Root of Unity (27 page)

My fists were clenched so hard my fingernails stabbed into my palms. “Who asked you? Maybe I like my life just the way it is!”

“And maybe whatever made you lose your memory has something to do with why you can’t do math anymore!”

Everything stopped. The retort I had been about to spit curdled and choked me. Checker’s words hung in the air, echoing.

He took a deep breath, straightening and blinking rapidly as if he was only just hearing what he’d said. But he set his jaw and let the words stand, meeting my eyes defiantly.

“What did you say?” I whispered finally. Dangerously.

“I’m sorry,” he said. “I’m sorry. But—”

I didn’t wait to hear the rest of it. I banged out of the Hole. My tires squealed against the asphalt as I peeled away.

Chapter 27

Everything was
wrong. Crumbling. Disintegrating.

Enough emotion welled up to swallow me, drown me. This job was nothing, my life was nothing…I was nothing. A speck of dust in a hurricane. Powerless.

We couldn’t find Martinez, and we didn’t even know why she had stolen the proof in the first place. I was mathematically and mentally broken, and to top it off I couldn’t even finish one goddamn commission and track down one seventy-year-old woman. And Checker…what Checker had said…

I couldn’t have cared less about my memory. My brain shied away from it. Not remembering was just
fine
with me.

The math, though. The math was everything.

If only I could fix that, then nothing else would matter. Not the two-decade long blank spot in my head, not the fact that I was failing so miserably in my work, not that fact that I’d left myself a note in a freakin’ graveyard like some kind of sadistically creepy fortune-teller…not the fact that my so-called friends only seemed to give a damn about me as suited their own needs.

Not the fact that
something
in my head had prevented me from even noticing how crippled I was until the work with Halliday.

Fuck.
Just fix the math
—it all sounded so simple, when I put it like that. So simple, for something so fundamentally unattainable. I might as well wish myself to Mars.

Mars I’d have a better chance at. After all, I could do the fucking math.

I drove around the city for a while with an aimless vengeance, going in circles as if I were on a mission to wear out the car. I ran out of gas, refilled the tank, and kept going.

Where was Martinez? That was the only problem I seemed to have any shot at solving right now. The only thing I might not be useless at, even though I’d had less than zero success at it so far.

I drove to her condo.

I didn’t know why I was here. Arthur was far more observant than I was; I wasn’t going to find anything of relevance that he hadn’t. I broke in and walked back through the rooms, looking for something, anything, that would give me a clue as to where she had run to.

I passed by her shelves in the living room, running my hand along the dust fronting the empty spaces. She’d denied anything was missing, but she’d clearly been lying. Why? What did that mean?

I had no idea.

I let myself out the back door. The building had a small paved area behind it, the plants in proscribed plots around the cement almost making it a backyard. There was a high fence that gave it a false sense of privacy and solitude, some lawn furniture, and a portable fire pit in the corner of the patio. It was all pleasant and well-groomed and totally generic. I turned to go back inside.

“Are you a friend of Rita’s?”

A little old man had appeared. A permanent stoop bent him over his cane, and he had scraggly white hair and a face that was more liver spots than skin. He leaned on the cane as he took a shuffling step toward me. “Yeah,” I said, and made to move past him.

“She in some sort of trouble?”

“No,” I said automatically, and then paused. “Why would you say that?”

“Well, ’cause those government people were here asking about her. When the other lady got snatched. I didn’t tell them nothin’.” He grinned at me. Half his teeth were missing, and the other half were yellow. “Are you her daughter? She never talked about family. Painful, it was. I could tell. I think the government murdered them.”

“Why would you think that?”

“Because I don’t trust them. They watch us, you know.”

Well, yeah, but I still thought it highly unlikely the government had randomly murdered Martinez’s family. “I’m not her daughter,” I said. “I’m just a friend.”

“Oh,” he said. “I have such
respect
for her people, you know. So in tune with nature all the time.”

I wondered what Martinez would have thought of
that.
To be fair, I supposed mathematics was the greatest natural law of all.

“The government doesn’t like her kind. I think that’s why she was in trouble. Maybe why she burned everything.”

“Wait, what?” I said, my brain latching onto the one cogent piece of information. “She burned everything? What do you mean?”

