While I see lots of discussion about AI solving these problems, I feel like there's a more sinister undercurrent that's is less discussed - about who did the solving. It wasn't academics empowered by AI, but OpenAI themselves.
I feel like it's a sign of what's to come - large AI companies with resources academia never had, at some point deciding that selling access to AI is not as important as just doing the research themselves with models inaccessible to anyone else. The end game is all scientific advancement will be done by one or two companies, who will reap all the profits. Why would they give access to a model that develops a cure for cancer when they could develop the cure themselves and get all the money?
(Kind of like Amazon coming out with their own products - use the greater community for ideas, then become a competitor at a scale they often cannot match).
100%. Thinking tasks cost money now. Some colleagues and I were having this very conversation this morning. Universities don't have the resources to access unlimited compute to do this kind of work. There are a lot of very cool projects being done but it's always like I'm spending 50k in tokens for X project.
The Dark Forest era of the Information Age. Everyone trying to keep things as secret as possible. I wonder if private intranets will be more widespread in the future.
I think you are right to note the undercurrent missing of "empowering" the people doing the solving.
This is in notable contrast to the "PC revolution" in the late 70s/early 80s, the marketing was all about equipping people, empowering individuals. It was a "personal" computer after all, not a big mainframe owned by corporate... designed to make you more powerful.
That messaging is wildly absent from the EA/SV-centric LLM/AI boom.
Instead it's about replacing you, the singularity, inevitability, fear-mongering, etc. And there is much more of a flavor of information asymmetry to the business model because of the Internet connectivity and SaaS structure to it all designed to enable the fastest possible feedback loops for the inventors combined with a bunch of pinkie promises with no actual controls possible on the user side at least for the frontier large models. What exactly did OpenAI peek at when doing Navier-Stokes and do they even know or would you trust them to tell you? You are right, it is a very different vibe.
Indeed. I think this will ultimately require government intervention and regulation to keep it from destabilizing and monopolizing the entire economy. They’ll have to make AI more like a public utility than a private SaaS subscription.
Mathematics is much easier that way to train. Science in general. Governments will again need to become powerhouses of resources for compute to generate public research.
I feel it would be effective and prudent to protest the current use of AI and to effectively unionize and ostracize AI use until many of these demands are met. The companies that own the models and the infrastructure will never be more vulnerable.
They have fired a salvo. Fire Back.
Trump already spilled the beans on this. They want to just dump public money into these companies they can buy calls on and end the whole research model as we know it, replacing it with what exactly, they don't care as long as they can skim off the trillions spent on research.
Such a depressing time to be a knowledge worker with domain expertise.
What if the trend of open models being a few months behind the frontier continues to hold true?
Wouldn't it be nice if anybody could cure their cancer from home, all you have to buy is some time on the mainframe and send off an order to a chemical company
I also feel like state-sponsored inference is inevitable. Just like fiber and 3G, I suspect Asia will get there ahead of the west yet again.
I wonder how many chat logs they did use in model's training data? If model consumes human’s reasoning (the chat logs) and then presents results as its own, it's a kind of parasite right?
Harvesting collective output of human consciousness to build AI that then replaces the very people who provided the input.
Replacement isn't bad as long as it doesn't strip people of dignity, and that's the tricky part.
Google, in a large sense, replaced librarians, service desks, 411, and many other specialist people and services whose purpose was "The knowledge is somewhere, and there is an index, but most people don't know where the index is or how to read it."
But librarians aren't really diminished as a result (while service desks may have kind of quietly evaporated to go do something else).
If the system becomes "People talk about mathematics and then an analysis engine reads that zeitgeist much faster than people can and pulls it all together into new insights," that's not apriori bad... Except that we have to consider how many people were in that conversation because their ultimate goal is to have an insight tied directly to them, i.e. to become the Hamilton in "Hamiltonian operator." Because the reality is that people practice mathematics both to advance the sum total of human knowledge and to roll the dice on getting stamped into the history books as the closest form of immortality that people get, and we can't just ignore both drives.
Grant Sanderson (3blue1brown) expressed thoughts on this topic space in a recent video, where he suggested one possible shift might be from the focus in the field being on frontier-pushing to the focus being on making the frontier more "human-shaped." There's a huge gap between higher math and what most people understand, and possibly ample opportunity to bridge it.
