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PaperclipPerfector  1mo ago (text post)   25566 thread views

Culture War Roundup for the week of September 7, 2026

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Navier-Stokes Millenium Problem Solved by GPT

OpenAI says they solved the Navier-Stokes Millenium Prize problem with an internal model that is more powerful than GPT6, so a GPT 7 candidate or something close. OpenAI has been on fire lately really casting a shadow on Anthropic. First the hugging face incident, now the first to crack the Millenium prize problems.

As for the solution to the problem, they are claiming that smoothness is disproved and that the equations do break down.

A fundamental open question for these dynamical equations has been whether the continuum approximation of the fluid can break down. Specifically, can the Navier–Stokes equations for a three-dimensional incompressible fluid with constant density develop a “singularity,” even when the motion starts smoothly? Here, a singularity means the dynamics lead to speeds in the fluid growing without bound within a finite amount of time. The development of a singularity would have to happen despite the presence of viscosity, which tends to smooth out motion. Because a real fluid cannot move infinitely fast, this would mark a breakdown in how the equations model the fluid. To continue modeling the system, one would then need to track the behaviour of each particle individually.

They say that the equation can develop a singularity, which apparently means it is not a perfect model.

This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time.

This is very exciting to me as I believe it to be the first scientific result of an AI model. Previous results have been basically irrelevant to the sciences. However, this result is of course still completely symbolic in nature, which is not surprising because LLMs are not embodied enough to collect data and analyze it autonomously.

While they are generating amazing PR recently, I will say GPT-6 is somewhat disappointing for coding. It is not the same leap that 5.5 to 5.6 sol was. It would appear that the models are getting better at running very long context chains while efficiency improvements and refinements in lower level tasks are lacking. Still, it's great work from OpenAI and it's plausible to me that if there's no singularity in general by 2030, there will be for mathematicians. They will no longer be meaningful for producing math, rather they will only be humans who understand it.

The question I find most interesting with regards to AI right now is the discontinuity between benchmark capabilities progress and the utter lack of impact on pretty much everything in the real world.

Certainly most doubters of AI on a capabilities level have continually been proven wrong in terms of LLM's hitting a wall. On the other hand, the boosters have also been continually proven wrong in terms of the effects in the world. I think it's a reasonable generalization to make that conditional on LLM's being somewhere between at parity and superhuman at translation, writing most code and at being able to prove mathematical theorems, most boosters would have expected at least something to change in the real world, probably significantly more than what's actually happened.

I've written about translators a few times now, but they've been first on the chopping block for close to a decade, and yet have held on admirably with no particular impact on their employment at a macro level.

Count is doomposting artists below, when in practice the impact of AI art on artists looks much more complementary than rivalrous except at the margins; for most applications of AI art no artist would have been paid to produce it in any case, and commercial illustrators, fine artists and Patreon goonsloppers are all doing about as well as they were prior to the advent of diffusion models.

Software engineers got a lot of doom around the start of the year once LLM's got good at writing code, but by all indications software engineering employment is continuing to improve from 2022 lows, and the production quality and quantity of useful software is still highly bottlenecked on software engineers who actually know what they're doing.

They will no longer be meaningful for producing math, rather they will only be humans who understand it.

Now it is the turn of mathematicians to feel doomed; in that context, I find this sentence very interesting.

Is the purpose of the Great Work not for humans to understand mathematics? What does it even mean to "produce" mathematics?

First silicon came for arithmetic, then it came for symbolic manipulation, and now it's come for theorem proving, this will certainly change the roles of working mathematicians and perhaps destroy the egos of some of their number, but the purpose of pure mathematics was never to sit there churning out proofs in the first place.

In general, I think most people tend to conceptualize jobs as individual tasks, and when those tasks get automated, then it's over for those jobs; in practice, automation of tasks generally induces demand and opens up previously uneconomical or unknown tasks. Additionally, many, perhaps most jobs in modern economies do not really exist to hill-climb tasks in the first place, but rather for social reasons, political reasons, legal reasons, just to name three. The reason many commission artists make a living is not primarily for the fidelity of their art, and the reason mathematicians get paid is not for their skill at proving theorems of no economic value. If, or when, these jobs change, it really has very little to do with technological capabilities and a lot to do with the evolution of society, which is certainly driven by technology, but almost impossible to predict.