He poked his cane at the fire pit in the corner of the patio. “Night after night. I watched her do it. I thought, something’s gone wrong, good for you, you burn that evidence, you show them how it’s done. Are you her daughter?”

“No,” I said again, and then wished I’d lied. “I’m, uh, a really good friend. When was this?”

“Last week? Two weeks ago? Or was it longer…I get confused sometimes. What kind of trouble is she in?”

“Big trouble,” I said absently, heading toward the fire pit. “Do you know what she was burning?”

“Papers.” He coughed mightily, wheezing. “I asked her once, she said it was her life’s work. She must have been in some mighty big trouble.”

Martinez had burned her own work, too? Or something else?

I crouched by the fire pit and poked at the ashes. They were cool and crumbled at my touch. I only found a few edges of paper that were even partially legible. Both looked like mathematical language—bits of Greek letters and brackets and the words “for every” and “there exists a unique.” Definitely math. In Martinez’s handwriting.

Why would she have burned her own work?

“Did she say why she was doing it?” I asked.

Martinez’s neighbor limped creakily to my side and looked over my shoulder. “She said it was too dangerous. She said it would, uh. She said it would ‘break the world.’ I said we’d already done a damn good job of that, what with the global warming and the economy and the aliens putting chips in our heads. She said no, this was different, that she was saving everybody.”

“Saving everybody from what?” If she’d burned Halliday’s proof with the same sentiments—maybe she thought someone nefarious
would
get a hold of it, inevitably, and that person would take down the whole economy. Maybe she thought the NSA having it would be evil enough. Could she have discovered a similar proof simultaneously with Halliday and burned that as well, burned everything?

“She told me it was her greatest desire, and it ruined her life,” said the old man. “She was lonely, I think. Her life was her work. Her work, her life. Then it made the world ugly, she said, and I think it broke her.”

It took me a while to untangle that statement, and when I did, it didn’t ring true. If Martinez had discovered the same factoring shortcut Halliday had, she should have been ecstatic, even if she ultimately decided to keep it to herself. Something wasn’t adding up.

I poked again at the ashes, frustrated. “Dammit.”

“I took a piece,” rambled on the old man. “She kept saying it was the end of the world, and I wanted to hedge my bets, you know. But I couldn’t make a lick of sense of it. I think maybe she’d gone round the twist. Poor woman.”

I stood up so fast I almost knocked the fire pit over. “You took some? Where is it?”

“You’re her daughter, right? Not with the government?”

“I’m not with the government,” I said. “I swear.”

“They’re spying on us, you know.”

“Yes,” I said ironically. “I know. Where’s the stuff you took? Do you still have it?”

“I still got it.” He squinted at me with rheumy eyes, thumping his cane against one leg. “I give it to you, you have to promise to visit her more. Rita never had any family come. You owe her that.”

“Sure,” I said, giving up.

“And you gotta explain it to me.”

“Explain?”

“Yeah. Why she kept saying it was the end. We already got earthquakes and police raids and all those dumb nuts in Washington mucking around printing money, and now there’s these papers that will collapse our country, I want to know why.”

“Okay,” I said. “It’s a deal.”

He sniffed like he had won. Then he turned and started shuffling back toward the building. “Come on, then.”

He was so slow I had to resist the urge to pick him up and throw him over my shoulder, but finally his fumbling steps came to the back door of the ground-floor condo, and he negotiated his key ring with shaky hands.

I followed him into a dim apartment only to be confronted with a hoarder’s paradise. Stacks of books and magazines climbed in threatening towers to the ceiling, and all manner of junk was crammed in at odd angles, from broken televisions to piles of clothing to at least two old bicycles. There were also mountains of bottled water, loose and in flats, and a row of five-gallon gasoline jugs behind a jumble of model rockets and bird cages. I was surprised the condo hadn’t broken apart at the seams.

“It’s here somewhere,” said the old man. He started poking through the piles.

I heaved a sigh and went to help, digging through clouds of old receipts and moving crusty paint cans to search for anything vaguely mathematical-looking, and trying not to breathe through my nose. This place was probably a health hazard—one that needed a card catalogue to find anything.

