Soon after, a boy was born to them, and they named him Srinivasa Ramanujan. He did not speak a word until he was three, but then he spoke in sentences and could write words in the sand with a stick. His parents by then rented an extra room in their hut to two students studying at the college nearby. Ramanujan, while still a young boy, read the books that these students left behind, and in this way he discovered the divine language: he discovered mathematics.
He was a star in high school, the best student anyone had ever seen. Much was expected of him when he went to the university, but Ramanujan became fixated on mathematics and only mathematics, and studying that to the exclusion of all other things, he failed out of college. Shocked and despairing, he ran away to live alone in a hut where he filled notebook after notebook with notes.
Alone, destitute, half dead with despair, he finally mailed pages torn from his notebooks to strangers he hoped would help him: a clerk, a deputy accountant, a professor. To those with any understanding, his pages were magic spells containing a rare power: they were keys to another realm. And so the clerk, the accountant, and the professor became his champions.
With their help, he sent his notebooks across the sea. In Cambridge, England, lived several famous mathematicians, and he wrote to all of them. The first two did not respond. A third, by the name of Hill, wrote back: “You have some talent, but clearly lack formal training. You will never have the foundation to be a real mathematician.”
But a fourth mathematician opened the notebook that had been sent to him, and saw what lay behind a seemingly nonsensical formula: 1 + 2 + 3 + . . . + ∞ = . Rewritten as 1 + 2 + 3 + . . . + n + . . . = 1 + + + . . . + + . . . = , it was in fact the calculation for Riemann’s zeta function ζ(s) = 1 + + + + . . . when fed with the number −1. The fourth mathematician, whose name was G. H. Hardy, was astounded. “Prove to me that you are who I think you may be,” he wrote back to Ramanujan. “Send me more.”
The notes Ramanujan sent next were stunning and strange and written in a wild notation. He claimed he could calculate the number of primes up to 100 million with an error of just 1 or 2. Hardy couldn’t believe it. This nobody from India had conjured up part of the Riemann hypothesis all on his own: Had he also solved it? It turned out he had not, though he had solved a dazzling number of other problems. But he didn’t know the language of proofs: he didn’t know how to show his work. Later, Hardy said his association with Ramanujan was “the one romantic incident in my life.” He said he had known Ramanujan’s theorems must be true, “because if they were not true, no one would have had the imagination to invent them.”
So a ticket was bought, and Ramanujan boarded a ship to England. There he became Hardy’s student—a student whose intuition surpassed that of his teacher. He had never been taught how to write a proper proof, but in some ways he seemed liberated by not knowing the rules—he seemed to simply know things so complicated, to recognize patterns so deep, and to find them so obvious, while the mathematicians around him labored for weeks on each declaration, just to check if he was correct.
If this sounds like a happy ending, beware. After all, every fairy tale has its dark side. At Cambridge, Ramanujan was cold and hungry and homesick. A strict vegetarian, he had difficulty finding food to eat. His British patrons thought him fastidious and ungrateful, a savage rescued from the wilds. His fellow students scoffed at him, made fun of his clothes, his food, how he always hunched over, how he always ate alone and without a knife or a fork. He didn’t even use a blanket, they said, shivering like a fool on top of his bed, a simpleton who had slept on the dirt and in the heat his whole life. Because he’d taught himself everything he knew—essentially deriving all of modern mathematics himself, sitting on the ground in a hut—there were huge gaps in his education. So what of his dazzling mental leaps, if he didn’t know the least of what any schoolboy in England did?
Ramanujan was aware of his enemies. He knew that he was a laughingstock. Like Kafka’s ape who learned to talk and drink and smoke cigars, he was a novelty act, expected to explain over and over again how he came to be so clever, while his audience patted themselves on the back for having discovered him. Oh, Ramanujan was celebrated, but he was always the object, he was always the prize.
