this notion, and you may have anything you wish.”
But the tenth muse would not be commanded thus, nor tempted, and in the end her sisters bowed their heads and, weeping, prepared to bid their youngest one good-bye. Their tears turned to stars that they hung in her hair, and formed a shimmering veil down her back. The sisters called the birds to sing to her, and the crickets and centaurs—all the sweet-voiced animals in the world. They gave her everything they could in that kingdom of immortals, hoping she would stay, knowing if she left she could take nothing with her.
But she would go.
And so the tenth muse was stripped of her title and her gifts, and immortality. I say stripped, though she was the one who shrugged them off, as lightly as a dress, and laid them quietly aside. What she received in turn was no more, no less than exactly what she’d asked for: a voice to sing with what she would. But of course her voice was now a woman’s voice, in a mortal woman’s body, and could bring her death, or worse. Still, she never once looked back, choosing to walk among us mortals to the end. She made her fate a human matter, and this is why of all the muses, I cannot help but love her best.
Since then she has told a thousand stories, she has lived a hundred million lives. She is born again in every generation: Sappho. Hypatia. Scheherazade. Woolf. And all the rest unhailed, unnamed, erased. Returning and returning, she is the tale embodied. Long may she live, again.
Chapter 1
THERE IS NOTHING AS INTRIGUING AS A LOCKED door. Which is why in 1900 when David Hilbert presented the first of his twenty-three unsolved mathematical problems in his address to the Second International Congress of Mathematicians in Paris, he changed the course of scientific inquiry, and thereby the course of the world. Twenty-three locked doors to beguile the foremost minds of his time: twenty-three locked doors to stand in front of and circle throughout the century. To this day, twelve of these problems remain unsolved. In my youth, I dreamed of scaling the heights myself and drawing forth a solution—as gleaming and perfect as Excalibur. One day, I told myself, I would open one of Hilbert’s fabled doors—join the honors class of mathematicians who have conquered one of those twenty-three problems, whose names will be known throughout time.
I’ve lived long enough to know now that no matter what one’s contributions, one falls in and out of favor. Even Hilbert, even Einstein. For now, I am in the amusing, slightly awkward position of finding that while my reputation is on the rise—my actual presence, my opinion, my thoughts, are less relevant than ever. I’m invited less and less to participate in things that involve actual math. Nobody asks me to advise or work with them anymore.
I suppose everyone is waiting for me to die. Certainly no one expects me to be on the cusp of a new discovery. But here’s a secret: I’ve recently found a key to a door that has long been hidden, a mystery I feel I was born to unravel. And not just any mystery, but a door that could lead to the solution of part of the eighth and most famous of Hilbert’s problems—the Riemann hypothesis, which predicts a meaningful pattern hidden deep within the seemingly chaotic distribution of prime numbers.
I’ve told no one yet because I know that until I have all the evidence in order, I’ll be laughed at—the same as if I suddenly announced I’d fallen in love. At my age, all passions look foolish to outside eyes. If I were a man, it’d be different. I don’t mean that as an admission of envy, but as a statement of fact. Because who has time for envy anymore? The days speed by so quickly, gaining momentum with each passing month. The fear that I’ll die before I get to the end fuels my work, and I wake with an urgency that feels like an echo from youth—a reflection of the desperation I felt in my early years when I feared I’d miss my chance.
Perhaps this is why I dream more and more of people from my grad school days, my old competitors and colleagues, my professors, and especially Peter. In my dreams, everyone is dying. They lie down one by one in perfectly ordered graves that proceed along a straight line, head to toe, forming a road that points at the horizon. I ask them where this road leads, and each time I ask my question, they smile and reach up to close their own coffins, shut their eyes, and die.
Good-bye and good riddance, I’d say, if the dream ended there, but then I notice that the closed coffins have numbers and symbols on them, and the string of them forms an equation strangely familiar to me—one that I know the solution to. So I walk up and down, trying to figure it out—whether I should be walking in the direction of the heads or the toes, whether what I need to find is the beginning or the end, until I realize that no matter what, in the line of infinite coffins that stretches out to the ends of the earth, one coffin is missing, and it is mine. And then I know that the missing piece of the formula, the key, is my death, and that I will lose the answer in completing it, and I wake up furious, and cursing, and filled with a terrible grief.
All my life I’ve been told to let go as gracefully as possible. What’s worse, after all, than a hungry woman, greedy for all that isn’t meant to be hers? Still, I resist. In the end we relinquish everything: I think I’ll hold on, while I can.
