Slopocalypse

Posted on October 6, 2026 by woit

OpenAI has just released a vast number of new results in preprint form, see here. These are the products of an internal frontier model. About the AGMAI, they say they “have drawn on their advice and public recommendations⁠ to inform how we release these results.”, although one of the recommendations at the top was “we ask them to stop testing advanced mathematical problems on proprietary models.”

Like everyone else, I’ll spend some of this evening sorting through the long list to see what is of interest.

Update: Some quick thoughts about the slopocalypse. Note that this is happening in a seriously polluted and dysfunctional information environment. Maybe it’s my incompetence at dealing with social media, but the only way I’ve found of finding out relevant news about the slopocpalypse is by supporting Elon Musk’s Fascist enterprise and scrolling through an endless sewer of crap on X to find the few instances where well-informed mathematicians are quickly tweeting out relevant information. Lots of problems with getting your information this way, including walking around all the time depressed and disgusted at the state of the world. That said:

  • A striking aspect of the paper dump is how sloppy it is at every level. The dump is a disorganized mess: after scrolling through long lists of papers and trying to read a couple, I realized that the huge list I’d gone through was only a fraction of the 722 papers, and that trying to find things this way would take forever. It’s hard not to think the people responsible for this just don’t care. If Astra is so great, couldn’t someone have taken 30 seconds to type into it a prompt “Please organize this in a coherent and useful way”?
  • When the Navier-Stokes trainwreck happened, there was a concerted effort from within the math community to get to the public a counter-narrative to that of OpenAI. I’ve seen nothing like that this time. The AGMAI group supposedly dealing with OpenAI last week put out an excellent list of recommendations. OpenAI completely ignored them, and AGMAI then issued a statement I don’t understand at all. They are the people in the best position to evaluate whether their recommendations were followed, but instead of doing this, they write “it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully.”
  • One thing you can learn on X today: some of the proofs are just wrong.
  • Another one: some of the slop is supposedly verified by Lean. Can we trust this? Maybe not for Navier-Stokes, what about the hundreds of others?.
  • Is Astra getting these proofs from its access to mathematician’s private work? See the first paragraph on page 3 here.
  • According to OpenAI, these proofs were all produced with simple prompts to next version of Astra, applied to 4000 open problems in mathematics. What was the point of doing this? If the goal of OpenAI researchers is to improve their product, it would make sense to try a much more modest number of problems, then use the results to figure out how to do better (e.g. provide writeups that are readable…).
    It seems to that the answer to this is that they were trying to exploit a weakness in the mathematics research incentive structure, where people earn credits by solving these sorts of problems, even though this is a proxy for what is really important (new understanding). What OpenAI chose to do was to carpet-bomb mathematics, grabbing as many as possible of the chips on the table.
  • I have a lot of trouble knowing what to think of the “AI alignment problem”, that of ensuring alignment between AI behavior and wholesome human goals. It does seem clear that the math community (and the rest of humanity) has a serious and immediate “OpenAI alignment problem”, with a huge misalignment between that corporation’s behavior and what is best for mathematics in particular and humanity in general.
  • Another thing you learn on Elon Musk’s sewer is that a factor generating enthusiasm for our tech overlords and their new world is the exploitation of resentment of “elites”. In particular, criticism of the slopocalypse is widely denounced as nothing but the whining of pointy-headed over-privileged intellectuals who finally are getting theirs.

Update: There’s a very interesting collection of reactions to the slopocalypse here.

Posted in AI | 17 Comments

Some HEP-TH News

Posted on September 25, 2026 by woit

In a previous posting, I’d noted that the number of arXiv hep-th preprints/month was significantly higher recently, clearly due to LLM use, but that I hadn’t heard of much in the way of significant new results coming from this. Around the same time, Matt von Hippel issued a challenge to the LLM agents:

So if AI companies want to impress people like me (or scare us, for that matter), then they need to tackle my old field. Show that an AI can take the kinds of computer resources an academic has access to, and solve one of the scattering amplitudes field’s big outstanding problems. Show that a computational limit everyone expected to be a problem doesn’t actually matter. Give us N=8 supergravity to seven loops, or N=4 super Yang-Mills to nine loops.