And he was a sickly prize at that, always in and out of the hospital, always shivering, undernourished, always sad. After throwing himself facedown in front of a train that braked, however, and did not hit him—he was taken to a mental hospital. In the hospital, he was told they would only give him firewood to heat his room on the days he was mathematically productive. He was not productive. Still, he could perform parlor tricks. When Hardy came to visit him, Ramanujan blinked awake from his stupor. “Your cab number was 1729?” he said. “How interesting. Have you ever noticed it is the smallest number expressible as the sum of two cubes in two different ways? 13 + 123 and 93 + 103.”
Luminaries had brought Ramanujan to England, but he only wanted to return to his heathen land, to India, back to the sun, the dust, and his mother’s voice. Hardy and his colleagues could not believe it. Did he not understand he was sabotaging himself? Did he not understand the marvelous opportunities before him? But Ramanujan had had enough: he would go home. And yet the fairy tale would not release him, and the man who said “An equation for me has no meaning unless it represents a thought of God” was dead a year later from the tuberculosis he contracted in England. He was thirty-two years old.
Graduate students and researchers still pore over his notebooks, and at some point someone discovered in one a list of all the primes up to 100 million that Ramanujan had compiled. But there was no formula, no notes to give them a clue as to how he had constructed it. In death, he was given the respect—even reverence—he was often denied in life. I’ve heard it said that you can judge a society by how it treats the lowest of its members. Let me say now, I’ve often been dismayed at how we treat our best.
Chapter 14
THE SUMMER CAME SOON AFTER THE CONFERENCE: A blur of weeks and studying and exams, and then my third year of graduate school was over. Leo and Rob left for summer jobs at Bell Labs, and I stayed on at MIT as a research assistant to Professor Pearce, a geometer working on multidimensional cones. Those early months of summer were glorious: I had many hours free to work on the Mohanty problem, which had been the first thing I read upon returning from the conference and which I had been thinking about ever since. Meanwhile, the weather mellowed out from the fragile warmth of spring into a string of progressively hotter days, and Peter and I spent nights at each other’s places, running the fans all day and all night long. Without classes or the structure of school or the attention of students and faculty around us, we went on picnics, we went on walks, pleasure and work flowing through our talks and long hours together.
One day, Peter and I went to the park to have a picnic and to work. We sat side by side, our papers secured by rocks we’d collected from the edge of a riverbank. I had on a red hat that kept blowing off. Peter was wearing my sunglasses. We were surrounded by huge trees, their branches creaking in the wind.
I taught him the exercise my mother had done with me with the trees, and at the end of it, Peter said, “Wow. I feel so calm.”
I smiled and leaned into him. He put his arm around me.
“Tell me more about your family,” he said. “I feel like you know everything about me, but you never talk about your childhood.”
“There’s not that much to know,” I said.
“That can’t be true,” Peter said. He squeezed me tight. Back then his physical proximity was still enough to make me swoon, and I caught my breath and laughed.
“What do you want to know?” I asked.
“Well, how’d you get so good at math?” he asked. “When did you get interested in science?”
I told him about the ham radio my father had built for me. I told him about my mother and the lightning. “You know,” I said, “I always thought it was my father who encouraged my interest in science, and it’s tru
e that he did. But I don’t think I ever understood how much I got from my mother. She’s the one who taught me to start paying attention to things. She’s the one who encouraged me to think.”
“That’s wonderful,” he said, and then he frowned. “Have you ever tried to track her down?”
“I’ve thought about it once or twice. But I don’t know where to start.” I paused. It was difficult to say the rest. “The thing is, I don’t think she wants to be found. It’s not like we moved. It’s not like we don’t have the exact same home address and phone number. She could have written or called at any time. If she wanted to see me, she could. So I can only assume that she doesn’t.”
Peter rubbed my shoulder.
Eager to change the subject, I said, “Actually, could I show you something?” All our talk of childhood had reminded me of my German notebook, which was in my satchel. I took it out and opened it. “It’s a relic from the war that my father saved for me,” I said. “Do you see anything familiar in there?”
