This is the part that gives me the strangest feeling about it all, because you're not the only one with this experience. I've experienced this too on different problems, as have many researchers across many fields.
I disagree with the Fields Medalists on the majority of their complaints. AI math is happening and there's no going back. However, on one point I increasingly agree: virtually none of this stuff is possible with technology any normal citizen has access to. I have no problem with AI models making revolutionary advances in math or science. Where I start to have a problem is when the AI models making these advances are tightly withheld, proprietary, and seemingly never released with these capabilities intact. This has been the case for all of 2026 so far.
I suspect that this is in fact the source of much of the angst. None of this progress is reproducible outside of one or two teams inside OpenAI and Anthropic. It's becoming an incredible concentration of power that I don't know that we've ever quite seen before. Right now, it feels harmless because it's being used for wonky math problems that aren't (yet) practical for anything. But great power never stays harmless. History has taught us that countless times, in countless different forms.
Why do you "suspect" this as if it's some hidden motivation when the very first paragraph of the advisory group's statement (linked from the OpenAI post) says:
> 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.
Tao and others in that group have been strongly and publicly pro AI from the start. They are not advocating "going back". They're objecting to the strip mining of open problems using proprietary technology.
There are myriad circumstances where the values of most practitioners differ from the status quo, which is nevertheless well-entrenched. This can arise from inertia, or from outside forces, such as broader cultural milieu, integration with larger institutions, or contending with economic realities. If you think that these do not and haven't historically played a role in determining the job economy and that math is a pure field where mathematicians could comfortably shape it according solely to their own ideals then you are naive
For example, if you look at Terry Tao's blog, he has a tremendous amount of first-class expository writing. So, too (to some extent) do junior mathematicians -- but, unfortunately, this tends to not be highly valued by the job market. Grad students and postdocs have learned that to succeed they need to play by the existing rules of the game.
Well, the board has just been yanked from underneath them. People like me can afford the sort of idealism and soul-searching that the parent comment describes, but junior mathematicians face a very unenviable set of circumstances.
2) Mathematicians didn't create this economy; it was foisted upon them by the same managerial mentality that brought us "publish or perish" and "the monthly sales quota".
3) I can't tell if you honestly don't get why the strip-mining analogy resonates, or...?
Here's another analogy: if we suddenly discovered personal teleportation, and marathon runners were complaining that it was ruining the sport, would you say "they're pulling a 180 and claiming that marathon running was never really about getting to a point 26 miles away as fast as possible, but that's contradicted by their revealed preferences"?
The strip mining analogy is better though, because it captures the sense of irreversible goal-loss when a problem goes from being "unsolved" to "solved".
I like your marathon example, but maybe not for the reasons you intended. The community of marathoners decides the rules of a marathon. You don't need a hypothetical teleporter; you're already not allowed to use a bicycle, performance-enhancing drugs, or shoes that don't fit the specifications. The rules are updated to adapt to changing technology. Yes, I'm arguing that the strip-mining analogy doesn't make sense because mathematics is in the same situation. There's nothing stopping peer reviewers and hiring/tenure committees from changing the rules about which kinds of effort confer recognition and career advancement.
Imagine a mine has an unknown number of rare materials. And you know the general location of a few of the most valuable spots. But you don't know what may be valuable right next to it. If the pieces that we know are valuable are suddenly gone, the incentive to mine that particular area drops considerably, dropping the chance to discover potentially brand new materials that would have been found the normal way.
FWIW, I think the metaphor breaks down with this framing. This isn't really a problem associated with strip mining, what's left behind is generally low or negative value (toxic). I'd suggest a different metaphor, from Wikipedia:
> This process involves the removal of all ground vegetation in the area, which is a detriment to the environment.[19] Topsoil may be placed over the tailing along with planting trees and other vegetation. Another reclamation method involves filling in the hole with water to create an artificial lake. Large tailing piles left behind may contain heavy metals which can leach out acids such as lead and copper and enter into water systems.
This feels very similar to the issues with algorithmic problem "mining". It has the potential to destroy the human ecosystems surrounding these problems, leaving barren wasteland behind where nothing can grow or flourish.
Wolfram Mathematica ($890/yr)
Magma ($2500/yr)
Maple ($680/yr)
COMSOL ($1500,yr)
Matlab ($500+/yr)
Seems like a very strange position to take, in my opinion.
