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