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Shattered Genius

Grigori Perelman is one of the greatest mathematicians of our time, a Russian genius who solved the Poincare Conjecture, which plagued the brightest minds for a century. At the height of his fame, he refused a million-dollar award for his work. Then he disappeared. Our writer hunts him down on the streets of St. Petersburg.

I HAD NEVER BEEN ON A STAKEOUT, but I knew how it was done. I took a book. I brought a few sandwiches. I flipped on the radio and listened to the traffic report in Russian. That kept me awake as I waited for the mathematician.

I’d first heard of Grigori Yakolevich Perelman about nine years ago as news of his achievement leaked beyond the international mathematics community into popular headlines. Word was that someone had solved an unsolvable math problem. The Poincaré conjecture concerns three-dimensional spheres, and it has broad implications for spatial relations and quantum physics, even helping to explain the shape of the universe. For nearly 100 years the conjecture had confused the sharpest minds in math, many of whom claimed to have proven it, only to have their work discarded upon scrutiny. The problem had broken spirits, wasted lives. By the time Perelman defeated the conjecture, after many years of concentrated exertion, the Poincaré had affected him so profoundly that he appeared broken too.

Perelman, now 46, had a certain flair. When he completed his proof, over a number of months in 2002 and 2003, he did not publish his findings in a peer-reviewed journal, as protocol would suggest. Nor did he vet his conclusions with the mathematicians he knew in Russia, Europe and the U.S. He simply posted his solution online in three parts—the first was named “The Entropy Formula for the Ricci Flow and Its Geometric Applications”—and then e-mailed an abstract to several former associates, many of whom he had not contacted in nearly a decade.

I liked his style. The more he did, the more I liked. In 2006 Perelman became the first person to turn down the Fields Medal, the top award in mathematics (there is no Nobel Prize in math). He has declined professorships at Princeton, Berkeley and Columbia. In 2010, when the Clay Mathematics Institute in Cambridge, Massachusetts awarded him a $1 million prize for proving the Poincaré conjecture, Perelman refused it. Unemployed these past seven years, he lives with his mother in a former communal apartment in St. Petersburg, the two subsisting on her monthly pension of $160. “I have all that I need,” Perelman has told his concerned Russian math colleagues, with whom he has severed all but the most perfunctory telephone relations.

Perelman last gave an interview six years ago, shortly after a collective of Ph.D.s finished a three-year confirmation of his proof. Since then, the domestic and international press have harassed him into reclusion. Perelman has spurned all media requests, muttering tersely through his apartment door against a wave of journalists. “I don’t want to be on display like an animal in a zoo,” he told one reporter. “My activity and my persona have no interest for society.” When one journalist reached him by phone, Perelman told him, “You are disturbing me. I am picking mushrooms.”

While Russian society has largely passed judgment on Perelman—misanthrope, wacko—I admired him for his renunciation of the modern world’s expectations, his devotion to labor, his results. He had not solicited fame or reward in proving the Poincaré, so why should he be required to react to public notice? His will was free, his results pure, and therein lay his glory.

There was more than one path to glory, I reasoned, and some glory might be found were I to solve this riddle. Perelman was the riddle, speaking through mathematics, the complex language of his Poincaré proof incomprehensible to all but a few hundred mathematicians. For the rest of us, eager to grasp the meaning of exceptional behavior, there was only silence. With slight hope, I booked my ticket to St. Petersburg.

In advance of my trip I phoned Sergei Kislyakov, director of St. Petersburg’s Steklov Institute of Mathematics, where Perelman had worked as a researcher. In late 2005, two years after his Poincaré proof had made him the biggest name in his field, Perelman handed Kislyakov his resignation, stating that he had been “disappointed” in math. He was abandoning math altogether, he said.

Kislyakov knew how obstinate Perelman could be. When I explained that I planned to speak with Perelman, Kislyakov interrupted me. “I discourage you from coming here,” he said. “Perelman talks to no one, but he particularly hates journalists.”

