Chapter 15: Ripple
I woke up on Saturday morning to twenty-three emails. By the time I'd brushed my teeth and come back there were twenty-five.
I sat on the edge of my bed scrolling through them. My brain couldn't keep up with my thumb. Every time I finished reading one and went back to the list there were more. I recognised some of the names from the papers I'd been reading all week. People I'd been citing in my own proof were now emailing me about it.
Then I found the Twitter thread.
Some maths blogger with forty thousand followers had posted a link to my paper with a breakdown of the proof. The thread had hundreds of retweets. People I'd never heard of were arguing about my eigenvalue calculation in the replies. Someone had made a diagram of the sign-flip. Someone else had written "this is either the most elegant proof I've seen in a decade or I'm missing something massive" and the replies underneath were all saying no, you're not missing anything, it's just that good.
I put my phone down on the bed and stared at the wall for a bit.
"This is mental. This is actually mental."
I picked the phone back up. Twenty-seven now.
I went downstairs. Mum was in the kitchen making toast. Biscuit was sitting by his bowl looking tragic.
"Morning, love. Tea?"
"Yeah. Please." I sat down at the table and put my phone face-down because if I kept looking at it I was going to lose my mind. "Mum, you know how I said some people had read my paper?"
"The professors in America. Yes."
"It's not a few people anymore. It's dozens. Someone put it on Twitter and it's everywhere. Mathematicians are sharing it and writing about it and arguing about it in the comments and I have no idea what I'm supposed to do with any of this."
She put a cup of tea in front of me and sat down across the table.
"Is it still right? The maths?"
"Yeah. Nobody's found a mistake. Not one."
"Then you don't need to do anything, love. You just let it happen."
She was right but letting it happen was harder than it sounded when your phone buzzed every twenty minutes with another professor from another country telling you that your proof had changed their field. I drank my tea. Mum went back to making toast. Biscuit gave up on breakfast and lay down on my feet instead. Normal Saturday morning. Except it wasn't.
University of Bonn
Lena Richter put her printed copy of the paper down on Professor Weber's desk and sat back in her chair.
"The Cauchy interlacing step," she said. "That's where I expected it to break. Every other attempt I've read falls apart right there. But it doesn't. The eigenvalue bound feeds directly into the interlacing theorem and the whole thing locks together. I've checked it twice." She shook her head. "It's annoying how clean it is."
Klaus took off his glasses and cleaned them on his shirt. He'd worked on the conjecture himself fifteen years ago. Two years on a modified approach that collapsed when he couldn't get the bound below logarithmic. He still had the notebooks in his drawer.
"I looked at that matrix for two years," he said. "Tried changing weights, restricting to subgraphs, everything I could think of. Never tried flipping the signs. Not once." He picked up the paper again. "I've written to him. The paper gives the result but not the journey. I want to know what made him look at the matrix and see something different from what the rest of us saw."
"You think he has more in him?"
"I think someone who sees a problem this way at nineteen doesn't stop at one result." He put the paper down. "Go home, Lena. It will still be correct on Monday."
Cambridge
I don't read papers from students I haven't heard of. As a rule. The pile on my desk is too tall and most unsolicited submissions from unknown undergraduates are what you'd expect. Ambitious, earnest, and wrong.
Michael Hargreaves sent this one to me on Friday evening with a note that said: "Eleanor, read this before Monday. Trust me."
Michael doesn't say things like that. So I read it.
The title was clear enough. A proof of the Sensitivity Conjecture. I've seen that title before. Usually attached to fifty pages of machinery that collapses around page thirty when the author runs out of rigour and starts relying on hope. Seven pages. The proof itself, less than two.
I started reading with the intention of finding where it broke.
The sign-flip on the edges of the hypercube. Deliberate. Tied to the structure of the graph itself. I followed the eigenvalue calculation. The largest eigenvalue of the modified matrix came out to the square root of n.
I put the paper down. Picked it up again.
I read it a second time. Slowly. Every line. Looking for the hidden assumption, the hand-wave, the step where he'd hoped nobody would check.
There were no hidden assumptions. The argument was clean and complete and irritatingly short.
I sat at my desk for a long time after finishing. The office was dark. My tea had gone cold and I was holding two pages that had just turned a twenty-four year old open problem into a theorem.
Liam Reed. Undergraduate. A university I would not normally associate with work at this level. No previous publications. No departmental page. He had appeared from nowhere.
I composed an email. Carefully. I wanted him to know that his work had been read by someone who understood what it meant. And I wanted to have a conversation with him before Oxford and Imperial started circling.
Subject line: "Congratulations."
I reread it twice, adjusted one sentence, and pressed send.
Then I called David Alderton in admissions. Saturday evening. He didn't answer. I left a voicemail.
"David. It's Eleanor Shaw. Monday morning. A prospective student called Liam Reed. You won't have heard of him yet but you will by the end of the week. I want us talking to him before anyone else does."
Liam POV
I sat at my desk staring at the forum and tried to remember the last time I'd opened Tor.
A week. Maybe more. The whole Liam side of my life had swallowed everything else. The emails, the maths, the anxiety of sitting around waiting for someone to tell me I was wrong. Null had been sitting here the whole time. Eight completed jobs. Clean record. BlackVault's message from last week still unread.
I scrolled through the listings. A job near the top caught my eye. Posted two hours ago. Security audit on a cryptocurrency exchange in Estonia. Their cold wallet implementation was supposedly airtight. Bounty was 0.3 BTC.
I turned on System Insight. Took me about thirty seconds to see three different ways in.
"Pfff. Airtight. Right."
I took the job and started working. And it felt good. After a week of refreshing my inbox and second-guessing myself, sitting here with a target and a clear path felt like stretching after sitting still too long. No waiting. No wondering. Just the work.
In and out in twenty minutes. Documented everything, posted proof, collected the bounty. 0.3 BTC. About ninety quid. Not the point. The point was that I'd been gone for a week and the forum hadn't forgotten me and Null still worked and I still had this. Whatever happened with the paper and the emails and whatever came next, I still had this.
Nine completed jobs. Clean record.
A message from BlackVault. New one. "Thought you'd gone quiet. Good to see you back."
I closed the laptop and went to bed. Biscuit was already on the pillow.
"Budge over."
He didn't budge. I worked around him.
I was almost asleep when my phone buzzed on the desk. I nearly didn't check it. Nearly. But my hand was reaching for it before my brain had finished deciding.
One new email. The subject line was one word.
"Congratulations."
I sat up so fast that Biscuit jumped off the pillow and gave me a look like I'd personally offended him.
Professor Eleanor Shaw. Department of Mathematics. University of Cambridge.
She'd read my proof. She called it clean, complete, and significant. She wanted to arrange a conversation at my earliest convenience.
I put the phone down on my chest and lay back in the dark. Biscuit settled against my leg.
"Cambridge," I said quietly. "Fucking Cambridge."