Peter flipped through the pages. “I’m not sure what this is,” he said. “Whether it’s original work or notes picked up from a book or a talk or random doodles. It’s not really clear.”
“Yes, it’s hard to tell,” I said. “I don’t know, either, and I’m not sure where it’s trying to go, but I see some familiar theorems, like here.” I flipped through several pages. “Here are the Friedmann equations, and look here, that’s the Boltzmann equation.”
“Yes, but I can’t tell what he’s trying to do with them,” Peter said. “How old is this notebook?”
“It says Göttingen 1935,” I said. “See? S. M.”
“It’d be interesting to track this fellow down. But I can’t tell just from a quick glance how promising this is. What else did you find?”
I showed him another equation. “This also seems familiar, but I don’t know from where,” I said.
Peter tapped his pencil. “Yes, I’ve seen it too,” he said. “It’s from invariant theory. When we get back to the office, remind me to pull out one of Klein’s monographs. I believe I saw something like this in there.” He rubbed his chin. “I don’t know what the equation has to do with the rest of it, though.”
We sat next to each other, our arms touching, flipping through the pages of the notebook and trying to make sense of it together. A lone beetle with bright yellow geometrical markings circled the edge of the table, the filaments of its antennae waving wildly. “Look at that guy go,” Peter said.
Watching him watch the beetle with a delighted smile on his face, I felt as happy as I’d ever been, like someone was finally helping me put something from my childhood back in order. It was more than that, of course—I was in love, I was making progress in my work, and I had the companionship and support of an important mathematician. I felt as if I’d imagined my life into being, as if my luck would keep growing, and never run out.
THAT SAME SUMMER I started work on the second part of the Mohanty problem—the extension to odd numbers. This time, Peter was on board and excited, but I didn’t invite him to collaborate. I felt a little selfish not offering, but I wanted to do it myself, and Peter was only too happy to let me do this, as penance, I think, for his earlier discouragement. He insisted, however, on talking through my ideas with me, on helping as much as he could while leaving the main work to me.
We saw only a handful of people—Pearce, the professor I was working for, made almost no demands of me, and so I was more likely to see him socially than at school. We entertained only once, when Maria Mayer happened to be passing through Boston. She was an old friend of Peter’s—she’d worked with him and Sal at Los Alamos, and she was one of three scientists to propose the nuclear shell model for the atomic nucleus. I was excited beyond reason to have her and her husband over for dinner: she had won the Nobel Prize in Physics during my first year of graduate school, and I’d sent away for her speech with a feeling of gratitude and pride for what she’d accomplished.
Maria Mayer had been born and raised in Germany and started out studying mathematics at the University of Göttingen, where she met her husband. But she was seduced by the nascent field of quantum mechanics and switched her focus to physics. When she and her husband moved to the United States, first to Johns Hopkins, where she was introduced to chemical physics, and then to Columbia, neither of these universities would consider hiring her as a faculty member, so she took what she could—a modest assistantship at one and an office space at the other. When her husband moved to Chicago, she was again denied a paid position so she worked as a volunteer professor for the Institute for Nuclear Studies at the University of Chicago, and eventually as a half-time Senior Physicist at the Argonne National Laboratory. Here, she learned nuclear physics, and like a fairy story, where all the elements come together in the unlikeliest way at the end, this is how Maria Mayer would end up winning the Nobel Prize: the combination of mathematics and physics and chemistry that she acquired led to the discovery of the subatomic structure of an atom. “San Diego Housewife Wins Nobel Prize,” her local newspaper read. Peter always told the last bit of the story with a disbelieving laugh.
In any case, it was with great expectations and excitement that I prepared to meet Maria Mayer. I chose my clothes and rubbed rouge on my cheeks and lips, like a girl preparing for a date.
