Root of Unity

by SL Huang

  The man with the handgun had five friends with him, none of whom had weapons out at the moment, but their hands were hidden in jackets and sweatshirt pockets and they were all undoubtedly armed. A more discreet kidnapping team, like at Halliday’s apartment—no AKs where people might see.

  I pressed a hand to the dressing on my side. I’d wanted to get captured, but this was not the best timing of events. “Are you the ones who have Professor Halliday?” I said, trying to sound scared.

  “You’re coming with us,” the man with the gun said. “We have a job for you.”

  I flicked my gaze across his burly friends. “Yeah, okay.”

  To be perfectly honest, I was kind of glad it was part of the plan for me not to fight right now. Of course, this whole scheme depended on me being able to fight our way out once I found Halliday—

  One of the other men prodded me from behind and I almost fell. I hadn’t realized he’d come that close. Shit.

  Well, at least I wasn’t having any trouble pretending to be a helpless street mathematician.

  They took the gun I’d stolen from my friendly neighborhood DHS agent, along with the burner cell and everything else in my pockets. I followed them into another van—they must’ve had a freaking fleet of vans and SUVs, for Christ’s sake—and one of them handcuffed me to the door.

  A man sat in the back of the van, out of sight of the security cameras. He was a middle-aged, long-faced, lantern-jawed fellow with bronze skin and greasy brown hair that surrounded a bald spot and then fell to his shoulders. He had a set of those meditation balls you can get in Chinatown going round and round in one hand, clack, clack, clack, and an intricately carved walking stick by his other knee. A tablet computer was balanced on his lap.

  “What happened to you?” he said, his gaze on the bloody jacket I still held in one hand. His eyes were intense. Piercing.

  I figured it could only help my case to tell a small version of the truth. “It seems like there are a lot of people after me,” I answered.

  “Have you guessed why?”

  “Because I helped Halliday with her proof.” I swallowed. “In case you’re wondering, it wasn’t worth it.”

  One of the men snickered. They’d all piled in with us; one slid the door shut and with a slight lurch the van started moving.

  Clack, clack, clack, went the meditation balls.

  “Are you the Lancer?” I asked. Or maybe his boss…

  The meditation balls stopped. The piercing gaze leveled itself at me.

  Oh, Jesus. How would I have known that name? “The NSA mentioned—they tried to grab me. They thought I was working for you,” I invented rapidly.

  The eyes stayed on me a moment longer, evaluating, and then the meditation balls started up again.

  I let out a slow breath.

  “I have many names,” the man allowed with a sneer. “The United States National Security Agency and their stupid games. They think they have so much knowledge.” He said something to one of his men in a different language, and they laughed.

  “Yeah,” I said, too relieved to keep my mouth shut like a proper kidnap victim. “Stupid. They tried to offer me a deal.”

  “And you refused? That seems unlikely.” The Lancer evaluated me like a bird of prey considering the rodent that will be its next meal.

  “They weren’t offering enough,” I said recklessly. I probably should’ve thought through how I wanted to play this.

  The Lancer raised bushy eyebrows. “I see.” Clack, clack, clack. “How do you like this offer: you help us, we won’t kill you.”

  Like I believed that. He’d want to make sure he was the only one with the proof. Killing Halliday and me once we helped him understand and apply it would be a no-brainer.

  It was on my tongue to agree—to play along, let him think he had me—when I remembered how another woman had bluffed when we’d been up against a villain with a supervolcano. She’d pushed him, not given in too easily, and it had made him buy our act. “Not good enough,” I said. “Pay me.”

  “What did you say?”

  “Halliday paid me to help. I don’t do this for my health, you know. I do it for the money.” The proclamation almost sounded true, probably because this sort of story was right in my comfort zone.

  The Lancer settled back, looking satisfied. Probably because he did plan to kill me, so could get all his money back. “How much?”

  Jesus, now I had to think. “You’re going to use this proof to make millions,” I said. “Billions, if you do it right. Aren’t you?” What was the value of such a thing? What would I demand, if this were a normal job?

