The harbour becomes the sea / And lighting the house keeps it collision-free / Understand the lay of the land / And don't let it hurt you / Or it will be the first to /  The water, the water / Didn't realize / Its dangerous size /  

About

P=NP

leo smith
 
P vs NP was a major unsolved problem in computer science. It asked whether every problem with a solution that can be quickly verified by a computer (NP) can also be solved quickly by a computer (P). Proof that P = NP was expected to have major impacts on computing, cryptography, and numerous other fields.


I was at “work” behind the archives desk, doing a crossword puzzle. I was done with my homework, of course—I had much more free time since I switched from math to econ. Much more free time, I thought, savagely crossing the T in CHARLATAN, for important, useful things, like crossword puzzles. I was brooding my way around that familiar track when I saw her again.

Her hair was longer now, and she wore it down. She had a textbook under her arm. It had been a year since I’d last seen her. She was a math grad student—computational complexity theory, to be exact. That put her about ten orders of math-whiz magnitude above me.

I looked back down at my crossword and thought, if she comes over for help, I’ll ask about her book.

And then she did. “Hey,” she said. “Hey,” she said again, in a different tone, as I looked up. “You were in Fischer’s intro class last fall, weren’t you?”

“Hey—yeah,” I said. “Yeah, I was.”

It had been, for several reasons, my favourite class.

“I remember you,” she said, smiling like she’d just paid me a compliment, which she had. “How did Bose treat you in intermediate?”

“I changed majors, actually.”

“Whaaat? But you were so… on-it.”

“Not on-it enough, I got a B on the final.”

“A B isn’t bad, nothing to be ashamed of.”

“My—parents would disagree,” I said, managing a polite exhale-laugh. “They made me switch. To econ. So, still math. But easier. What was it you um, wanted help with?”

“Oh, right,” she shook her hair back off her neck. “So, I want to put in a special request for some papers from another university’s archive. Do you guys facilitate that? Or do I go straight to them?”

“Depends on if we have a fileshare relationship with them,” I said, opening the database. It booted up slowly. “What’s the university?”

“TU Berlin,” she said.

“In Germany?” I asked in surprise.

She nodded.

When the database had loaded, I ctrl+F’ed. “There it is. Yup. We can put in a request with them. I’ll print out the request form for you. What’s the book?”

“Not a book,” she said as I sent the form to the printer. “Papers.”

“Like, someone’s papers?” I asked stupidly.

But she nodded, with a dazzling grin. “A mathematician. A dead mathematician. His letters and notes are archived there. I want to take a look.”

“Who?”

She searched my face for a silent interval, making me feel like a spider she had found in her apartment and trapped under a glass.

Then, she said: “Otto Tendring.”

Behind me, the printer whirred to life.

“Oh. Oh,” I said. “He—the one who killed himself?”

“That’s the theory,” she said.

In 1993. And left a coded suicide note. 10 years later, it was still unsolved.

“You’re requesting his—”

“His letters,” she said.

She was looking for something in her bag. I looked down at the book she had rested on the counter. It was a cryptography textbook.

The printer beeped.

I brought her back the pages, and stapled them together. I handed them up, watching her eyes flick down at the paper.

I hesitated, watching her write, then said:

“Are you trying to crack the code in the suicide note?”

She glanced at me, then back at the form, and kept writing.

“The letters of Otto Tendring and Dr Daniel Fischer,” she said. “Friends, collaborators. Tendring lays the groundwork for P vs NP, then dies. Then, a year later, Fischer publishes a proof. P = NP. Overnight, he becomes one of the most famous mathematicians of his generation. Outstripping even his friend. Right?”

I nodded.

“Well I don’t think he solved it. I think Tendring did. I don’t think this is a suicide note. I think it’s P=NP, and that Fischer cracked it, didn’t tell anyone, and then claimed it as his own discovery.”

My eyes were wide.

“Aren’t you his TA?” I finally said.

