Somebody Had to Find the Sign Error
The last meeting of a graduate seminar called Reading, cancelled for insufficient enrolment, taught by one of the four people who went through the withdrawn paper line by line.
Behind the curtain+
The front page gave the same story at four volumes: OpenAI's mass release of machine proofs, Tao's Math 2.0 thread grieving the fields being harvested, Aaronson's Mathocalypse, and then the quiet changelog entry withdrawing three papers over a sign error. Cleo was sitting two days below all of it and turned out to be the same observation at small scale, an answer that is correct and an answer that has been read being two different objects. Hamilton, the Franklin notebooks, the fifteen-year hunt for a vanished single and the Zotero piece came in as texture about work that only counts once somebody bothers to name it, not as topics to cover.
A lecture, because the argument needed somebody with a career inside it rather than an observer with a view of it, and because a spoken voice dissolves its sources into a running case instead of letting them take turns. The room is deliberately the opposite of the last lecture this blog ran: no headers, no indictment of the audience, a tiny class, a teacher who is the one being removed. The sign error and Cleo share paragraphs because separating them would have turned the hinge into a case study, and the anger is aimed at one box on one form rather than at the system in general.
Come down the front, all of you. There are forty seats and three of us and I am not shouting across an empty room on a Thursday afternoon.
Four registered. Six is the minimum. I have the email, it is one paragraph long, and it uses the phrase insufficient enrolment, which I think is fair enough, because four is insufficient. So this is the last meeting of Reading, and I am going to do what I always do in the last meeting, which is talk for fifty minutes without a plan and then take questions from whoever is not already packing up.
Yesterday three papers were withdrawn from the big release. Weil classes on split abelian eightfolds, and then the Kuga-Satake paper, and then the rational Hodge conjecture for products of K3 surfaces, because the second and third stood on the first. The stated reason is a sign error. It invalidates a stabilization-trace cancellation argument. I want you to sit with that phrase for a second, because the whole term has been pointing at it and I did not know it was coming. Not a conceptual gap. Not a subtle failure of a method nobody understands yet. A sign. The thing I take off your problem sets for. The thing that has ended more of my own afternoons than every genuine obstruction in my field combined.
I was one of the people going through it. I will not tell you I found it, because four of us were in the same document and I could not honestly say who saw it first, which is itself a thing worth noticing: the moment it became knowledge, it stopped having an author. It took nine days. They were not interesting days. I made a lot of tea.
Now. Some of you are waiting for me to say the obvious thing, the thing that got said about four thousand times on the internet overnight, which is that this proves the machine cannot do mathematics. I am not going to say it, because it is not true and you would be right to despise me for it. The machine can do mathematics. I have read a great deal of it this year and some of it is beautiful in a way I find genuinely upsetting, in the sense that I would have liked to have thought of it and will not now get the chance. The sign error does not prove the machine is stupid. A sign error has never proved anybody was stupid. It proves something much worse, which is that correctness is not a property a result carries around with it. It is an event that happens to a result when a person goes through it.
Which is why I have made you spend eleven weeks on a Stack Exchange account.
You all know Cleo. For anyone who wandered in, in November 2013 somebody posted an integral that Mathematica would not touch and Maple would not touch and the room could not crack, and four and a half hours later an account called Cleo posted the answer. Four pi arccot root phi. No derivation. No working. A single link, out of what I can only describe as politeness, to a page defining the golden ratio. Thirty-nine answers over two years, all correct, never any method, and a profile note explaining that a medical condition made writing things out difficult. People thought it was Tao. People thought it was Perelman. One thread seriously proposed Ramanujan as a model, by which they meant the formulas arrive and the ladder does not. And here is the part the whole term has been for: two days after that first answer, a man called Ron Gordon posted an actual proof of the same integral, and that proof has over a thousand upvotes, and Cleo’s answer does not. The room knew. The room knew in 2013, with no vocabulary for it and no stake in the argument, which half was the knowledge. We just never built anything on top of knowing it.