My editor has told me to go,” I explained.

Kislyakov sighed. “Then I guess you must.”

IT WAS SPRING. St. Petersburg was preparing for the Victory Day parade. Tanks lined the central canals. Banners crested the streets. In Kupchino, the southernmost stop on the blue Metro line, far from the palaces that give Petersburgers their proud self-possession, it looked like any other new day. The red-and-white trolleys coursed up the grassy center lanes of the avenues. People strolled in the courtyards that connected the battered housing projects. Russian prime minister Dmitry Medvedev had grown up in Kupchino, but this neighborhood was so removed from fame and influence that it made a perfect home for someone who preferred to escape all notice.

In my search for Perelman I thought I might rent an apartment, find one with a good view of his building’s entrance. A real estate agent walked me all over the neighborhood. “Isn’t there a well-known scientist around here?” I ventured casually.

He lives somewhere on this street,” said the broker.

Have you ever seen him?”

Seen him?” he said with a laugh. “Sure, I’ve seen him. Like I’ve seen Putin—on TV.” The guy showed me one dump after another.

To get around, I rented a Hyundai, all that was available at the leasing agency downtown. I parked outside Perelman’s building. A dozen stories high, made of unadorned concrete panels in the dull Brezhnev style, the structure covered half the block. A handful of people gathered in front of the brown steel door to Perelman’s stairwell, smoking, passing around a morning beer. In this place it appeared there was little rush to achievement.

On a previous day I had met one of Perelman’s neighbors, a teacher at a local school. She said that she and others in their building joked about pleading with Perelman to accept the $1 million prize on their behalf. I couldn’t tell which was the source of greater amusement to her, the idea that Perelman would accept the million or the idea that he would engage her in conversation. Perelman mixed with no one, she said, refusing even to ride the elevator unless he was the only one in it.

And with whom would he mix? The people I saw were roughly drawn, the elderly leaning on spindly wooden canes, the teenagers darting between the kiosks, wasting the day. An androgynous bum with dirty blonde hair nosed around the garbage. An old lady in a coarse gown looked at me through the windshield, then spat.

Ragged as these surroundings were, Perelman exceeded them. As a younger man, he had been handsome, with soft, dark features. But recent pictures—taken with a cell phone camera in a subway car and then transmitted across the web—projected a different image. Perelman’s clothes were dirty and rumpled, his black beard mangy. Ringing the bald crown of his head was a nest of hair that stood on end. He looked disturbed as he gazed out from under thick eyebrows, chewing a nail. How would he react when I approached him?

My mark did not appear that first day, and I cautioned myself to have the patience of Perelman. He had spent seven years proving the Poincaré conjecture, seven years displaying the sort of patience that is well beyond most people. The editors of one Russian tabloid ran out of patience tracking him. When they sent a reporter to Kupchino, the reporter got nothing. A female clerk said she had once exchanged a few words with Perelman. The next morning the headline read, “The Secret Love of Grigori Perelman.”

When I met Sergei Rukshin, Perelman’s closest friend, I realized that my respected counterparts in the Russian press had complicated my task. “Nice to meet you,” I said when I arrived at Rukshin’s office in a St. Petersburg high school. He replied, “We’ll see if it will be nice or not.” But like a rusty faucet, once turned, Rukshin gushed, speaking about Perelman for more than four hours. It was Rukshin, serving as the instructor of a specialized Leningrad math club, who recognized Perelman’s talent in 1976.

It was Rukshin, along with other supporters in academe, who piloted Perelman through the anti-Semitic Soviet policies that nearly prevented the young Jewish genius from obtaining an education commensurate with his mind. And it is Rukshin who now grieves over the condition of this favored pupil: “He lives in a blockade.”