Why does the field of mathematics suddenly now need to be "fair" and give everyone access to the same tools? Has that ever been the case in academics? It's always been a competition for name-recognition, grants, institutions, etc.
Macsyma / Maxima was an MIT developed CAS system back in the 60's that was proprietery until they sold it off to IBM for a tidy sum. Magma actually has free access if you're in the US, otherwise you pay. That's not to mention proprietary MATLAB toolboxes or specialized Stata modules.
Likewise, a lot of the above packages have pretty sweet site-wide deals with R1 universities. If you're at a smaller, foreign one, you're out of luck.
Then I realized I was spending 3600.00 USD for Anthropic and OpenAI per year.
Unfortunately being "pro AI" means relinquishing any control over what the AI, or more importantly the company running it, might be doing.
We've relinquished control over just about everything we use or consume. We can't compete with larger enterprises for production of food, clothing, machinery, medicine, energy, services. Mathematics is just the latest thing to be industrialized.
What keeps large companies under control is competition with other large companies. This competition causes the surplus value they produce to flow to consumers, not be hoarded via monopoly prices. Do we see strong moats that are going to cause monopoly in AI? I don't see it, and in particular I don't see it persisting if it exists transiently.
> Do we see strong moats that are going to cause monopoly in AI?
Ownership of the capital assets used to train and inference new models. Yes, we may end up with more than one firm. But as we see with big tech today, a small number of fantastically wealthy firms in "competition" does not an open market make.
Somehow you have to argue either that society itself is bad, or that math is somehow different from all these other human activities.
I think the obvious fact that people prefer to live in places with large commercial organizations shows they don't really care about that, at least to the point of foregoing the benefits these organizations bring.
Computers and computer programs are tools. Humans always remain sovereign over their tools.
At the same time, there's a new note at the bottom of agmai.org stating how they've been in contact with OpenAI about this particular release, and they say that “we consider these discussions constructive, it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully”.
So, what's going on there; is this British English for “they didn't follow anything at all”? Because from my perspective, it looks like they doubled down on the Navier–Stokes approach of trying to maximize PR gain while being as lazy as possible about actually contributing anything back to science, releasing only slop that may or may not be correct and may or may not be straight up plagiarism, as has been the case earlier.
If I were on the AGMAI board, I'd feel terribly exploited when reading that press release, yet their response is modest.
Hairer, if you're reading this: is there any indication whatsoever that AGMAI was anything but a cheap way for OpenAI to science-wash their press release?
Yes, but the subtext is even stronger.
Now I know there are issues with the field and how just answering these questions may cause broader problems, but I feel like the posted results is far from slop. We can't just call any output slop, or it loses all meaning.
If it was slop, it'd not be causing the issues the group are concerned about - they're not saying "the problem is we're getting loads of incorrect proofs thrown about that are nonsense".
What about a filtered set "all well formed books"? Or "all well formed books that are plausible enough that they could convince a reasonable person, regardless of their accuracy"?
It's generally taken that a cup of sewage in a barrel of wine makes a barrel of sewage. Surely a reasonable person could claim that a barrel of sewage was still sewage, even if it contained several cups of wine?
University boards want the prestige of successful research programs. Doing the hard work to get something demonstrably true is going to lose out economically in this paradigm, where we are all being conditioned to uncritically ooh and aah at the incantations being elicited from these magic boxes. The oracles even have legions of zealots who will berate you for not being sufficiently deferential and reverent, or worse, accuse you of blasphemy. If for no other reason, I agree with using the term to express all of the above succinctly, even if LLMs can be helpful tools generally.
Also you can see in the papers where an idea is introduced but in the bibliography you can see where the foundational idea comes from. So the narratives are not unmotivated as some claim (proof without intuition claims).
The degree to which these issues feature will differ, but it is generally the case that converting the output to proper research requires significant effort, hence the AGMAI recommendations being what they are, and not performing that effort tends to come off as laziness or incompetence, so I can see how slop has become the popular term.
The term “ai slop” is not supposed to discriminate good ai output from bad, the entire purpose of the phrase is a blanket term that delegitimizes all ai output.
Or in this specific case, why would someone call these proofs (no one is saying they are wrong) AI slop if not to delegitimize all AI output?