  “If your work pans out,” he said. “It may be too slow to be practical, even in polynomial time.”

  Polynomial time? This man knew at least something of what he was asking, if not enough to understand the proof himself without Halliday and me. I thought of the binders full of math papers. “It’s not too slow,” I said aloud.

  “Then what do you want?”

  Hmm. If I were really doing this job…he didn’t have the money the proof would be worth yet; he’d only get it after I worked for him. “I want in.”

  He tilted his head, studying me again. I’d managed to surprise him. Clack, clack, clack.

  “I want a royalty,” I pressed. “A percentage. Of whatever you get from this.”

  “Done,” he said. “To be negotiated after we see what your work is worth.”

  “How do I know you’ll be fair?” I demanded, wondering if I was pushing too hard.

  “I could always shoot you now,” he said languidly. “On the other hand, I’m always fair to those who join me.”

  Huh. There was a very slight possibility here that he actually would want to recruit me permanently and not kill me no matter what. Too bad my allergy to authority kept me from being tempted.

  The Lancer sat back, self-satisfied, clacking his meditation balls.

  ♦ ♦ ♦

  We drove north, and north, and after many miles and a few stops we pulled up among some overgrown concrete ruins on a bluff overlooking the Pacific. One of the men uncuffed me from the door and hustled me out with them, not overly roughly. Perhaps he was being respectful of the implication that I might someday be one of them.

  The Lancer levered himself out after us. He was a tall man, and large-framed, with a slight limp that he used his walking stick to mitigate. “Deliver,” he said to me factually, “or we’ll kill you.”

  “Okay,” I said, looking around. This place must have been an old collection of war bunkers, or…or something. I wasn’t sure.

  I wiped a sleeve across my forehead. I was sweating, and my self-inflicted surgery hadn’t stopped bleeding. The bandage I’d stuck over it had gotten heavy—I could feel it when I moved.

  My kidnappers nudged me toward a large gray cube that was taller than the rest, a proper building squatting on the cliff with tiny square holes punched in it instead of windows. The foundation was cracked, and tangled vines scraped themselves up the south side. We stepped around a rusted metal sculpture of discarded junk as we approached the heavy door.

  Someone catapulted out.

  “Hey hey, you’re back, you found the chick, fucking brilliant. Now I need to send some of these overgrown house pets for supplies, because you brought us to a challenge, and not that I don’t like a challenge, but if I’m gonna make this place go boom I need a lot lot lot more boom-makers. I gotta wire this up tighter than a goat’s sphincter. If your oafs hadn’t been too motherfucking pansy to bring my lab along—”

  The Lancer waved the personage off with, as far as I could tell, a genuine smile. “We’re temporary here. No need for any of that.”

  The fast-talking explosives expert pouted. I finally got a look at him—or her? I wasn’t sure. Charcoal-dark skin and a mop of dreadlocks, and a round face that sat atop a round body that constantly shifted its weight around like he (or she) was rolling back and forth. “But it’s a challenge,” the person whined. “I like
a challenge. And now you gotta go shittin’ in my Cheerios.”

  “A little,” said the Lancer, putting a hand on his hyperactive friend’s shoulder.

  “You motherfucking cunt,” said the small person amiably. “Hey, I’m working on the foundation. You gotta see what I’ve put together. It’s balls-out cool, I’m telling you…”

  The two of them disappeared into the darkness of the bunker.

  “That’s D.J.,” said one of my escorts, the one with a hand on my arm and a Glock pointed casually at my head. “Would as soon shove a stick of dynamite up your ass just to see how the shit spattered.”

  And who was apparently a right little sociopath who was kindred spirits with the Lancer. Wonderful. “Not sure why you put up with them,” I needled my captor as we followed the Lancer and his little friend into the cool darkness. “A whole lot of you have been getting killed on this job.”

  He shrugged. “More money for the rest of us when the pie splits.”

  Yeah, that seemed like airtight logic.