I am, of course, not implying that nothing will ever happen, and to the contrary expect many changes to reverberate throughout the world; rather I think that the boosters heralding mass unemployment or very rapid change in the world have not properly thought through why nothing of the sort has yet happened, what capabilities are yet missing before such things might be possible, and how such capabilities might be elicited from existing technology, as opposed to the almost tautological framing of RSI or AGI where all this is true by definition.

In some sense, it's not really that surprising though; the vast majority of people barely understand their own value and why they get paid what they do, let alone anyone else's value at their firm or in their profession, let alone the value of everyone else in the economy.

I've written about translators a few times now, but they've been first on the chopping block for close to a decade, and yet have held on admirably with no particular impact on their employment at a macro level.

I wonder if this is because the labor stats aren't looking at the right thing. It's over for translators, like major streaming services are just slapping ai translations on most new shows.

The stats clinging on are probably mostly in asl interpretation, which doesn't get helped by gpt, and in person translation like legal, social services, and illegal alien resettlement.

It's over for translators

Everyone says this as a kind of self-reinforcing meme, but objectively it's not true.

For example, as just one example I'm familiar with, Japanese/Chinese book/game/show translation began booming in the last ten years and has been booming even harder in the last five years even with AI. Ten years it was extraordinarily difficult to find translations of Japanese/Chinese media outside of the most mainstream anime, while nowadays there is an enormous translation-industrial complex that employs many people I'm acquainted with, and that is dedicated to pumping out simultaneous localizations of even extremely niche media into English/Japanese/Chinese, because of massive consumer demand.

I'm certainly not saying translation is a growth field in the age of AI, and it's not something I'd advise anyone to get into in 2026, but the point is how these technologies diffuse into the economy and interact with demand is extraordinarily hard to predict and often times very counter-intuitive.

As another example, someone could have watched the DARPA Grand Challenge in 2004 and realized that self-driving trucks were a matter of time, but someone else could have started driving a truck in 2004 at the age of 18, have reached 40 in 2026 without meaningful threat from self-driving, and have had a good chance of making it into retirement as well, based on the current pace of self-driving rollout.

A traditional approach to symbolic artificial intelligence frames problem solving as a search of a tree. Do you go depth first, dodging infinite branches? Or breadth first (do you have enough memory?). What about iterative deepening? Sometimes the solution is in the tree, but it is too deep, and one runs out of time before it is found.

Statistical based learning acts as a branch predictor. Sometimes guiding the search to go very deep in the right place and find the hidden solution. Sometimes guiding the search to go very deep in the wrong place; one runs out of time as usual.

Notice the strength of a hybrid approach. One isn't accepting the probably correct answer of the statistical part. It is only a guide, and if the answer is found, and the symbolic part of the software is correct, the answer will be reliable. This hybrid approach is being spectacularly successful in pure mathematics. Notice the deep historical roots, going back to Hilbert and Ackermann's 1928 book Grundzüge der theoretischen Logik (Principles of Mathematical Logic). The formalization behind the symbolic AI software was a major human achievement. This strikes me as an extension of the successful creation of AI to play the game of Go. Underneath Alpha Go lies a hand coded rule engine implementing the rules of Go.

Then we ask about practical applications. For example, I've been receiving my neighbors gas and electric bill due to errors in the gas meter database. If Ovo energy starts using an LLM to do customer service, will this fix the problem? The humans haven't fixed it. The front line staff have a script to go through that assumes that the gas meters are in a common area and the confusion is that meters are swapped. Having the database place two meters in a single flat isn't part of the script. There is a lot of slop in the database. "34 Top Flat Left" could be 34/7 or 34(4F1). It strikes me that there is little training data. What little there is, applies to a different problem. An LLM, deployed as customer service agent, will just hallucinate (I prefer to call such things Runge Spikes. The spectacular successes in pure mathematics depend on an intellectually rigorous formalization of the domain. But no Hilbert or Ackermann class intellect is coming to formalize gas meter databases and how that works in blocks of flats and conversions of big houses to flats, and the like.