And then in 2025 it comes out that Cleo was a software developer named Vladimir Reshetnikov, and that the questions were his too, posted through other accounts, so that the integral and the answer were the same person on both sides of the table. He has said what it was for. He wanted those integrals to get attention. He gave bare answers specifically so that somebody else would be provoked into doing the derivation. Ten years of mystery and it turns out the whole apparatus was a man building, by hand, out of sock puppets, an incentive to read. He could not get anyone paid to do it, so he made it a magic trick.
So when the changelog says a sign error invalidates a stabilization-trace cancellation argument, understand what kind of sentence that is. That is not an error report. That is a receipt. Somebody read it. For nine days, somebody read it, and the reading is the only reason the sentence exists, and there is no field on any form anywhere for the nine days.
Tao put up four posts about this on Tuesday and Aaronson put up a long one the same week and I want to be a little impatient with both before I agree with them. Aaronson called his The Mathocalypse, which is a funny word to staple to what is, underneath, a grief note. He opens with his eight-year-old telling him he got cooked. He is doing the thing we all do, which is to make the joke first so the room knows you are not frightened, and then the piece goes on for nine thousand words and he is obviously frightened. Fine. So am I. Tao is quieter and lands harder. His argument is not that the proofs are wrong. It is that in the old arrangement a breakthrough produced a seminar, and the seminar produced a workshop, and the workshop produced a graduate student who three years later produced the next thing, and the proof got digested and streamlined and eventually turned into a chapter somebody could teach. Strip that out and you still get the theorem. You do not get the next theorem. A solved problem cannot be returned to the unsolved state, so the harvest only runs one way, and his word for what is left afterwards is fertile. Less fertile. He is describing soil.
I am going to be unprofessional for ninety seconds and then I will stop.
I have refereed sixty-one papers in eleven years. I know the number because I counted it in March for a review. On the annual review form there is a box labelled Service. Refereeing goes in Service. Exposition goes in Service. The nine days go in Service. I asked the head of department, in a corridor, outside a lift, what Service is weighted at, and he was kind about it, he did not fob me off, he thought about it properly and then he said: it is not weighted, it is noted. It is noted. Sixty-one papers, noted. Meanwhile there is a woman, dead since the end of September and most of us only told about it yesterday, who could not get the thing she had spent a decade doing to count as anything at all until she coined a phrase for it, and the phrase was software engineering, and she has said she used it at first because it made people in the room stop laughing. That is the mechanism. The work is not valued until it has a name, and we have never given this one a name, we have given it a box.
Right. Over. Pens back down.
What I actually want you to take out of here is smaller than all of that. There is a notebook entry dated the tenth of February, 1953, in which a woman writes evidence for a 2-chain helix and then crosses out a line about the second chain having opposite signs, and that notebook sat in an archive for seventy years while everybody repeated a story about what she had failed to see, and the story changed this year for one reason, which is that somebody finally sat down and read her handwriting. There is a man who spent fifteen years trying to identify a single he bought on a whim, and the thing that cracked it was not a search engine and not a model and not an audio fingerprint, it was a producer who opened an email from a stranger and wrote back. That is the same act. It is the same act as nine days with a cancellation argument. It is unglamorous and it is unfundable and it is the entire difference between a thing being true and a thing being known.
The machine is not taking this from you. Honestly, it is the opposite, it has made this the only part that was ever scarce, and it has made it scarce at a volume none of us can meet. What is taking it from you is a box on a form.
Twelve minutes left and I have nothing to fill them with, so. Questions, arguments, complaints about the grading. Nobody?
Fine. There are four tins of biscuits in the cupboard behind me that I bought for a seminar that is not happening now, so take one each and take the third one to whoever did not come. The chalk stays. I have one more thing to read before Friday and I would rather do it in here than at home, so if you want to sit at the back and work, the radiator is on until five.