* even pretty amazing advances like this one
Good AI output is indistinguishable from human output. The whiff you mention is the reasoning pleonasm and tautology (intended) escaping into the output and the "author" not proof-reading/editing it out.
Then it's a useless term and we should all stop using it.
He argues that the supply nay be very large indeed but the interesting subset is not. Figuring out the interesting problems is difficult so strip mining the good known problems may lead to scarcity. I am not a mathematician myself, can not judge this accurately.
I have a really hard time reading AI proof so this might be a biased statement, but most of them feels like having a superpowerfull machine, that would have bruteforce all the possible words of finite length in your logical syntax. You have the path to the solution, using tools that where already known and even direction that where abandoned because they seemed to fail for our human brain. But at the end, as a mathematician, you don't learn anything that is really new.
To me this is the main risk with AI and in general the one most mathematican try to explain but fail, we might miss a lot of alternative path that would have raised more interesting questions (I think this is already more or less what is happening). On top of that, we will run out of mathematicians as no one wants to pursue a career in the field anymore.
It's the same argument which is invariably wrong yet comes up over and over again.
There's no real reason to think AIs solving lots of problems will stop further work on alternative paths - certainly a machine which never tires and can be trained on its own solutions is going to continue to improve.
There's precedent for this: just look at any overconfident post regarding what China will clearly never be able to do, despite decades of steady if frequently flawed progress.
There's no persuasive argument being presented as to why machine mathematical research should have a limit beyond hardware capabilities.
If a human had solved these problems, we'd expect it to take years for people to digest them and formulate significant new advances.
Every company is about to have a staff Ops Researcher who has a better grasp of the underlying math and theory than any university professor. That is an unambiguous win.
Not sure about the unambiguous win. Are we entering the age in which mathematics is industry-dominated?
1) Any university professor can spend their 24 years on a problem with little progress. 2) company has sudden interests. 3) industrial resources brute force the Lean proof. 4) Max PR for AI company 5) professors are left to rewrite the AI Lean slop into real human-readable math? {disclaimer non-math university professor}
Initially, yes. Long term, however? Perhaps still yes.
> 5) professors are left to rewrite the AI Lean slop into real human-readable math?
6) AI writes the proof into something easier to follow than a PDF document.
Hmm. Oh shit.
I don't know but this phrasing comes off as gatekeeping.
Imagine there's a very advanced crossword club where anybody can join and take a stab at these crosswords for the love of solving puzzles. Many of them are so difficult that no one's been able to solve them yet, but we know they're all solvable.
One day, someone comes along with a super advanced crossword solver application, and it makes easy work of these crosswords. They run it on a few to prove how powerful it is, and then the community says, "Oh wow, that's cool, but please don't run it on any more of our advanced crosswords because they're very hard for us to come up with, and we really enjoy solving them by hand."
That's really what this compares to. I wouldn't call that gatekeeping; just respect. Respect for the game, respect for people's desire to have these hard problems to continue to work on, solving by hand.
If the company with the super advanced crossword solver then continues to use it and publish the results, they're effectively stealing the crosswords from this community. Soon, all the puzzles will be solved, leaving nothing left for the community to work on for fun.
That doesn't sound like gatekeeping to me. That just sounds like someone asking "Please be respectful and leave the remaining puzzles for us to solve by hand.” A simple plea not to be an asshole.
And yes, fun counts. Nobody said this had to be only a hardship.
I'm well aware that if at some point AI is good enough to replace me as a software engineer then I won't have a job. I don't expect a company to continue to pay me simply because I enjoy it if there are cheaper options out there.
Math is no different.
Total compensation includes fun.
Perhaps that won't matter if we enter an era where AI participants are the main participants who matter for discovery-level mathematics. But it would likely be what economists would see as a market failure if only a small oligopoly of AI participants, closely held behind closed doors, is able to fill that intellectual role.
New theories and insights are typically created while working out proofs. If proofs now suddenly fall out of the sky (cause LLMs create them) then that work is not done which means the substrate on which new theories and questions and conjectures used to be grown disappears. It's in that sense that the math community (and thereby society as a whole) will lose something.