People at Anthropic took up the challenge, and today announced that Yes, Claude can do Nine Loops. Supposedly this was a “one-shot”:

after asking Claude which problem it was most likely to be able to tackle, they gave it a simple prompt:

“The problem is to compute the Six-particle (hexagon) amplitude in planar N=4 SYM at nine loops.”

From there, they just kept telling it to keep going, with comments like:

“I’m going to sleep and won’t be available for another several hours. Keep working on this until I tell you to stop. Give me updates every 4-6 hours.”

After using one to two thousand dollars worth of Claude time, they got a result. This was sent on September 1 to Lance Dixon, who had techniques that allowed him to validate the result.

The computation of amplitudes like this has become a significant part of hep-th in recent years, heavily promoted by Nima Arkani-Hamed. There’s no practical application of knowing things like this nine loop amplitude, but Arkani-Hamed always has emphasized that the motivation is to use such calculations to get inspiration for a very different fundamental definition of the theory in terms of new geometrical objects. I have no idea whether this nine loop result is helpful for that. It appears that Claude did not come up with a new method, just used known calculational methods. This is an extremely complex sort of calculation.

It will be interesting to see how these new tools change the way those in the large community of theorists doing such calculations pursue their work and publish their results. Will the new AI tools help them come up with new methods for computing amplitudes and new insights into their structure, or will they just make them obsolete, replaceable by any button-presser with a couple thousand dollars and no expertise?

At the other end of hep-th, there’s the even larger community of theorists who, inspired by AdS/CFT, believe the right way to understand quantum gravity is in some sort of quantum information/holographic terms (“it from qubit” is the slogan). Writers at Quanta magazine have always been quite enthusiastic about this direction in hep-th, and today Charlie Wood has a piece about it, entitled Gravity Seems Holographic. What Does That Mean for Reality?. Wood explains the background and latest thinking in this research direction, concluding:

At this point, I subscribe to a more extreme variation of the it from qubit interpretation — mostly just following the rumble of the stampede. I’d bet that the qubits are the real things, but that they don’t live on anything as familiar as a flat screen.

Physicists have tried to stretch the AdS/CFT correspondence to fit de Sitter space — which has no obvious screen — for decades, with limited success. In recent years, they’ve started to get more creative. Susskind and other teams have made progress (opens a new tab) on holographic de Sitter models (opens a new tab) that differ radically from AdS/CFT. Instead of squashing a volume into an area, these universes seem to cram all the dimensions into a lone quantum point. I imagine a bunch of quantum pixels all coexisting in one spot, rather than spreading across a screen. That might be hard to visualize, but we’re already accepting the idea of dropping one dimension of space. Why should tossing the others be so different?

Balasubramanian suspects that even this kind of radical model doesn’t go far enough. Einstein’s theory fused space with time, and so if the three dimensions of space emerge from a spaceless point, then time should emerge from something timeless. Somehow, we and everything we experience exist within an unblinking dot of no size.

I don’t think we’re there yet, but if Claude does become super-intelligent, way beyond our best theorists, we should be able to soon ask: “Claude, is this bullshit or not?” I’m not super-intelligent, but bet that I already know the answer…

Update: More from Matt von Hippel.

Update: Claude has made a new contribution to theoretical physics, finding a computational error in an Appendix of a well-known paper from the 1980s.

Posted in AI, This Week's Hype | 17 Comments

A Modest Proposal

Posted on September 9, 2026 by woit

The announcement yesterday by OpenAI of a solution to the Millennium Prize Navier-Stokes problem has been causing a great deal of discussion among mathematicians. There’s a lot to be said about this story and its implications, most of which I’ll leave to those better informed than me (for one thing, I understand basically nothing about the problem, or its solution).

While talking to people I started to realize that one thing that really bothers me about these kinds of announcements is that they’ve been coming with no information at all about how the result was achieved. Emphasis has been on the question of whether the proof is correct or understandable, but I now think people should start asking another sort of question: exactly how was this done?

Sam Altman yesterday explained that

we tried this because there were rumors on the internet last week that Anthropic’s models had solved a millennium problem and we were curious if ours could do it too.