One of the frustrations of dealing with Ovo energies customer service is describing the layout of the property by email. There are meter readers who visit to read meters, but the UK gas supply companies subcontract that to service companies. Ovo energy's staff know nothing. But at least they live in houses and have gas meters of their own. The LLM lives in the realm of language, and doesn't know that the real world exists. It cannot accompany a meter reader and see for itself. It only has second hand knowledge, allowing it to talk-the-talk, based on the discussion of the real world in its training data.

Getting LLM's to do banal customer service jobs without adding new and Kafkaesque confusion will wait on the Zermelo–Fraenkel of gas meters. Who will create it? Perhaps the newly unemployed pure mathematicians will be hired to create rigorous formalizations of daily life. Probably not. I'm expecting five or ten bad years when LLM are deployed in customer service roles and make things worse. After that, my crystal ball gets cloudy.

Getting LLM's to do banal customer service jobs without adding new and Kafkaesque confusion will wait on the Zermelo–Fraenkel of gas meters. Who will create it? Perhaps the newly unemployed pure mathematicians will be hired to create rigorous formalizations of daily life.

I guess the theory is pretty much this! People will figure out how to automate the production of good training data from company files and ever increasing quantities of video, audio and chat logs. Then in x years, the ai will have learned how to problem solve edge cases like yours from precedent.

It seems inconceivable that all service companies will be able to do things well enough via their existing humans plus the unemployed mathematicians to train ai to be actually competent though. More likely the ai will end up being trained to emulate all the bad traits of service desks as well as the good, and the mathematicians will discover themselves brought low by bureaucracy like the rest of us.

Especially because the company's most pressing incentive is to get some form of ai talking users in circles for an hour to use up time before a competent person becomes available.

Now it is the turn of mathematicians to feel doomed; in that context, I find this sentence very interesting.

Is the purpose of the Great Work not for humans to understand mathematics? What does it even mean to "produce" mathematics?

Isn't it proven by Godel's Theorem that any complex logical system should have an infinite number of potentially provable theorems? And no easy way to know which ones are provable? So I guess the field of mathematics will go on forever, just with AIs proving more and more abstract, ridiculously complex theorems. The "job" of human mathematicians, if you can call it that, is to simply marvel and appreciate what they've done, like an art critic.

Yes, we can continue to build beautiful towers of abstraction into infinity for the rest of time; frankly, pure mathematics has already lost all pretense that it's trying to do anything economically useful.

Even if AI becomes strictly superior to humans at proving and disproving conjectures, as is the clear trajectory of the technology, it means nothing for the profession of mathematics in and of itself; the limiting factors are the interest of mathematicians in continuing to pursue mathematics under the new paradigm, and more broadly the interest of society in economically subsidizing their pursuits, which are both profoundly social and not technological questions.

Even if AI becomes strictly superior to humans at proving and disproving conjectures, as is the clear trajectory of the technology, it means nothing for the profession of mathematics in and of itself;

Productivity for research mathematicians today is mostly evaluated as contributions made to resolving “important” open math problems.

If / when AI advances to a point where humans can no longer meaningfully contribute to this process then, at the very least, we'll need to reconsider how we evaluate human research math productivity.

Your statement above reads to me like, even if we get rid of the hoop, it means nothing for the profession of basketball in and of itself.

even if we get rid of the hoop, it means nothing for the profession of basketball in and of itself

I think a slightly better analogy is that tomorrow there's a new rule that lowers the hoop in official basketball games to 8 or 9ft.

What are the first-order implications?

Height is less of an overwhelming advantage; many former basketball players quit the game out of disgust at the new rules, or because they're less competitive in short-hoop basketball, but other players formerly genetically barred from the apex of basketball become more competitive and perhaps there ends up being more basketballers overall.

Perhaps basketball becomes less popular because nobody wants to watch short-hoop basketball and basketballers suffer financially, or paradoxically it gets more popular because the game is less about the three-pointer meta and more about dunking again, and basketballers are more in demand than ever.

I don't think we really disagree that there are going to be large changes to how mathematics is practiced; the point is that technological changes cannot inherently alter anything in a system that is already artificially constructed by humans, and it is the impossible to predict societal changes arising as a result of technological progress that are what really going to affect mathematicians and basketballers.