Meanwhile, Peter went grocery shopping and came home with charcoal and hamburgers for the grill, and a case of beer. We sliced vegetables and slid them on skewers. He laughed at me for being so nervous to meet her. “She’s the most down-to-earth woman in the world,” he said. “You’ll love her, you’ll see.” Still, I was nervous. Back then, I didn’t know how rare it is for a person to actually meet your expectations, but Maria Mayer did. She exceeded them.
She was in her sixties and wearing a simple linen suit. She had frizzy curls she hadn’t even attempted to tame. She had two children around Peter’s age, and she treated us with a sort of maternal fondness that put me immediately at ease. It’s that ease I remember now, along with her astonishing graciousness. Her husband, Joseph, was just as easygoing and warm.
“I want to sit next to Katherine,” Maria said as we escorted them through the backyard and settled them on matching lawn chairs. “Tell me all about yourself,” she said, leaning forward.
For the rest of dinner, she ignored everyone but me, focusing on the food in front of her and my descriptions of the paper Peter and I had published together, and the problem I was working on now.
“How interesting!” she exclaimed. “Bravo for you! This is why I love talking to young people. Are you going to go on the market in the next couple years?”
“That’s the idea,” I said. “Though my father’s convinced a math department isn’t going to hire a woman faculty member. Not that he’s an academic.”
Maria nodded thoughtfully. “Well, in my experience, he’s not wrong,” she said. She shared that she hadn’t gotten her first tenure-track job until six years ago. She’d done the bulk of her work for free. “It isn’t that I didn’t try to get paid,” she said. “At first the universities said they couldn’t hire me because of anti-nepotism rules. They all wanted to hire Joseph, you see,” and here she shot her husband a wink.
Her levity astonished me. “But doesn’t that make you angry?”
“Angry?” she said.
“That you were turned away. That you had to work for free when you were so much better than everyone else who was getting paid. That it had to be so much harder for you.”
“Oh, it could have been much, much worse,” she said. “I mean, at least I got credit and the Nobel Prize! How many women were denied their medals and not even acknowledged? There was poor Rosalind Franklin and the double helix, God rest her soul. And Peter!” Here she reached over and slapped him on the shoulder. “There’s your friend Chien-Shiung Wu, who disproved the law of parity. Even you said it was a shame Wu wasn’t included on the Nobel Prize. And don’t get me started on how women get written out of textbooks. Oh, K
atherine, don’t kid yourself. Among the rare subset of women who could have won a Nobel Prize, I am one of the even rarer ones who was actually recognized with one.”
“This is all turning out to be a much more depressing conversation than I’d expected,” I said. “And here I was thinking you were going to say something encouraging.”
She laughed. “How’s this? I got to do science,” she said. “I didn’t have a paying job for most of the time, and I do think I had to work a little harder than everyone to get my foot in the door. But I got to do science, and that was the most important thing.”
“It isn’t fair you had to work harder,” I insisted, but I felt very aware of Peter and Joseph. I wondered if this was the same conversation we’d be having if we were alone.
“Oh, Katherine,” she said. “Life’s not fair.” She said it very simply. “I could have spent my time fighting the unfairness of it all, or I could dedicate my time to science. There wasn’t time for both.”
AFTER MARIA AND HER HUSBAND LEFT, Peter and I had our first argument. We’d cleaned up and settled down together on a blanket outside in his backyard to watch the fireflies blink in and out above the lawn.
“I can’t believe she didn’t get paid all those years,” I said. “Her and Emmy Noether!”
Peter nodded. “Luckily, it turned out just fine for both of them,” he said. He nuzzled my neck.
I pulled away. “That’s not the point,” I said. I thought of my father telling me he couldn’t imagine any department hiring me over a man. This was a source of immense anxiety, because I had no idea if I would be able to make a living. If I didn’t get an academic job, I’d have to get work doing something else. “Don’t you think that women should be paid for the work they do?”
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