> Initially, the rumors about these OpenAI results had it that there were solutions to 400 problems, and now the rumors are that further dumps are arriving soon.
That is mental if true. Though if once again most of them will lack a Lean proof, bit hard to feel confident about their correctness. They might trust their model, but given the community impressions on manuscript prose quality, I have a hard time imagining they are any better than its coding output, where closed loop verification continues to be essential. OpenAI might have great trust in their internal model, but this seems like a needlessly hazardous way test that trust out. The optics of those retracted papers from a few days ago were bad enough already.
I have separately heard of efforts regarding Lean proof optimization. Since it's all self machine checkable, might be valuable to do before a release like this too. I'd imagine a shorter Lean proof means a shorter manuscript too.
I read somewhere that 56% of the problems had some Lean Proof, but upon inspection, there are gaps between what Lean proves and what English says about the proof.
Making an English language description of a problem and proof steps match the Lean proof is apparently harder than the halting problem and is not something that a Lean proof alone or the current dump or even the Navier-Stokes dump solves.
I had Sol tally things up on my own end and I got closer to around a 33% coverage. OpenAI calculates differently (they count in manuscript coverage), I had Sol calculate per novel assertion. Even it noticed prose vs Lean gaps.
These math advances are more or less zero-sum wins, as in there's not much gained for the outside world, and a chance to prove an important theorem is taken away from humans. In a sense it's hard to celebrate it. If, however, they were able to advance medicine, science or technology, it would be a different story.
While I see lots of discussion about AI solving these problems, I feel like there's a more sinister undercurrent that's is less discussed - about who did the solving. It wasn't academics empowered by AI, but OpenAI themselves.
I feel like it's a sign of what's to come - large AI companies with resources academia never had, at some point deciding that selling access to AI is not as important as just doing the research themselves with models inaccessible to anyone else. The end game is all scientific advancement will be done by one or two companies, who will reap all the profits. Why would they give access to a model that develops a cure for cancer when they could develop the cure themselves and get all the money?
(Kind of like Amazon coming out with their own products - use the greater community for ideas, then become a competitor at a scale they often cannot match).
100%. Thinking tasks cost money now. Some colleagues and I were having this very conversation this morning. Universities don't have the resources to access unlimited compute to do this kind of work. There are a lot of very cool projects being done but it's always like I'm spending 50k in tokens for X project.
The Dark Forest era of the Information Age. Everyone trying to keep things as secret as possible. I wonder if private intranets will be more widespread in the future.
I think you are right to note the undercurrent missing of "empowering" the people doing the solving.
This is in notable contrast to the "PC revolution" in the late 70s/early 80s, the marketing was all about equipping people, empowering individuals. It was a "personal" computer after all, not a big mainframe owned by corporate... designed to make you more powerful.
That messaging is wildly absent from the EA/SV-centric LLM/AI boom.
Instead it's about replacing you, the singularity, inevitability, fear-mongering, etc. And there is much more of a flavor of information asymmetry to the business model because of the Internet connectivity and SaaS structure to it all designed to enable the fastest possible feedback loops for the inventors combined with a bunch of pinkie promises with no actual controls possible on the user side at least for the frontier large models. What exactly did OpenAI peek at when doing Navier-Stokes and do they even know or would you trust them to tell you? You are right, it is a very different vibe.
Indeed. I think this will ultimately require government intervention and regulation to keep it from destabilizing and monopolizing the entire economy. They’ll have to make AI more like a public utility than a private SaaS subscription.
Also mathematics itself won't grow like it did before.
Learning and building New Mathematics from the activity of solving problems is what'll be missing.
Mathematics is much easier that way to train. Science in general. Governments will again need to become powerhouses of resources for compute to generate public research.
I feel it would be effective and prudent to protest the current use of AI and to effectively unionize and ostracize AI use until many of these demands are met. The companies that own the models and the infrastructure will never be more vulnerable. They have fired a salvo. Fire Back.
Trump already spilled the beans on this. They want to just dump public money into these companies they can buy calls on and end the whole research model as we know it, replacing it with what exactly, they don't care as long as they can skim off the trillions spent on research.
Such a depressing time to be a knowledge worker with domain expertise.
What if the trend of open models being a few months behind the frontier continues to hold true?