  The goon steered me up a metal staircase with another guy following behind us. His fingers on my arm dug trenches in my tired muscles. My breath lurched in and out too fast by the time we reached the top; I tried to slow the inhales, breathing through my nose, but only had moderate success.

  We headed down a dark concrete hallway to a heavy metal door with a slot in it; the second guard dragged it open and they shoved me inside. I stumbled, my side stabbing, and fell against a table.

  The door banged shut before I registered the arm under my shoulders trying to hold me up. “Oh my God,” said Sonya Halliday. “What did they do to you? Are you all right?”

  “Hey,” I said. “Found you.”

  “For God’s sake, sit down.” She helped lower me into a chair. The room was dark; a dim fluorescent light gave it some cold illumination, but the solid walls and ceiling made it a concrete box. I sat on the sole chair at a wooden table covered in scribbled-on pages and stacks of printed-out mathematics papers. There was a mattress on the floor against one wall. And a bucket. Well, that accounted for the smell.

  “Where are you injured? What can I do?” Halliday was still hovering over me. Her neat look had devolved into dishevelment, her clothes streaked with dirt and her hair sticking out from its tight knot, but she didn’t appear hurt. That was good.

  “It’s okay,” I dredged up. The dizziness was fading. I hadn’t realized I was dizzy. Shit. “I’m okay. It’s not life-threatening. Just inconvenient.”

  Especially considering my own goddamn plan was predicated on the idea I’d be able to get us out of here. I glanced around the disappointingly impregnable room. Not many options. We might have to change some variables—but what?

  “The, uh, the accommodations were better the first place they held me,” said Halliday dryly. “I think they’re moving somewhere else soon.”

  I tried to do a subtle eyebrow-raise at the door; it felt more contrived than anything, but she seemed to get it.

  “Are they watching, you’re asking? I don’t think so. The first place they had me, yes—it was a proper sort of prison they’d made up. But I don’t think they’re set up for it here. I had a blood sugar episode when we first got here—I’m hypoglycemic, but I’d been all right before then.” She cleared her throat. “They didn’t hear me and didn’t notice for some time, and then they were quite angry. So I don’t think they’re watching. I get the feeling…I think things are going wrong for them. They don’t seem happy.”

  “Yeah, that was us,” I said. “We’ve been poking the bear. You do it enough times, he runs into a trap.”

  “Forgive me for saying so,” said Halliday, gazing down her nose at me a little like she had back in her office, “but the bear does not appear trapped to me.”

  For some reason Halliday’s doubtfulness amused me this time. The woman had a spine—excellent. “Oh, that’s because you don’t know me,” I said, hoping it was true. “I’m very good.”

  “At what?”

  “Math.”

  Halliday blinked at me, then said with a perfectly straight face, “As am I. I do not believe that’s given me a solution for escaping through solid walls.”

  “I’ll figure something out,” I said. I leaned on the table and pushed myself up, ignoring the fact that I had to lean on it hard, or that I needed a moment to get my balance.

  The pages covering the table were filled with dense mathematical writing, in what I could only assume to be Halliday’s precise hand. I covered for my lack of equilibrium by frowning at them. The printed papers stacked to the side weren’t Halliday’s work, from what I could see—just background references. And the longhand sheets…

  “These are the notes you had stolen?” The bits of the algorithm matched up only raggedly, the connections between the insights missing. “Sorry, Professor, but this doesn’t exactly look complete.”

  “I know.” Frustration bled into her voice. “I can’t—this was decades of work. I can’t recreate every—” She took a deep, shuddering breath.

  She wasn’t making sense. I hadn’t figured I was that out of it. “I thought they had the proof already, and they only needed you to interpret it. Wasn’t that the whole point? That they stole it from you?”

  “Yes, except whoever stole it—” She took another breath and moderated her tone, as if she were back at the university about to address a lecture full of students. “It wasn’t them. They don’t seem to be in possession of it.”

  “Wait, so there’s someone else out there with your proof?” I sat back down in the chair, hard. Maybe I needed another minute before getting up after all. “Say that again.”