The rumor of this kind circulating was this one, with first appearance on September 4. Altman appears to be claiming that OpenAI solved the Navier-Stokes problem over the weekend, starting just with the information that maybe Anthropic had a solution. Altman is famous though for being “unconstrained by the truth.”

Tristan Buckmaster and Levent Alpoge had been working for a year on Navier-Stokes with some AI agent help, see here. The rumor I’ve heard is that Levent told colleagues at Anthropic that he and Buckmaster were close to a solution, and that this news somehow got to people at OpenAI, possibly including some information about the methods being used.

The new AI agents have profound implications for mathematics research and I think the math community needs to start discussing specific ways to deal with these. Here’s a modest proposal: the math community needs to adopt a version of the ethical standards of experimental science. If you are using AI agents, you can’t just give a proof (formalized or not), but need to also provide a detailed explanation of how these agents were used to get the result.

In an experimental science you cannot just publish results of an experiment, you also need to precisely describe the experimental setup that produced the results. One reason for this is reproducibility: other scientists need to be able to check the result by performing the same experiment. This is not so much of a concern in mathematics, where it is traditional to instead focus on the checkability of the proof.

There are other reasons though for having this standard in experimental science. Publishing the details of how to perform an experiment makes it possible for other scientists to adopt the same experimental method and make further progress by improving it or using it to get other results. I’d argue that it is now extremely important for the math community to see exactly what AI agent methods are being used, so that they can be adopted by others who want to try and use them.

In the Navier-Stokes case, I suggest that the community should demand that OpenAI provide documentation of exactly how they got this result. This would help others who want to use these methods, and it would also resolve questions about priority. What AI agents and training data did they use, what prompts were given to them and when was this done?

Besides issues of priority (which are going to be challenging since they involve the training data), this could also help with the problem of what’s a publishable result. If a result was achieved just by prompting an agent with “solve problem X”, it can be treated in a different way than results achieved through original human work and insight.

The new AI tools are going to change mathematics research. It’s critical that mathematicians have access to the details of what they are and how they are being used (as well as access to the tools themselves, a separate issue). One can imagine a future in which AI agents leave no role for human mathematicians (or, humans at all…). More hopefully, they will get integrated into human-driven activity to continue to make progress in exploring and understanding the world of mathematical objects (as well as the relations of such objects to those of the physical world).

Update: A helpful correspondent points me to the the OpenAI writeup, which says

On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved… Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge…

They don’t specify though the source of the rumors, or when they found out this was a rumor about what Levent Alpöge was doing. Altman says the source was “rumors on the internet”, but I’m not seeing a source for internet Sept. 1 rumors. Another description of the rumors, appearing on the internet on Sept. 5 is here, which characterizes the rumors not as “rumors on the internet” but as third-hand private communications starting at OpenAI.

From what I can tell, there has been a cottage industry for a while of people trying to solve the Navier-Stokes problem with AI agents (Sabine Hossenfelder describes her efforts here). It seems likely the AI companies have been regularly trying out their new models on Millennium problems, but have had limited resources to do so. In this particular case they devoted resources estimated at more than \$10 million to the Navier-Stokes problem. In their writeup they say this was because they were seeing positive results with an easier problem.

Update: Kenneth Chang has a detailed story at the New York Times that discusses backstory of the OpenAI Navier-Stokes claims.

I’d like to emphasize that this posting only deals with one small part of the new AI problem for math, a part where I thought I could make a positive suggestion. For a passionate discussion of the larger picture, I can recommend David Madore’s Sur la destruction des maths par les boîtes d’IA.

Update: The Advisory Group on Mathematics and Artificial Intelligence, which was formed to provide OpenAI advice on what it should be doing with its claims to have solved major problem in mathematics, has released a statement on the Responsible Release of AI-Generated Mathematics. They make several excellent points about how this should be done (including calling for the release of details of how results are achieved).

They start with a strong demand, that the AI companies stop using unreleased proprietary models to solve mathematics problems:

At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community. Our recommendations are formulated with this practical context in mind. However, ideally, they would not do so. We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.