DAY TWO OF MY STAKEOUT. A truck pulled up and parked, obstructing my view of the entrance to Perelman’s wing of the building. As I opened the door of my car, a few guys with fresh cuts on their faces straggled by carrying a 10 a.m. bottle, looking for something to do. I stayed where I was, grazing on chips, and kept my eyes on either side of the truck, where I could still see people passing by. A man in an ink-black coat appeared in front of my car. He waved his hands at me wildly, yelling, “No, no.” Then he turned away. I couldn’t figure out what that meant, except to say that the locals were beginning to notice me. The potential for violence mounted hourly.

There wasn’t much I could do about that, and I thought instead about Perelman’s evolution. Rukshin told me that as a child Perelman had interacted with other students, that he had not been antisocial. Besides math, he enjoyed Ping-Pong and the opera. According to Rukshin and others who have known him since adolescence, Perelman is heterosexual, but as Rukshin noted, “If Grisha ever looked on anything with loving eyes, it was on the blackboard.” No friend can recall the name of a girlfriend. Shortly after Perelman earned his Ph.D., the Soviet Union collapsed. He left for the U.S., where he performed postdoctoral research at NYU, Berkeley and the State University of New York at Stony Brook. He was out in the world, interacting with contemporaries. He was doing things.

Yet he was already turning inward. When the top mathematicians in Russia were earning roughly $100 a month in salary, Perelman was exposed to a Western world of tenured professors, academic grants and funded research labs—the business side of academe. “It’s possible to sell a theorem and it’s possible to buy it,” he told Rukshin when he returned to Russia, disenchanted, in 1995. “Even if you don’t have anything to do with it.”

Perelman had already begun his work on the Poincaré conjecture, a theorem expounded in 1904 by Henri Poincaré, a French polymath and the founder of topology, the mathematical study of abstract shape. Because the problem had a history of false proofs, Perelman told no one about his work lest he be discouraged. He was also wary that unsolicited input would cloud his mind. “For Grisha, it was complete self-restriction,” Nikolai Mnyov, a friend and former colleague of Perelman’s, told me.

Had I such industry, my life might have carried me to a position loftier than the seat of a Hyundai on St. Petersburg’s provincial fringe, waiting for someone who would be displeased to see me, should he appear at all. The hours passed. I bit into a sandwich, bundled my windbreaker and used it as a pillow.

Who was I to complain? Perelman had truly suffered, acutely. He withstood a claim—since refuted—on his Poincaré proof from a rival Chinese mathematician. He turned down the Fields Medal, believing that acceptance would be, as Rukshin explained, fundamentally dishonest. Perelman once rebuffed a TV crew from Russia’s Channel One when they barged through his apartment door, pushing aside his mother. He withstood the procrastination of the Clay Mathematics Institute, which took its sweet time—five years—to offer him the $1 million it had committed to the person who solved the Poincaré. “Grisha is tortured by the imperfection of humanity,” Rukshin said.

All this was going through my mind when, suddenly, Perelman appeared. Over a field of parked cars, his wild hair bounced along as he walked away from me on the path by his door. I had to chase after him. I opened the car door. When I looked up from the handle, relocating my mark, I saw that it was not Perelman. It was simply a man with wild hair, fleeing the pleas of the androgynous bum.

IT WAS DAY THREE of the stakeout, and still no sign of Perelman. I was secretly relieved, since I had no idea what to ask him. I’m not much of an interviewer. I approach my subjects as if we were in a bar, chatting over a beer. A standard swindle but enjoyable, if I’m not mistaken. People like talking about themselves. You just have to give them the chance.

But how do you talk to somebody who doesn’t talk to anybody? Every question I thought to ask, I knew Perelman wouldn’t answer. I couldn’t take direction from the Russian press, which had deluged him with questions about why he wouldn’t accept the money, why he had turned down the Fields Medal, why he wouldn’t talk to them.

I didn’t want to bother Perelman. I didn’t want to be like all the others who had forced him into exile. I believed there was a delicate way to approach him.

