Gardner Dozois - The Years Best Science Fiction, Vol. 18

Everyone remembers where they were and what they were doing when a member of the great and the good is assassinated. Gandhi, the Pope, Thatcher-if you were old enough you remembered where you were when you heard, the ticker-tape of history etched across your senses. You can kill a politician but their ideas usually live on. They have a life of their own. How much more dangerous, then, the ideas of mathematicians?

I was elbow-deep in an eviscerated PC , performing open heart surgery on a diseased network card, when the news about the traveling salesman theorem came in. Over on the other side of the office John’s terminal beeped, notification of incoming mail. A moment later my own workstation bonged.

“Hey, Geoff! Get a load of this!”

I carried on screwing the card back into its chassis. John is not a priority interrupt.

“Someone’s come up with a proof that NP - complete problems lie in P! There’s a posting incomp.risks saying they’ve used it to find an O*(n?2) solution to the traveling salesman problem, and it scales! Looks like April First has come early this year, doesn’t it?”

I dropped the PC’s lid on the floor hastily and sat down at my workstation. Another cubed-sphere hypothesis, another flame war in the math newsgroups-or something more serious? “When did it arrive?” I called over the partition. Soroya, passing my cubicle entrance with a cup of coffee, cast me a dirty look; loud voices aren’t welcome in open-plan offices.

“This just in,” John replied. I opened up the mailtool and hit on the top of the list, which turned out to be a memo from HR about diversity awareness training. No, next…they want to close the smoking room and make us a 100% tobacco-free workplace. Hmm. Next.

Forwarded e-mail: headers bearing the spoor of a thousand mail servers, from Addis-Ababa to Ulan Bator. Before it had entered our internal mail network it had traveled from Taiwan to Rochester NJ , then to UCB in the Bay Area, then via a mailing list to all points; once in-company it had been bounced to everyone in engineering and management by the first recipient, Eric the Canary. (Eric is the departmental plant. Spends all the day web-dozing for juicy nuggets of new information if you let him. A one-man wire service: which is why I always ended up finishing his jobs.) I skimmed the message, then read it again. Blinked. This kind of stuff is heavy on the surreal number theory: about as digestible as an Egyptian mummy soaked in tabasco sauce for three thousand years.

Then I poked at the web page the theorem was on.

No response-server timed out.

Someone or something was hitting on the web server with the proof: I figured it had to be all the geeks who’d caught wind of the chain letter so far. My interest was up, so I hit the “reload” button, and something else came up on screen.

Lots of theorems-looked like the same stuff as the e-mail, only this time with some fun graphics.

Something tickled my hindbrain then, and I had to bite my lip to keep from laughing. Next thing, I hit the print button and the inkjet next to my desk began to mutter and click. There was a link near the bottom of the page to the author’s bibliography, so I clicked on that and the server threw another “go away, I’m busy” error. I tugged my beard thoughtfully, and instead of pressing “back” I pressed “reload.”

The browser thought to itself for a bit-then a page began to appear on my screen. The wrong page. I glanced at the document title at the top and froze:

THE PAGE AT THIS LOCATION HAS BEEN WITHDRAWN.

Please enter your e-mail address if you require further information.

Hmm.

As soon as the printout was finished, I wandered around to the photocopier next door to the QA labs and ran off a copy. Faxed it to a certain number, along with an EYES UP note on a yellow Post-it. Then I poked my head around into the QA lab itself. It was dingy in there, as usual, and half the cubicles were empty of human life. Nobody here but us computers; workstations humming away, sucking juice and meditating on who-knew-what questions. (Actually, Idid know: they were mostly running test harnesses, repetitively pounding simulated input data into the programs we’d so carefully built, in the hope of making them fall over or start singing “God Save the King.”) The efficiency of code was frequently a bone of contention between our departments, but the war between software engineering and quality assurance is a long-drawn-out affair: each side needs the other to justify its survival.

I was looking for Amin. Amin with the doctorate in discrete number theory, now slumming it in this company of engineers: my other canary in a number-crunching coal mine. I found him: feet propped up on the lidless hulk of a big Compaq server, mousing away like mad at a big monitor. I squinted; it looked vaguely familiar…“Quake? Or Golgotha?” I asked.

“Golgotha. We’ve got Marketing bottled up on the second floor.”

“How’s the network looking?”

He shrugged, then punched the hold button. “No crashes, no dropped packets-this cut looks pretty solid. We’ve been playing for three days now. What can I do for you?”

I shoved the printout under his nose. “This seem feasible to you?”

“Hold on a mo.” He hit the pause key them scanned it rapidly. Did a double-take. “You’re not shitting?”

“Came out about two hours ago.”

“Jesus Homeboy Christ riding into town at the head of a convoy of Hell’s Angels with a police escort…” he shook his head. Amin always swears by Jesus, a weird side-effect of a westernized Islamic upbringing: take somebody else’s prophet’s name in vain. “If it’s true, I can think of at least three different ways we can make money at it, and at least two more to end up in prison. You don’t use PGP , do you?”

“Why bother?” I asked, my heart pounding. “I’ve got nothing to hide.”

“If this is true-” he tapped the papers “-then every encryption algorithm except the one time pad has just fallen over. Take a while to be sure, but…that crunch you heard in the distance was the sound of every secure commerce server on the internet succumbing to a brute-force attack. The script kiddies will be creaming themselves. Jesus Christ.” He rubbed his mustache thoughtfully.

“Does it make sense to you?” I persisted.

“Come back in five minutes and I’ll tell you.”

“Okay.”

I wandered over to the coffee station, thinking very hard. People hung around and generally behaved as if it was just another day; maybe it was. But then again, if that paper was true, quite a lot of stones had just been turned over and if you were one of the pale guys who lived underneath it was time to scurry for cover. And it had looked good to me: by the prickling in my palms and the gibbering cackle in the back of my skull, something very deep had recognized it. Amin’s confirmation would be just the icing on the cake confirmation that it was a workable proof.

Cryptography-the science of encoding messages-relies on certain findings in mathematics: that certain operations are inherently more difficult than others. For example, finding the common prime factors of a long number which is a product of those primes is far harder than taking two primes and multiplying them together.

Some processes are not simply made difficult, but impossible because of this asymmetry; it’s not feasible to come up with a deterministic answer to certain puzzles in finite time. Take the traveling salesman problem, for example. A salesman has to visit a whole slew of cities which are connected to their neighbors by a road network. Is there a way for the salesman to figure out a best-possible route that visits each city without wasting time by returning to a previously visited site, for all possible networks of cities? The conventional answer is no-and this has big implications for a huge set of computing applications. Network topology, expert systems-the traditional tool of the AI community-financial systems, and…