Posted in AI | 21 Comments

The Situation at Columbia XXXVII

Posted on September 7, 2026 by woit

Ever since a new Columbia president (Jennifer Mnookin) was appointed by the trustees back in January, many have been wondering if she would do anything to try and change Columbia’s reputation as “Vichy on the Hudson”. The reason for this reputation is obvious if you try to get on the Columbia campus, which historically has always been open. Nowadays to enter the campus you’ll need to show your papers (or QR code) to the guards at “Checkpoint Charlie”. This is because of the necessity of “keeping the Columbia community safe.”

If you try and figure out what “safety problem” the checkpoints and the large new security force are there to protect against, you’ll quickly realize that the danger is that you might hold up a “Free Palestine” sign and start shouting anti-Israel slogans. If that happened, people would take pictures and video, soon social media and the New York Post would be full of stories about “anti-semitic violence at Columbia”, and Steven Miller would again take away the university’s federal funding.

Since Mnookin was appointed, the question many people have been asking is whether she would take action to remove “Checkpoint Charlie” and restore free access to the campus. Most local politicians have now taken a stance against the closing of the gates, often pointing out that it was probably illegal (a city street, 116th street, runs through the center of campus). With a new mayor (Mamdani) and new local congressional representative (Darializa Chevalier) possibly applying more pressure, most people were assuming Mnookin would have to reopen the gates.

Today she gave her answer to the question, which could be summarized as “No Way”. More specifically she announced the following steps:

  • Appointment of another committee, charged with advising her not on how to get rid of “Checkpoint Charlie” but with tuning how the QR codes work (i.e. “further increasing access”).
  • As of 8am tomorrow, accompanied minors under the age of 12 will no longer need their own QR code.
  • A new structure will be erected in front of “Checkpoint Charlie”, the “Checkpoint Charlie Kiosk”. The Kiosk staff will be responsible for dealing with the annoying small crowd that accumulates daily of people whose QR code isn’t working, tourists whose guidebook tells them to visit the campus, parents who want to accompany their child onto campus, children above the age of 12 without their own QR code, etc.

If you want to better understand how Columbia ended up where it is, you can read the 36 previous postings in this series. In retrospect, this is all about support for the ongoing Israeli campaign of ethnic cleansing and genocide, which continues with daily slaughter of civilians and demolitions of their homes and communities in Gaza, the West Bank, and now southern Lebanon. The Fascist regime now ruling the US both enables this and has effectively used bogus accusations of “antisemitism” to damage and exert control over prominent institutions they consider to be enemies.

The campaign to paint anti-genocide demonstrations as “antisemitic”, violent and threatening to people’s “safety” began not under Trump but under the Biden administration. For a clear explanation of the logic of these accusations, I can recommend the writings of Scott Aaronson, especially his essay on Deep Zionism. In his view, Palestinians want to murder him and his family. To him what’s going on in Gaza is not genocide but the necessary murder of the families of those who want to murder his family (for some reason he feels that this should be done with “middle-finger raised high”). If you chant pro-Palestinian slogans, you too want to murder his family. Hard to argue with the idea that allowing potential murderers on campus is a safety concern, so, here we are.

Update: The Columbia Spectator has an article about this. They point out that advisory committee is not new, but was announced back in January 2025 (see here). Mnookin’s announcement doesn’t mention this or say anything about what happened to the older version of the same committee.

Posted in The Situation at Columbia | 12 Comments

The 92-Year-Old Mathematician and the Teenage Apprentice

Posted on September 7, 2026 by woit

As an antidote to the overwhelmingly depressing news of the world, I highly recommend reading the new article in the New York Times about this mathematical result.

There have been some articles about this earlier in places like Scientific American that emphasized the role of Joan Birman, who is still active at 99. I’ve been hearing from Joan regularly over the past few years about this project, and she always described it to me as largely the work of a talented young woman, Vasudha Bharathram. The New York Times story does a great job of explaining the story of this remarkable collaboration.

Posted in Uncategorized | 3 Comments

This Week’s Hype

Posted on August 25, 2026 by woit

The Economist today reports that New theories and experiments should shine light on string theory. This is more of the promotional campaign for Cumrun Vafa’s “dark dimension”.