I consulted those who knew him. When I met with Alexander Abramov in Moscow, he described the last phone call he had had with Perelman, three years prior. Abramov, a professor, has known Perelman since 1982, when he coached the Soviet team at the International Math Olympiad. (Perelman won a gold medal, posting a perfect score.) Exasperated by Perelman’s solitude, Abramov asked him what he should do in order to meet with him. Perelman suggested that Abramov move to St. Petersburg. “Forever?” Abramov asked. “Maybe,” said Perelman before hanging up the phone.

Maybe Perelman didn’t like Abramov anymore. Maybe he didn’t like anybody anymore. “I’m afraid he is at the level of a nervous breakdown,” Rukshin said. “If this was still the Soviet Union, he would be forced into psychiatric treatment for this behavior.” In 2008 Perelman asked Rukshin to limit their phone calls. Now they speak about once a year.

It looks very much like the story of Bobby Fischer,” Abramov said. “And Bobby Fischer couldn’t be called a happy man.”

IT WAS THE AFTERNOON of day three, and the androgynous bum pleaded through my car window for a few rubles. Even up close I could not tell if this was a man or a woman. I watched the bum move along a little richer. When I refocused my eyes on Perelman’s door, I heard myself gasp, “There he is!”

It was Perelman all right. The beard, the hair, the expression of uncertainty as he stumbled into the sun with his mother, Lyubov, by his side. He shuffled toward the garbage bins stacked by the door, looking as if he might rummage through them. He wore a black ski jacket, a black shirt, black pants. His mother was dressed in a red overcoat and a white beret. They turned down the lane, heading toward the courtyard behind their building. I locked the car.

The courtyard was the size of a city block, with trees, parking lots and playgrounds. Trailing at a considerable distance, I saw Perelman and his mother moving across a grassy field. I decided to approach him headon rather than sneak up from behind, taking all measures to avoid agitating him. Even though I knew he had known English quite well at one time in his life, I thought it best to speak Russian with him to put him at ease.

I walked along one edge of the courtyard, hoping to meet him as he reached its far side. I hurried past a trash heap, around the fencing of a dead tennis court. I circled around a small school, and when I reached the far edge of the grassy field, Perelman and his mother weren’t there. I had lost them.

Frantically I searched the courtyard. I located them again, along a row of parked cars. But when I made another loop in order to get in front of them, I didn’t see them. When I spotted Perelman and his mother once more, they were heading back the way they had come. I didn’t have the luxury of positioning. I would have to approach them from behind. I walked briskly. I was 20 yards from Perelman and closing. Still I didn’t know what to say.

Then I was at his side, and there was no more time to think. “Grigori Yakovlevich?” I said, employing his middle name, in polite Russian form. “Is it you?”

Perelman’s head rotated slowly. He appraised me from the corner of one eye. He said nothing. “Excuse me, please,” I continued. “I don’t want to bother you. But I have come from America to speak with you.”

Up close, Perelman looked about fivefoot-10 and slighter than I had imagined. He was less menacing than he appeared in pictures. He did not waste thought on his appearance, though. Dandruff caked the shoulders of his coat. His clothes were streaked with stains.

Perelman spoke with a high-toned, birdlike voice. And he knew what to say. “You’re a journalist?” he asked. His mother peeked at me from behind his shoulder, then pulled away. I nodded. Perelman looked at the sky, letting out a pained sigh. We took several small steps together. “From which publication?” he asked.

I told him. He nodded in recognition but said, “I don’t give interviews.”

I know,” I said. “That’s okay.” Perelman and his mother stopped walking. They looked me up and down, as though what I’d said had confused them. I didn’t know how this was going to go, but at least Perelman had not run away. So I put on a big smile. “Good weather today, huh?” I said. And to my surprise, both the terrifying recluse and his nervous mother let out a laugh. They were disarmed. I was in.

HOW DID YOU KNOW we would be here?” Lyubov Perelman asked, stepping out from behind her son. She wore thick glasses, and her cheery face puffed out beneath the beret.