It's similar to how software engineering will need to find a solution to train their next generation. Current generations have all been through manual steps of designing things from scratch and writing them by hand. That's what allows your 10x engineers to understand whether what their LLM tools are doing is good and how to massage those tools to do the right thing. A junior engineer who has only ever used LLMs to write code and create architectures does not just not have that experience but also won't acquire it. You can't just say "we don't pay them to have fun and learn, we pay them to produce results". In the short term that is the case, but in the long term you as a company and we as a community will lose out.
I'm not saying don't use AI tooling. I'm saying that this is a hard problem which we yet to have to find solutions and approaches to. As a software community as well as as society in general.
My ego tends to agree, that how can they be ever competent, if they have not endured the same hardships as I had crunching trough problems and getting allmost lost in the details.
But I rather suspect, they will turn out fine. I know LLMs are great for me to learn and I think the young generation will learn what they need to learn to get the job done.
Most people have trouble not peeking at the answers. Look at Stack Exchange's long success.
The increasing pervasiveness of technology in US education has not produced more capable graduates.
But your argument is nonsensical because even if Gauss and von Neumann appeared, they wouldn't go into random fields and just prove things mechanically. They'd have to attend seminars, teach others, collaborate with others, and generally inspire others with their brilliance. It's the precise lack of this activity that makes AI in math so reprehensible.
Your argument encapsulates a contradiction because human mathematicians wouldn't be dropping proofs arbitrarily like AI is doing. They would do something completely different. Even the best of them.
Give it six months and models might be able to explain things better than any human. They can already collaborate perfectly well if you ask them to. e.g. there was a post here a couple months ago where Tao shared his ChatGPT logs[0].
If you're not inspired by the ability to talk to a superintelligent machine, and can't find what you'd want to know, that's a you problem.
Ah, the "six months till AGI" meme, but unironically :)
Also, before citing Terence Tao on LLMs maybe you should read what he has to say about it...
Not sure what your definition of AGI is, but it clearly has superhuman performance on most knowledge work already. Do you think after already having demonstrated that it can solve top problems, that the final frontier it won't be able to cross is explaining its solutions to the experts that were researching those problems, and eventually to e.g. grad student or postdoc level practitioners as a lecture course/set of notes?
I have to assume OpenAI is only prompting to solve problems, presumably they could also prompt to not interesting new theories or paths of research found along the way as well.
Largely I thought that this is what you do once you're established in math (or any field) anyway. You have some ideas, but the details are kind of too tedious for you to work out, so you give it to grad students/postdocs. Senior engineers have some ideas, but the details are tedious to work out, so you give them to junior engineers.
Now, obviously in the meantime, there's the question of how do we train the next generation? Or do we need to train the next generation? And maybe while we work that out the answer becomes more shadowing/apprenticeship instead of farming out easy tasks.
Yours is more likely in my opinion though, mainly because universal high income is completely infeasible and shaky even at the level of definition.
If someone can solve open problems in mathematics then they should do so, isn't it as simple as that?
They should let the public use the models as well, but I guess they have no real moral imperative to do so.
But asking them to stop solving problems is just weird.
It’s not a human focused civilization, which is where the issue comes up.
As an example: A constant issue I am seeing with AI productivity is that the most productive use of AI is when it is paired with more experienced users, while AI also does more work for entry level workers, if not replacing them entirely. It has become a question where will the future buffer of experienced seniors come from.
This is an example of where simply chopping down trees for today, doesn’t make civilization better off tomorrow.
AI is producing more content than ever before, but our ability to understand and verify it is not keeping pace.
We don’t know if these are unsolvable problems at this stage. Society could come up with workarounds and solutions to these issues in several years.
The request to stop, is part of the process by which the issues are debated and solutions found. It doesn’t mean their position is weird or moot.
If there is a prize associated with doing a puzzle, and a machine does it, then what incentive is there to pursue it.
Again, if you are only concerned with the outcome, and you have a preferred answer that you want (in this case "just use AI to advance faster"), then any information that doesn't support that case is useless or misguided at worst.
I am not trying to dissuade you from your preference. I am flagging that there is a set of other factors that influence the behavior of others, how that behavior is critical to the creation of expertise and drive, and thus why others hold different positions.
If another human was likely to get the answer before you would you also discourage them from doing it because they would rob you of the chance to do the thing you're concerned about?
Would it be unethical to dissuade someone else from enjoying the benefits of the process you wish to enjoy ?