Respectfully, I don’t think I’m following this reasoning. I think (?) you’re expressing several inter-related points with which I broadly agree:

We should view those pronouncing confidently about the future with skepticism (yes). Some aspect of research math has always involved aesthetic considerations (yes). If / when AI achieves manifestly superhuman capabilities in math, we’ll likely continue to see some humans devote attention to some forms of math exploration (yes). Support for modern research math projects is often promoted through reference to supposed diffuse economic contributions that are actually mostly a fiction (yes). Many job roles in modern economies are less directly related to profit-maximization than we may commonly assume, and are instead largely shaped by various traditions and social expectations (yes).

But the suggestion that “technological changes cannot inherently alter anything in a system that is already artificially constructed by humans”? I just don’t know what this means, concretely.

Baseball’s a system that’s artificially constructed by humans. Professional baseball has also struggled notoriously (and perennially) to police the use of disallowed “performance enhancing substances” (particularly steroids), which are a technology change. Now, imagine someone tomorrow develops a drug that makes players much faster & stronger - and its use is substantially impossible to detect. Wouldn’t we expect that development to significantly alter baseball?

I think (?) you’re expressing several inter-related points with which I broadly agree

I think that's a good summary of my viewpoint.

I just don’t know what this means, concretely.

I worded that quite poorly; perhaps a better way to put it is that "the direction and magnitude of technological changes on human social structures can't be determined ipso facto".

Undetectable steroids would certainly change baseball, but do more or less people aim to go pro in baseball once it's widely known that you'll need to get onto steroids under the table to compete? Do audiences become more interested in the increased athleticism of the game, or do they lose interest because the game is now less about technical baseball prowess? Which types of baseball players ultimately end up better or worse off once these steroids are made available?

Questions like these are what mathematics and other professions are struggling with right now, but I think the answers to them can't really be determined by any way other than waiting and seeing what happens.

perhaps a better way to put it is that "the direction and magnitude of technological changes on human social structures can't be determined ipso facto".

Yeah, strong agree on that point - Prediction is very difficult, especially about the future.

There's delay time because some people are fast adopters and feel extraordinary change is imminent based on their own personal experience... but most people are really slow adopters.

They answer my email a week after I send it, set up a meeting 2 weeks after that. They don't look into things themselves, except maybe what Microsoft Copilot shoves in their face in the most obnoxious way possible. Other things have much higher priority, I'm sure they have more pressing matters to deal with.

That's why things aren't changing fast. I confess I didn't appreciate this in prior years.

But I think there is a certain point where things 'rip' and fast change happens irregardless of mass adoption. The fast adopters at the frontier will reshape reality directly. AI agent swarms running fully autonomous digital businesses for instance. Or fully autonomous cyberattacks. Autonomous killer drone swarms rising out of a container ship, a terrifying banshee shriek of massed rotors as a city gets depopulated in hours.

It's like packing more and more weight onto the bridge, nothing happens for the first hundred tonnes. Tonne by tonne, the bridge alarmists are sitting there looking embarassed and saying they hear funny sounds, well maybe that was just the foundations settling. They're making arguments from principles that are being contradicted by reality. But then, all at once, the bridge collapses.

The situation reminds me of the early days of computers. There was a lot of hype. For example, I had a high school English teacher who had all of the students write a paper using a word processor. Which was very cumbersome to use and the dot matrix printout of the essay looked pretty lousy. A Schoolhouse Rock! type video came out which, as I recall, promoted the use of home PC's to store recipes. Something which really wasn't practical for computers at the time. It was very common for kids to go to computer camp in the summer.

I was going to link that Schoolhouse Rock! type video (it was called "Scooter Computer and Mr. Chips") but it was so cringe, I just couldn't bring myself to watch.

Basically the early boosters of computers were ultimately correct, it's just that apparently there is a Moore's Law of Hype which is even more potent that the Moore's Law of computer chips.

My best guess is that the situation with AI is analogous; that right now we are in the mid to late 80s.

What interests me about this is that for all of the retrospective mocking of Paul krugman's comparison of the internet to a fax machine, in terms of economic growth it didn't really change much.