MY RECENT DISCOVERY is rooted in the work and time of another mathematician, named Emmy Noether, and those who orbited around her. It was during her time that we began to anticipate how complex things might get without yet being entrenched in t
hat complexity—like standing on the brink of chaos. And what company she stood with, on that very brink! It was the time of Bohr, of Heisenberg, Wittgenstein, Gödel, Einstein, and Turing. Quantum mechanics was being born, as was modern atomic theory, relativity, the computer, the uncertainty principle, the black hole, and the nuclear bomb.
It was an exciting time, but everything was in disarray—there was the rubble of creation, the rubble of destruction. We were at the heights, from which we imagined we could see everything—not just what we knew, but all the possibilities as well—a theory explaining everything, and its inverse: the collapse of science, of language itself. We were on the brink of understanding God, or killing him forever, we didn’t know which. Exhilaration and dread came together, and the knowledge that no great discovery can come without bringing an equivalent terror.
It was around that time that Schieling and Meisenbach exploded onto the scene with a brand-new theorem that dazzled everyone who read it and seemed to sketch a possible opening to the Riemann hypothesis—a hypothesis some mathematicians say is too beautiful not to be true, and others say would be akin to proving the existence of God.
This theorem captured the attention of every major mathematician who mattered then and was quickly labeled a triumph for the side of order and beauty: an attempt to knit together the chaos. And even after the proof was reviewed, and tested, after a public cheer went up, even after Einstein himself made it known that he would like to shake their hands, neither Schieling nor Meisenbach stepped forward. It eventually became known that Meisenbach had been a student of Noether’s at the University of Göttingen before she was exiled by the Nazis. Though he’d remained there in Göttingen through the war and afterward, his partner Schieling had disappeared shortly before publication of their paper.
In deference to his partner, in silent vigil, Meisenbach refused to appear for any of the honors offered to him, and he never spoke of the man who’d coauthored what would be his greatest contribution to the field. Instead, he waited for word or news of Schieling’s whereabouts. Word never came. And so Schieling, vanished, and Meisenbach, silent, were both forgotten, lost to the turmoil of their times. It would be shocking how quickly this happened, given their contribution, but they were working during one of the most exciting times for science, and also the most dangerous. The world order was changing on every level: to quote Newton, for every action there is an equal and opposite reaction, and the earnest idealism that had briefly ignited the hearts of students all over the continent of Europe in the aftermath of the First World War had been overtaken by fury and nationalism.
The sky was opening. The gods had fallen. Fascism had gained its foothold: Mussolini was leader in Italy; Hitler was on the rise in Germany. The mood of the times was turning murderous. And so the war came, and bombs were dropped and schools were closed and the Jews and homosexuals, the dissidents and handicapped were led away as their neighbors watched on, and so many, so many were killed.
Emmy Noether was the first of the mathematicians in Göttingen to lose her job, and she went to America to live and work, where she died very soon after. Göttingen, that haven, that bastion of mathematics and science, was overtaken by Nazis. Courant was gone. Klein was gone. Everyone who could escaped to England or America. When asked what would happen to the famed mathematics department, now gutted, Hilbert responded, “What mathematics? There is no mathematics in Göttingen anymore.” And such was the loss in the realm of mathematics and science, and such was the loss in the world, that no one noticed too much when both Schieling and Meisenbach were forgotten.
Until me.
I entered their story decades after they were lost to anonymity—their beautiful theorem referenced and used, but old enough that no one asked anymore what had happened to its authors, no one questioned where they’d gone. But now I’ve discovered the truth of what happened to them, and why they never published again. And I believe I’ve found how their work may open a door to the heart of the Riemann hypothesis—where, if I’m right, I could be the first to go.
Chapter 2
I SUPPOSE I SHOULD WARN YOU THAT I TELL A STORY LIKE A woman: looping into myself, interrupting. Things have never seemed straightforward to me, the path has never been clear. When I was a child, first discovering numbers, the secrets they yielded, the power they held, I imagined I would live my life unchecked, knocking down problem after problem that was set before me. And in the beginning, because I outstripped my classmates, my parents, and even my teachers, it seemed possible that it would be so. That was pure hubris. I would have been better off reading Greek tragedies.
The first thing I remember being said of me with any consistency was that I was intelligent, or quick—and I recognized even then that it was a comment leveled at me with disapproval as much as admiration. Still, I never tried to hide or suppress my mind as some girls do, and thank God, because that would have been the beginning of the end.