We’re told that a torsion balance experiment in Austria will “according to Dr. Vafa’s calculations” possibly detect the “dark dimension”. Vafa has convinced The Economist that

in the dark dimension, string theory has made a testable prediction. And for a topic that has been stuck in the mud for half a century, that should be lauded.

This is complete nonsense, a shame that The Economist has been taken in by it.

Update: Sabine Hossenfelder gives this a 10 out of 10 on the bullshit meter.

Posted in This Week's Hype | 8 Comments

HEP-TH and AI

Posted on August 16, 2026 by woit

I’ve been talking to people and seeing a lot of discussion about the effects of AI agents on math research, but haven’t found much serious discussion of what is happening in hep-th research. I’m curious to hear from those involved about exactly what is happening as researchers try and exploit these new tools.

Back in February I tried to generate some data about trends in hep-th submissions, initially got this wrong by using “recently modified”, rather than “initial submission” dates. I’ve started playing with some AI agents, and one thing they’re good for is generating python scripts to gather and plot this kind of data. Here’s what hep-th submissions (not including cross-listings) look like for the past three months, compared to earlier years.

There’s a very clear pattern: the rate of hep-th submissions is now about 1/3 higher this year than in previous years.

I haven’t tried to count submissions acknowledging AI use, and from a quick look at the submissions, there are relatively few that explicitly advertise dependence on AI generated results.

One thing that is showing up is that, in hep-th as elsewhere, AI is being used to scam the public. A new press release from King’s College London announces that String theory finally testable with power of AI, which is based on this hep-th preprint, recently published in Phys. Rev. D. The press release includes:

Overturning decades of popular conjecture that theoretical string theory cannot be tested, scientists have robustly proved that it can be for the first time…

Author Dr David Marsh, Ernest Rutherford Fellow at King’s College London, said “The popular understanding that you can’t experimentally test string theory is no longer true. While previous studies have tested a few different models of string theory, our computational approach improves on this with rigorous testing across millions of different models.

“Rigorous falsification is the core of scientific experiment, and by finally applying this to string theory we finally have the tools to test this vaunted ‘theory of everything’. Finally touching experimentation here is an exciting step forward for theoretical particle physics.”

So, it’s clear that AI agents can produce hep-th papers designed to be promoted as outrageous bullshit, but I’m interested to hear about the opposite end of the credibility spectrum. What are examples of serious advances in the subject that are coming from AI tools?

Update: Numbers for August.

The rate of increase year to year is accelerating, up 49% in August.

Update: Yes, I’m aware of the news today (9/8) about Navier-Stokes. It’s not a topic though on which I have anything much to contribute. I may very well write something later, once the details of how this happened become clearer.

Posted in AI, This Week's Hype | 26 Comments

Requiem for a Field?

Posted on July 26, 2026 by woit

Kevin Hartnett posted the following Friday:

My profile of @Jacob_Tsimerman, published the morning he won the Fields Medal, and hours before he announced he’s going to @OpenAI, reads like a requiem for a field.

While I’m trying to not spend too much time thinking about the ongoing story of the effect of AI agents on math, the story of Jacob Tsimerman’s Fields medal award coinciding with his announcement that he’s leaving research math to go work of OpenAI is hard to ignore. If you do want to spend time thinking about the implications of this, it’s worth reading the profiles at the New York Times as well as Hartnett’s at Quanta Magazine. Also very much worth reading is Tsimerman’s own explanation (in an exchange with Daniel Litt) of how he sees things. This was written before the OpenAI announcement, but goes a ways towards explaining Tsimerman’s decision.

A few personal comments: I’ve never had any interest in the kind of problem-solving Tsimerman specializes in, so have no idea if he’s right that humans will no longer be able to compete with the AI agents in this area within the next few years. His current situation makes him a very special case. In the Quanta profile he explains that he quit math competitions once he got a perfect score at the 2004 IMO, figuring it best to stop at the top of his game. Winning a Fields medal puts one in an analogous situation professionally: there are lots more awards you could get, but that’s the big one.