  “They aren’t the ones who stole it,” she repeated. “I believe they are the people who attacked you and Arthur, to avoid word of my work getting out—they must have been watching, or listening. I presume they escalated in order to beat whomever does have my work, but they’re not the ones who took it. They kept haranguing me at first, insisting I tell them who had stolen it, or accusing me of lying and demanding where I’d hidden it all.”

  “That doesn’t make any sense,” I said.

  “That there would be more than one interested party?” she asked. “Why not? I think…I forget sometimes, that mathematics is not merely a playground of ideas, but intersects with the real world in profound ways.”

  “So we have to get out of here, and still find out who took your proof and get it back from them?” That sounded like a lot more work, work I wasn’t in shape to tackle.

  Whatever. Getting Halliday out of danger was the first priority; I’d think about the rest of the job after that.

  “The man who has me—he is obsessed with the P versus NP problem and efficient solutions for any question that might lead him there,” said Halliday. “Though I do believe he intends to use my work for economic gain, I gather his greater dream is for it to lead to a proof that P equals NP.”

  “That’s idiotic,” I said. “Factoring isn’t NP-complete. There’s no reason your proof would mean—”

  “I know,” she said. “But he’s said things—said he’ll keep me here until I generalize my work to an NP-hard problem, which does not make the least bit of sense, but he said he’ll do—he’ll do things to me if I can’t…” Her voice trailed off. “He won’t hesitate to hurt us. I think he’s delusional.”

  Delusional was right. Halliday had a fantastic result, but it sounded like the Lancer was after the Holy Grail of mathematics.

  I remembered the notated shelves of binders. Someone with a middling talent for mathematics who had become obsessed—obsessed with a dream he’d never be good enough to realize.

  I pressed a palm against my temple, hard, trying to think. “So this guy’s a computer expert and, uh, let’s say an armchair mathematician, and he’s got a fanatical obsession with algorithmic complexity. Okay. So he’s probably keeping up with the pros who are doing this work, maybe hacked your email along with the email of every other person who’s workin
g on this stuff, and wrote a program scanning for whoever might be close to solving it.” Dr. Martinez’s words came back to me: You could write a program that scans for keywords quite easily. It’s not paranoia, it’s just fact; you accept it and live in the modern world or you don’t. “His program gives him a ping when you email the NSA and talk to your friend Zhang. So he starts spying on you, arranging to kidnap you. If he bugged your phone, too, at that point—he would’ve picked up your first conversation with Arthur, when you told him your work was stolen. When he had his guys run us off the road, I’m betting he wasn’t so much worried about us knowing what was going on as that he knew we were going after the missing proof, too, and he’d go to any lengths to stop us from getting there first.”

  It fit. Christ. We were lucky the Lancer hadn’t bugged Halliday’s office; if he had, he’d have known I’d just met her then, and we wouldn’t have been able to pretend I’d been helping her all along. “That still doesn’t tell us who stole your work in the first place.”

  “The worst part is, I don’t think I can do it.” Halliday lowered herself to sit on the mattress. “I don’t think I can recreate it. I’ve been trying—slowly, because I knew Arthur would be coming, but…the man who has me—has us—he knows enough to check my work, so I can’t stall too much. And most of my hesitation…it hasn’t been faked.” I could tell she was trying to speak plainly, but her shoulders hunched, and her fingers clenched against the mattress as if she was fighting to keep her composure. “I don’t think I can do it. I think…I’ve lost it. That’s the worst part of all.”

  Personally, I thought the potential bodily harm to us and the potential economic threat to the world at large from whoever did have the proof ranked as being a lot worse than Halliday not being able to recreate her notes, but I didn’t say anything. Instead, I pulled over some of the pages and flipped through them.

  Interesting. The structure of the proof was scattered but apparent—I could see it, one insight that should jump to the next, but with the steps in between left blank and unarticulated.

  Well, that was only a little harder than reading a particularly dense paper. The intuitive leaps were already there. “Don’t let that get you down. I think I could finish it from here.”