I GREW UP in the 1940s and 1950s in the small town of New Umbria, Michigan. The women there were mothers or grandmothers, a handful of elementary-school teachers and maids, the town librarian, and the school nurse. Back then, we were expected to get married and settle down, not go to college or have careers. But my family and I were newcomers where most residents went back multiple generations, and so while I never really fit in—or perhaps because of it—I also never felt that such rules applied to me. Before, we had lived in Virginia, but we had moved when I was young enough that I had no memories of this. When anyone asked me where I was from, I didn’t know how to answer. All I knew was the answer was not New Umbria or Virginia, because whenever I gave those as answers, I was always met with more questions. “No, where are you really from?” Or, “Where are your parents originally from?”
When I asked my parents, “Where am I really from?” they would change the topic, or look sad, or tell me not to be bothersome. “You were born in Virginia,” my father said, “as was I. And that’s the end of it.”
My mother had been born in China, but when I asked her anything about it, she always said, “I don’t know.” And I believed she didn’t know in the way I didn’t know. I thought perhaps China had been for her like New Umbria was for me, a place she didn’t belong, which had never felt like home, and that was how she ended up in America, with us.
Neither of my parents had any living relatives, so there was no one else I could ask. To some degree I accepted this uncertainty as part of who I was in the context of our town, but also in the larger context of life and history. I felt as if I lived outside of time and place, like in a fairy story.
Many of the things I believed to be true would turn out to be wrong, but this is what I was sure of back then: my father was a war hero with a medal to prove it, and he had been hired as the lead machine engineer at the New Umbria Glass Company, so he was treated with respect wherever he went. As his wife, my mother was usually afforded some modicum of courtesy, but she was Chinese by birth, and so we were never very sure what response she—or I—would provoke, wherever we went, where we were always the only ones of our kind. I heard her called a dirty Jap once, and China Doll, and Red China, and while I flushed red with shame, my mother never so much as flinched at the slurs, so that I was never sure that she heard them. In any case, she was also very young and beautiful, and drew looks and comments wherever we went.
These facts alone made her extraordinary, but she was different for other reasons as well: she was happiest, it seemed, lying in our backyard on her stomach, watching lines of ants file by, or the grass wave in the breeze. She was always dressed as if for winter—in long sleeves and thick stockings—and did not do typical mother things; it was my father who took care of us, the one who cooked and bought our groceries and clothes. My mother’s attention drifted elsewhere—to the seeds spiraling down in the wind, or the distant wingbeats of birds, or the passing shadows of clouds. For the most part she was quiet, often subdued, and prone to periods of sadness. She touched me very rarely, and even those instance
s were less and less as I grew older, though I longed for them.
Between my mother and father there was kindness, and I think respect—but there was also an unbreachable distance. They never touched each other, and in fact rarely spoke, though it seemed to me my father was always trying to make her happy—bringing home pretty scarves that he draped over her chair, or leaving heart-shaped rocks on the kitchen counter, which she tucked into her pocket with a smile. She spoke with an accent and told me stories about brave princesses and angry kings, and the story of the tenth muse. Everything she told me felt like a secret, with a message hidden inside.
I told her secrets, too—about the spiral I saw twirling out from the cut side of a cabbage when she sliced it in half, and how it echoed the spiral I’d once seen on the shell of a snail. The way one half of a leaf was a perfect mirror of the other half. I told her about the games I played with numbers, how I’d noticed that two odd numbers added together always made an even one, or how an odd number and an even always made an odd. And my mother listened, and nodded, and told me there were patterns everywhere in nature, and that numbers held their own hidden stories that unspooled if you followed them far enough along—stories that once you knew the beginning ran on and on. Even back then, I realized the power of what my mother was telling me: that numbers underlay the mysteries of nature. That if you could unlock their secrets, you could catch a glimpse of the order within.
I did quite well in school until third grade, when I was assigned to the class of a teacher who took an instant dislike to me. Mrs. Linen was a stiff, lean woman with little patience, and was in the habit of giving us busywork, which we were supposed to complete in silence. I had gotten in trouble more than once for completing this work too quickly, but it came to a head one day when she asked us to solve 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 and went back to her desk.
I raised my hand immediately, and when she sat down at her desk and took out a folder, and seemed likely not to notice my outstretched arm, I waved it around, stretching forward in my chair.
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