She signed the bottom of the form and held it out for me.

“Yes. I am. So don’t mention anything to him, all right?”

︎

Even though the B had tanked me, I had liked Professor Fischer’s class a lot, and not just because of her. Students behave oddly around such a famous professor. Some shut down. Some act up. In the lecture hall, Tendring always hovered overhead—the anxious, tantalising possibility that he might be mentioned. But Fischer never did, of course, bring his dead genius friend up to a bunch of sophomores. He was very private.

She started coming by every couple of days to ask after her delivery. Once, when I wasn’t there, she left a note on my keyboard saying to call her as soon as it came in. Underneath, she printed a phone number.

Two weeks later, I heard my supervisor shout from the back office: “Who ordered a tea-chest through the fileshare?”

I jumped up and hurried in. Her files had been delivered in a wooden crate, like they’d travelled from Germany on a pirate ship.

Back at my desk I picked up the phone, rummaging around my desk for the note with her number. I found it and dialled.

A man answered.

“Fischer.”

My eyes widened.

“Hi,” I said, voice pitching up. “This is the archives desk. I’m looking for—one of your TAs.”

“Oh. It’s for you,” Fischer said. “Someone from the archive?”

I heard her reply, her words indistinct but her tone warm.

“She’s right here,” he said back to me. “I’ll send her your way.”

“Thank you,” I managed, mortified, and hung up, cutting off the noise of their amiable voices in his quiet office.

My heart was fluttering against my ribs like a moth searching for light. I imagined the two of them sitting on either side of a heavy desk, surrounded by shelves cluttered with books, the Fields Medal hanging on the wall among his other awards.

A few moments later, she arrived.

I took her to the back room, where the tea chest sat on a table. “We have them for the month,” I told her, “And they have to stay in here.”

She nodded, lifting a letter, tagged and individually filed in a plastic sleeve.

“But you can come in as often as you want. And I’ll check them out to you.”

She started laying them on the table, one by one.

“That coded note has whole web forums devoted to cracking it,” she said. “But they’re missing a huge amount of data. They’re missing all these letters.”

She opened a plastic bag, and pulled out an envelope. The return address, typewritten, read D. Fischer. She tapped the folded edge, and a letter slipped out. Neatly typed lines of ciphertext, signed at the bottom with a large, cursive F.

“You’re going to… decipher their mail?”

She gave a laugh. “You sound like my girlfriend. She says this whole thing is a fool’s errand—a nosy fool.”

My stomach was doing something; at the word “girlfriend” that something intensified.

“Yeah?” I said dumbly. Girlfriend as in female friend, probably, I reasoned. “Why?”

“Why do I want to do it? Because if it’s true, Fischer’s a fraud. Tendring deserves credit.”

“Credit?” I frowned, discomfort intensifying. I opened my mouth to say—what? He’s dead, so why does it matter? I’d sound like a wet, morbid blanket.

“It’s just that crypto isn’t my area,” she went on. “I’ve been reading up but… I could really use an extra pair of eyes. If you wanted to take a break from crosswords.”

I shut my mouth, my unformed objection dying in my throat. I felt like something I wanted was flying past me on a freight train and I had to grab on to catch hold before it plunged away over the horizon.

I nodded jerkily. “Yeah—oh, I’d love to help.”


So it began. I spent the month of November, for several evenings a week, helping her crack the epistolary code of two world-famous mathematicians.

When I wasn’t there, in the archives with her, I thought of little else. But when I was, I was overcome with nerves—afraid of being insufficient, afraid she might replace me, afraid I was not justifying my inconvenient presence.

One night, her girlfriend came in to pick her up—and yes, she was her girlfriend, because they kissed. She was beautiful.

It was a challenge, much more so than my pointless economics homework, which did not suffer from my neglect. With her, I was writing algorithms, helping code a program, inputting letter after letter after letter.