I’m embarrassed to say,” I told her.

Well?” she said.

I nodded toward the street. “I’ve been sitting in a car out there waiting for you.”

Really?” she said.

It wasn’t so bad,” I said. “I had a book.”

How did you find out the address?” Perelman asked me.

I have a connection,” I said. “With the police.”

His eyes went wide. “The police?” he said.

Are you Russian?”

American.”

He looked at me curiously. “Are you sure you’re not Russian?” By all signs that I could interpret, Perelman was eager to speak with me, glad for human contact.

Do you mind if I walk with you for a little bit?” I asked. Perelman shrugged and we kept on. He had laughed once, I thought. Maybe he would laugh again. “I was nervous,” I told him. “Everybody says you are frightening.” Perelman squinted at the sky as if contemplating something I would never understand. A man passed in front of us, walking a cat on a leash.

Lyubov Perelman said, “If you’re not getting an interview, what’s the point of this?” Perelman put his arm around her. “It’s okay, Mother,” he reassured her. “We’re just walking.”

Considering all I had learned about Perelman, this display of considerate behavior amazed me. And it emboldened me. No one had gotten this close to him in years. “I understand you’re not practicing math anymore,” I said. “Can you tell me what you are working on?”

I have left mathematics,” he said. “And what I’m doing now, I won’t tell you.”

I was ready with another question, but he had one of his own. “You’re really not Russian?” he asked. “You speak like someone who was born in Russia and left at eight or nine, then came back as an adult. You have this sound.”

Pressing my momentum, I asked him a few easy questions, hoping to open him up. “What are your plans for the May holidays?” “Did you enjoy your time in America?” “How often do you take these walks?” Each time, Perelman shrugged, stared into the sky and said nothing. I wasn’t sure if he had heard me. I looked at his mother, and she raised her eyebrows as though she didn’t know what to say either. A smile crossed her face.

We made our way toward the archway that led to his entry. I tried another serious question. “Considering your abilities and how young you still are, how might you return to science?” He wheezed. After a short silence, his mother asked if I was wearing a wire.

I resolved to draw him out once more. Trying to build common ground, I touched on the similarities between writing and mathematics, emphasizing the solitude that each discipline required. I looked at him with an open, friendly face. He stared again at the sky, blank page.

We reached the archway and stopped. Perelman and his mother stared at me, wondering how this would end. I looked at Perelman and asked, “How’s your Ping-Pong game?”

I haven’t played in a long time,” he said. He laid an arm across his mother’s shoulders. He was becoming agitated. We had walked and talked for 20 minutes, and what had I figured out? I had gotten a feeling for the man, but I had not solved the riddle. Would he help me do it? There was time for one final question. I put it to him in English, the single philosophical question that I hoped he would consider. Where does your life go from here?” I said.

Perelman stepped closer to me. I saw that one of his upper teeth was dark brown, decayed. “What?” he said, his English skills apparently dormant. Perelman’s face was focused in concentration as I repeated the question, and I thought that he might answer. But when I finished speaking, his face went slack, as before. He understood what I wanted to find out, the path of this unusual life. He mumbled, “I don’t know.”

We said our good-byes.

Walking to my car, I felt as though I had failed, having gained such rare proximity to Perelman, only to have the man slip through my grasp. But then I paused, for there must have been something I had missed. Perelman was as unadorned, yet just as complex as the conjecture he had proven. He had relieved the Poincaré Conjecture of its mystery, and in so doing had replaced it, becoming the puzzle himself, granting the world knowledge, yet diminishing its enchantment not at all. We don’t have to figure out everything. The unknown has its own value. 

Through the windshield of the Hyundai, I watched Perelman and his mother approach their entryway, the bums and the kids and the new mothers of Kupchino going about their lives. Perelman and his mother retreated into the darkness of the vestibule. The metal door slammed closed behind them. Perelman was out, he was in. He had gotten some air.