Forty-three minutes later, the old man was still mumbling, “I know it’s here somewhere…my eyes aren’t what they once were…” and I was starting to wonder if he’d put me on. Still, there was no way I was going to leave. This was the closest thing to a lead we’d had on this, and if I had to stay here for a week and dig through every last stale piece of trash in the place, I was going to do it.

Then I picked up a copy of
National Geographic
from the 1970s and saw something underneath.

The pages were crumpled up and crammed against an old-school boom box. I picked them up and smoothed them out. I recognized Martinez’s dense script from the note she’d left for Halliday.

I read them. Then I read them again.

Holy shit. I knew why she thought she’d broken the world.

Because…she had.

She had.

I moved toward the door in a daze.

“Are you leaving?” asked the old man. He sounded sad. “You could stay for dinner. I have the kind in the little trays.”

“I have to go,” I got out.

“We didn’t find your mother’s notes,” he said. He turned his head from side to side, lost. “I know they were here somewhere. She said the end was coming, you know.”

She had been right.

He’d better stock up on more of those dinners with the trays. I didn’t tell him that. I didn’t say anything. I just let myself out.

Once on the street, my legs went limp and I sat down hard on the curb. Martinez hadn’t found a factoring proof. She’d found something so much more explosive, so much more deadly.

She’d proven the Holy Grail of mathematics. The impossible dream. She’d solved the P versus NP problem, and she’d proven them equal.

Chapter 28

I didn’t
have enough of her notes to see how she’d done it. But there was enough context around the lemmas, enough explanation in her cramped handwriting, to know something of what she’d been doing. She’d been building a polynomial-time algorithm for 3-SAT.

She’d been right: this would break the world. Rend it in two and shatter humanity in the upheaval. Civilization would never be the same…if it even survived.

I sat on the curb for a long time. Everything around me—the cool evening air, the slight breeze, the deepening twilight, and the math, especially the math—felt different. It wasn’t, of course—except it was, because this so fundamentally changed our understanding of the universe that nothing ever
could
be the same.

Finally I steadied myself. Stood up. Went to the car. Drove to Halliday’s safe house. The cars passed around me on the freeway like it was a normal fucking day.

Arthur answered the door. “I need to talk to Professor Halliday,” I said. “And to you, too. Let’s go for a walk.”

“Course,” Arthur said. “I’ll get her.” He disappeared for a minute and came back with Halliday, who grabbed a coat from next to the door and shrugged into it.

We walked down by the lake. The night had deepened enough to make it hard to see each other. I pulled out the bug scanner that had become attached to my hip and pressed a button; it flashed green.

“What’s going on?” said Arthur. “Is everything all right?”

“I found out Martinez’s reason.” My tongue felt thick in my mouth. I didn’t know where to start.

“What is it, Russell?” Arthur prompted, when I hadn’t said anything. He sounded concerned.

He should be.

I pulled the crumpled pages I’d gotten at Martinez’s condo out of my pocket and handed them to Halliday. Arthur passed her a penlight.

“She burned Professor Halliday’s work after she burned her own,” I explained with a dry mouth, as Halliday read. “Because she was afraid. Because she had found something.”

Halliday let out a gasp.

“What? What is it?” said Arthur.

“She proved P equals NP,” I said. The sentence didn’t sound real. It felt like I was saying a line, lying, pretending this impossible thing was true. Halliday had her eyes fixed on the paper, frozen. I was pretty sure she had stopped breathing.

“Hey,” said Arthur, his voice low and tense as he put a supportive hand on Halliday’s back. “Help a layman out. What does that mean?”

“There’s a…a problem, in mathematics,” I said. “It’s called the P versus NP problem. What do you know about complexity classes?”

“Nothing,” said Arthur.

I closed my eyes. It felt absurd, somehow, that the world was ending and I had to stop and explain why. Absurd and surreal. “We can categorize problems according to how difficult they are computationally,” I said. “Any problem in the set we call ‘P’ is something that can be quickly solved. We say ‘quickly’—meaning we can solve it in polynomial time on a deterministic Turing machine, but don’t worry about that. Any problem in NP is something that, if we have a solution, we can
verify
that solution quickly—but we wouldn’t necessarily know how to solve it quickly.” I tried to steady my voice. “It’s like if you have the solution to a maze, you can walk through that maze and make sure the solution works. But if you’re trying to find the solution, it’s a lot more difficult.”