Late in those nights, when I looked at our reflection in the dark glass, the lights refracting away to vanishing points above our ghostly heads, I tried to communicate with my past self, transmit a message through time. To tell her that her beautiful, brilliant TA would confide in her, work long evenings with her on a secret project.

Or maybe I wanted to ask her, past-me, was this what you wanted? Would you want this?

It was a difficult code for us to break. But Fischer himself had proven it could be done.

Or rather, Tendring had. Because when she and I finally deciphered the text, her theory bore out; there it was, P = NP, the final brick of the proof that had made Fischer a household name.

We also discovered that the reason for their coded letters was that they were not only discussing math; they were lovers, or had been.

︎

“So you’re going to do it?”
“Yes,” she said, watching me pack the box with my special archive gloves.

“Post them online? All—all the letters?”

“Yes. Why not?”

“But he’d be… —outed.”

She looked up at me. “So?”

It was that simple for her.

I closed the crate, wishing I could send it backwards in time.

︎

“Why are you thinking of grad school?” my mother said sharply from the receiver.

I was standing in a phone booth. Outside, gloomy late November skies hung low. In my pocket, I fiddled with a scrap of paper—her little note to me, left on my keyboard weeks ago. A few days ago, she had stopped answering my calls.

“The long-term returns,” I said miserably into the phone.

“You don’t need a master’s to be an actuarial,” she said. I closed my eyes. “The longer you’re in school, the longer you wait to start a family…”

I was thinking about how Fischer’s own proof had proved that no code was unbreakable, and that the algorithms his work had spawned had evolved into the same program she had used to crack into his personal mail.

“Emma? Are you there?”

“Yeah.”

“Did you hear what I said about your hair?”

︎

I left the phone booth and stared down the street. The top corner of the math building was visible. I had to warn him. I decided.

I hadn’t been in this building since last spring. It was just as I remembered: dimly lit, concrete walls, cluttered bulletin boards.

On the fifth floor, his office door was open. But he wasn’t inside.

I looked in from the threshold. It was weirdly empty. Too large for its sparse contents—only a few bookshelves, no photos on the wall. I looked for his Fields Medal, but I didn’t see it anywhere. On his desk, by his computer and stacks of files, he had an old bronze lamp with a shade, looking out of place, like it belonged in a living room, not a mathematician’s office.

“Hi,” the professor said from behind me. “Were you looking for me?”

I started, shrinking towards the door frame. He passed me, somehow without coming within six inches of me, and entered his office. Fischer was thin, with glasses—the kind of man you knew, passing on the street, must be a math professor. Knowing everything else I knew, it was hard to look at him.

He took a seat behind his desk, rubbing his eyes and exhaling, before fixing his glasses and blinking up at me.

“Emma, right?” he said. “Come on in. Cath tells me you switched majors.”

“Yes,” I said, stepping into the room. “Econ.”

I felt like a butterfly getting pinned.

“That’s a shame,” he said. “I understand that it’s a more secure career path. But math really gets to the heart of things.”

“No future,” I said even more faintly.

“What’s that?” he said.

“Have you seen Cath?” I asked.

He shook his head. “Sorry. Are you looking for her?”

I opened my mouth, and almost said: “She hasn’t called me back, and I don’t know why…” But I did not, because I knew why. He was looking at me, frowning concernedly like someone who wants to give you a hand so you’ll stop bothering them. A vision of the future struck me: his fall from grace; that quiet, collected shell shattered; the shaming emails; the demotion; the awards revoked; the cruel notes tacked to the bulletin boards; the disgrace, the disgrace, the shame, the shame. I could see the word FRAUD spray-painted on the front door of his house, now surely as pristine as his cold, empty office.

I couldn’t back out, and I couldn’t look away from the vision. The real Professor Fischer frowned at me, unaware any of it was coming. But it was. And I prayed that when she published, she would give me no credit.
︎ ︎ ©Plates 2021
︎ ︎ ©Plates 2021