For all the promise of computers, the internet, smartphones, etc. first world economic growth has been stagnant since the 2000s. Even for the US, a relative success story, real GDP per capita growth has been slower in the last 25 years then it was from 1950 to 75 or 1975 to 2000.

What do we do if AI changes much of our lives, but doesn't produce anywhere near the promised economic growth?

Yes, I find Solow's paradox very interesting in the context of the massive GDP growth that lots of "AGI-pilled" people predict, while nobody really knows why the internet ended up living up to to most expectations of transformation, but almost no expectations of productivity improvement.

Personally, I think some combination of "dark consumer surplus" (e.g I can read books online instead of buying them, which is great for me but shows up as less GDP) and "growth compared to counter-factual" (i.e growth would have been even worse due to economic headwinds, without the internet) is plausible, but it really is extraordinarily difficult to predict these sorts of things.

there is a Moore's Law of Hype

Actually it's Gartner's

And yeah it's the same with essentially every technology, the longer you live the more of these we see, and the most common failure modes for looking at this are: "it's all tulip mania, no new technology has any use" and "everything is going to change forever tomorrow, it's the end of the world as we know it".

Nothing ever happens. Except change, which is always happening, slowly.

See also Roy Amara's law (1978):

We tend to overestimate the effect of a technology in the short run and underestimate the effect in the long run.

On the other hand, the boosters have also been continually proven wrong in terms of the effects in the world.

There are effects. Every white collar person I know is working order of magnitude less.

This is why it is so hard to measure. AI is absolutely revolutionary but in some amusing twist the majority of the value it generates is non monetarily

Which will make it all the harder to justify keeping salaried employees around once AI can do what little work those still do.

My experience matches with this. Ai makes be slightly more productive, and a shit ton more lazy.

I think this is somewhat bi-modal; there are certainly lots of people in bullshit jobs who use AI to bullshit harder and work less, but also plenty of AI-pilled SWE's and mathematicians are working much more and much harder as a result of AI.

This is kind of my point; for roles like administration or consulting where the output doesn't really matter, the raw capability of AI to replace those people isn't the operative term in terms of what happens to their employment or their role in the economy, and for many roles where AI is actually a substantial productivity enhancement, the effect of AI so far is mostly complimentary rather than rivalrous.

I really think this depends on what you are doing. For instance work that primarily involves relationships and interaction in meatspace? Unchanged. Physicians? Unchanged.

Ambient scribes are now common but they are of very poor quality, and in some specialities only replace low paid labor (ex: ED) instead of reducing work load. Poor choice for progress notes and admission notes, unnecessary for procedure notes, really the only thing AI helps with is hospital courses even then the edit process is going to be key because the reliability isn't there.

I should really do an effort post on this, but medicine is noticing and attempting to address never-skilling, mis-skilling and deskilling, which will absolutely be a problem in professional domains in the future (and is already a problem in education).

I agree with OP - yes we've seen some amazing feats but translators and cars still exist, both of which were promised to be replaced years and years ago.

Real medicine is not white collar work. I can assure you that your administrators and HR are slacking like never before.

I disagree but only on the grounds that they were never doing anything before.

Are they actually working less (starting work at 11 instead of 9, leaving at 2 instead of 5 or 6) or are they just doing (or ‘generating’) more to fill in the space? The thing about a lot of white collar work is that in substantial part it was already pretty fake (a consultant’s 10 page deck from 1985 became a 600 page deck in 2023 because research/word processing/powerpoint got easier, but they’re still about equally useful), so AI just changes the provenance of the bullshit.

I personally don't work less. I just work less smart, because I have someone to always always ask what to do, and sometimes to actually even do it. I don't think as much as I used to. That kinda wastes a lot of time as I'm going back and forth with the ai constantly instead of thinking myself and taking action. I think I'm slightly more productive than I was before ai. But not that much.

I am not sure they are working less, but they are definitely slacking more and having more unproductive time working 9 to 5.

I’m with the lefties that working hours should decrease to start matching increased productivity, with less demand for more luxuries vs more free time, especially with robotics improving and promising to further improve productivity in blue-collar jobs.

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