In addition, while a Fields medal comes with academic job offers that allow one to do whatever one wants and be very well-paid to do it, our tech overlords at OpenAI can and do pay a great deal more.

Finally, if you’re the competitive sort, what’s happening is making competitive problem solving much less attractive. It’s not just that the AI agents may beat you, it’s that the game is now being played very differently. When you’re competing against other mathematicians, there are strong norms about crediting ideas to those who came up with them, something that AI agents have no interest in doing. The situation isn’t quite like the situation in chess, where powerful chess programs got to the point they could beat humans, but human to human chess competition survived. Where we’re going could be analogous to chess playing where everyone is using, with or without acknowledging it, some sort of chess program. “Winning” at this will be something very different than pre-AI.

My own interests are quite different than Tsimerman’s. Math competitions never had any appeal to me. This was partly because I’ve never been competitive or much interested in “winning” anything. Also, why spend time on intricate math problems chosen mainly because they could be expressed in elementary terms and solved by elementary methods when there is so much beautiful and powerful non-elementary mathematics to learn about? As one learns mathematics there are always new depths to explore, and these depths seem to contain unexpected ideas that explain what is going on in fundamental theoretical physics, a subject with its own challenging depths to explore. So far I haven’t seen AI agents doing anything new and important that I would care about, but maybe that’s just a matter of time…

Update: Timothy Gowers (another Fields medalist and IMO winner with a perfect score) has a long blog post with his thoughts about the Leiden declaration at his blog.

Update: For an interview with Tsimerman at the ICM, see here.

Update: OpenAI has a promotional video for a program offering free access to their frontier models. Three of the four scientists featured are prominent theoretical physicists who had been working on string theory (Xi Yin and Eva Silverstein) or SUSY (Nathaniel Craig).

Update: Two new things this morning:

  • An interview with Tsimerman at the Atlantic
  • A new hep-th arXiv paper that demonstrates clearly why, in an intellectually dead field, AI will just produce worthless junk. If what you feed it is decades of complicated and meaningless computations, it will just produce even more complicated and meaningless ones.

Update: Yet another Tsimerman interview, at the Wall Street Journal.

Update: Probably not much blogging for the next two weeks. I’ll be traveling in Spain, hope to see the August 12 solar eclipse somewhere northeast of Madrid. Last week of August will be in Berkeley.

The past week or so I’ve finally gotten around to trying out asking questions to a recent version of an AI agent about things I’m working on. The results have surprised me: these things are a lot more capable than I had expected. It’s becoming clear that it would be a good idea to change the way I work, seeing if I can use these to get simple calculations done and different sorts of things I don’t understand explained to me. Current plan is to seriously get to work on this when I’m back from Berkeley at the beginning of September.

Unless there are specific comments about Tsimerman, I’d rather have further discussion about the capabilities and implications of these AI agents wait until I’ve spent more time with them in September. What would be helpful to me and I think to others is to hear from mathematicians and physicists who have been actively using these in their work with advice about which ones are most useful, and how to get access to them.

Update: Curt Jaimungal has a long, detailed interview with Tsimerman. Highly recommended.

Posted in AI | 26 Comments

Various and Sundry

Posted on July 15, 2026 by woit

Some things that might be of interest:

  • The ICM is starting next week in Philadelphia. One traditional aspect of the ICM is the announcement of the Fields Medal winners. This year there won’t be much surprise, since evidently someone found the names of the winners hidden in the website code (see here, English language news story here). It’s Yu Deng, John Pardon, Jacob Tsimerman, and Hong Wang. At least all science journalists who want to write about this now know the names, no controversies about who has embargoed information as in some past years.
  • Strings 2026 was held last week in Shanghai. Looking through the talks (see here, videos here), I see nothing that looks like a significant new idea or any evidence this isn’t a dead field. I watched the public talk by David Gross, which was just bizarre. Much the same talk Gross has been giving for thirty years about string theory unification, with no indication there’s any problem with the idea. For detailed discussion of a similar talk 22 years ago, see here. The main difference with that talk is that Gross removed all the slides about how SUSY was about to be found and would vindicate string theory. Gross argues against the “landscape”, saying that he thinks there will be some new insight explaining how all the constants of nature emerge from understanding the big bang, but this seems to be backed by nothing except wishful thinking.