Wouldn't it be nice if anybody could cure their cancer from home, all you have to buy is some time on the mainframe and send off an order to a chemical company
I also feel like state-sponsored inference is inevitable. Just like fiber and 3G, I suspect Asia will get there ahead of the west yet again.
Gift link: https://www.nytimes.com/2026/10/08/science/mathematicians-re...
>If a human did this, it would be an instant Fields Medal, no questions asked.
- Alex Kontorovich, chair of the department of mathematics at Rutgers
Not your fault - and thanks for the gift link - but NYT still wanted me to login to read it.
Their prerogative, but no thanks.
I get this comment so often when I post NYT gift links now, I guess I should always include the archive link to prevent them:
https://archive.is/ANnky
um, actually, one question must still be asked, as the Fields requires its recipient to be under 40 at some point in the year it is awarded
LLMs are like 6.
I wonder how many chat logs they did use in model's training data? If model consumes human’s reasoning (the chat logs) and then presents results as its own, it's a kind of parasite right?
Harvesting collective output of human consciousness to build AI that then replaces the very people who provided the input.
Replacement isn't bad as long as it doesn't strip people of dignity, and that's the tricky part.
Google, in a large sense, replaced librarians, service desks, 411, and many other specialist people and services whose purpose was "The knowledge is somewhere, and there is an index, but most people don't know where the index is or how to read it."
But librarians aren't really diminished as a result (while service desks may have kind of quietly evaporated to go do something else).
If the system becomes "People talk about mathematics and then an analysis engine reads that zeitgeist much faster than people can and pulls it all together into new insights," that's not apriori bad... Except that we have to consider how many people were in that conversation because their ultimate goal is to have an insight tied directly to them, i.e. to become the Hamilton in "Hamiltonian operator." Because the reality is that people practice mathematics both to advance the sum total of human knowledge and to roll the dice on getting stamped into the history books as the closest form of immortality that people get, and we can't just ignore both drives.
Grant Sanderson (3blue1brown) expressed thoughts on this topic space in a recent video, where he suggested one possible shift might be from the focus in the field being on frontier-pushing to the focus being on making the frontier more "human-shaped." There's a huge gap between higher math and what most people understand, and possibly ample opportunity to bridge it.
> Initially, the rumors about these OpenAI results had it that there were solutions to 400 problems, and now the rumors are that further dumps are arriving soon.
That is mental if true. Though if once again most of them will lack a Lean proof, bit hard to feel confident about their correctness. They might trust their model, but given the community impressions on manuscript prose quality, I have a hard time imagining they are any better than its coding output, where closed loop verification continues to be essential. OpenAI might have great trust in their internal model, but this seems like a needlessly hazardous way test that trust out. The optics of those retracted papers from a few days ago were bad enough already.
I have separately heard of efforts regarding Lean proof optimization. Since it's all self machine checkable, might be valuable to do before a release like this too. I'd imagine a shorter Lean proof means a shorter manuscript too.
I read somewhere that 56% of the problems had some Lean Proof, but upon inspection, there are gaps between what Lean proves and what English says about the proof.
Making an English language description of a problem and proof steps match the Lean proof is apparently harder than the halting problem and is not something that a Lean proof alone or the current dump or even the Navier-Stokes dump solves.
A good breakdown of the problem is here: https://arxiv.org/html/2610.08144v1 or also see here: https://terrytao.wordpress.com/2026/10/09/what-mathematician...
I had Sol tally things up on my own end and I got closer to around a 33% coverage. OpenAI calculates differently (they count in manuscript coverage), I had Sol calculate per novel assertion. Even it noticed prose vs Lean gaps.
I'm not sure about comparisons to the halting problem, it's not really related afaik. This is my understanding on the matter: https://news.ycombinator.com/item?id=49672339
I'll read those other two resources tomorrow.
Related:
Reactions to 100 Solutions
https://news.ycombinator.com/item?id=50019499
Is it paywalled just for me?
I pay, but always get a half screen popover asking me to upgrade to a family membership.
Sigh, no medical cures :(
These math advances are more or less zero-sum wins, as in there's not much gained for the outside world, and a chance to prove an important theorem is taken away from humans. In a sense it's hard to celebrate it. If, however, they were able to advance medicine, science or technology, it would be a different story.
Yes, because those have to actually go through the gauntlet.