    Gross started off the talk by complaining that he had had to work hard for the few days before his talk, since he had found that his slides were so old that the file formats now had compatibility problems with current software. I’m completely baffled by how anyone involved in this could think that going to the public with this sort of thing is a good idea.

    Also on the Strings 2026 topic, Stringking42069 is back.

  • Every so often I think it’s worthwhile to point to something about the “interpretation” of quantum mechanics that reflects my best understanding of the subject, so see here.
  • Quanta magazine a while back had a good article about the deep new mathematics being develop by Peter Scholze, Dustin Clausen and others. Clausen has a paper out on the Weil-Moore Anima he was lecturing about at the IHES earlier in the year.
  • Finally, something inspirational: my Columbia colleague Joan Birman is still active at 99 years old, and has an important new result on the Burau representation. This is the result of a project that began when a high school student, Vasudha Bharathram, came to Birman for help in learning more math and finding a problem to work on. Bharathram will be a beginning Ph.D student at Princeton in fall. The third member of the collaboration is Tara Brendle, a student of Birman’s. This collaboration must break some sort of record in math research for the age range of the collaborators.

Update: For a new documentary series about Bourbaki, see here.

Update: As a commenter here noted, the LANA project to try and formalize the controversial part of Mochizuki’s supposed proof of abc has issued a report and held a press conference today. From watching the press conference and reading the report, my conclusion is that this has ended up exactly where one could have predicted. The LANA people have identified a precise gap in the argument (which for some reason they call a “wall” rather than a “gap”), at the point where Scholze and Stix in 2018 claimed there was a problem. The gap is where Mochizuki says two different things are the same, while LANA sees no argument for this to be the case, and hasn’t gotten one from Mochizuki, Yoshi or anyone else.

Since no one now has an argument (other than “it’s obvious”) that fixes the gap, it’s clear that what PRIMS published was not a proof, but a proof with a gap, and that the refereeing process failed in this case.

Update: The big AI news of the day is the discovery using an AI agent of a counter-example to the Jacobian conjecture. For some more about this, background, and discussion of a recent AI-found counterexample to a conjecture of Grothendieck’s, see today’s blog post by Kevin Buzzard: Human mathematicians are being outcounterexampled.

Update: While in mathematics AI agents are starting to have a major positive impact on research (e.g. by resolving the Jacobian conjecture), the situation is very different in hep-th. For an extreme example, see this paper from today. It claims to derive interesting statements about QFT from the counterexample to the Jacobian conjecture posted on twitter at 2:19 UTC yesterday, and was submitted to the arXiv less than 15 hours later (15:09 UTC). Obviously it was pretty much completely AI generated (and this is acknowledged in the text). The result is something completely worthless, but not obviously distinguishable from many other things on hep-th, which is in serious danger of going from something sad and unhealthy to something completely overwhelmed with crud.

The director of the arXiv’s reaction:

We’re having an acute and abrupt misalignment of incentives

Really worried we can’t adjust systematically rapidly enough to avoid some really badly disruptive intermediate states

That the problem for hep-th is just “badly disruptive intermediate states” seems to me an optimistic way of putting it…

Update: Kirti Joshi has comments about the LANA project report.

Posted in abc Conjecture, Quantum Mechanics, Strings 2XXX, Uncategorized | 13 Comments

Notes on Wick Rotation and Chiral Field Theories

Posted on July 9, 2026 by woit

A few months ago I decided to try and sort out the two dimensional spacetime case of the Wick rotation issues that have been bothering me for years now. It took me a while to understand what goes on in two dimensions, but when I did, this clarified a lot for me the underlying problems with Wick rotation that I’ve been confused about. I’ve just finished writing something up about this, which you can find here.

Instead of writing more about this tonight, I’ll leave that for tomorrow. Will either write some more in the posting, or in the comments.

Update: My thinking about the implications of this keeps changing and I’m making progress at better understanding what’s going on here. This will take a while and be significantly different than these notes, so I won’t write more about them for now.

Posted in Euclidean Twistor Unification | 3 Comments