Vs
Would it be unethical to stop a machine from data mining all the possible questions you wish to explore/enjoy.
And on another level - I am concerned with a bit more than just the answer. I am concerned with what system is in place to ask more questions and get more answers.
There is nothing in this argument that says that we won’t find some other way to study the subject. Maybe people will become monks and do math as a hobby.
We may end up in a daemon filled world, like 40k, where any hope of understanding the tech around us is impossible. (More impossible that today)
They may very well have learned plenty of things and solved or discovered other puzzles, but if the first puzzle is worth pursuing because the solution is actually useful it seems liked we're better off with the solution than a bunch of failed attempts.
That said, I do question the value of solving many of these types of math problems. I'm no mathematician so I'm assuming I'm wrong here, but on the surface many seem mostly theoretical puzzles with little or no practical use.
I’ve made this point elsewhere but the debate here is between two different philosophical positions. Results vs process.
If all you care about is the results then the process doesn’t matter.
If a person is starving or needs medicine, then a long discussion on process is inhumane. They need results.
If the conversation is about process though, then focusing on the results is missing the point.
I’d say the question for results oriented people is what are the benefits of the process and at what point does it make sense to optimize for results vs process.
When the topic is about careers the question really has to be about results. Even if the results are made by solving different problems discovered along the way towards their original problem, it still has to be about those results.
There is absolutely a question of whether burning these resources is useful when the only outcome is a solution to a potentially obscure math problem, but that is more a question of prompting and goals rather than the use of these tools themselves.
Could you elaborate?
We spend most of our young lives (many of us our entire lives) studying physics, math, etc. that others have solved. (e.g Quantum Mechanics, Relativity, Calculus, etc.)
Biology consists, almost entirely, of studying solved problems in nature.
Aren't AI breakthroughs just more to study?
Terence Tao’s “don’t create the open problem strip miner”
Why is it a problem that the professor is now a robot, and that humans could spend arbitrarily long learning from it and even after 15 years of masters-style advanced graduate lecture courses still have deeper still levels of the topic that the AI could teach them?
And if they never do reach that level of ultra-competence, well, then we found the niche for humans to continue to exist within.
Mathematicians and academics in their ivory towers are forgetting that everything is getting automated. They want to carve out fun problem solving niches that's fine but who's going to fund that? If they want to be funded by the society/civilization their argument can't be leave advanced fun problems for their hobby.
https://proofsandprompts.com/2026/09/10/open-letter-about-th...
>Participation in an event so closely associated with Anthropic and OpenAI could plausibly negatively impact the future reputations of participants.
Given how much power advisors etc have over students in academia, interpret it as you wish.
People go to said crossword group to enjoy the process of solving the puzzles. It doesn't actually matter if they have been solved yet or not, case in point the NY Times puzzles are enjoyed by more than just the first to solve them.
Professional mathematicians are ultimately being paid to solve the problems for a (hopefully) practical reason. Its always excellent when a person enjoys the process of the work they are paid to do, but ultimately they are still paid to do the work. I really hope your argument isn't that we should collectively be funding mathematicians to solve problems simply doe the love of the game.
They are paid for the same reasons the NEA pays artists: out of a sense of obligation to demonstrate elite culture. The track record of practicality of pure math after WWII is essentially 0.
Similarly I wouldn't expect a good argument could be made that AI tools should be prevented from creating art because we want to continue funding artists.
If the goal of said funding is just to let them spend their time doing it then it doesn't matter that AI is doing it as well.
Despite nobody at openAI thinking of themselves as an asshole; despite society urging openAI not to be an asshole; despite the fact that being an asshole is entirely unnecessary even to accomplish whatever objective they are setting out to accomplish; despite everyone at openAI loudly declaring: we are not assholes!
They are still assholes.
If you listen to them, and you don't have to listen very hard to hear it, basically everyone at these labs is telling us that this technology is extremely dangerous and should be slowed down or paused entirely. Yet, they, the only entities with the power to actually do anything about it, are not acting AT ALL as if that's the case. They are all barrelling forward as quickly as possible. RSI, THE number one risk according to these guys, is being adopted at breakneck pace up and down the stack, from designing silicon, to training, to inference.
It's ridiculous and insane and I believe can be accurately summed up as, they are being assholes, because if they are actually right about this we are all gonna die. At the very least, and far more likely, every fun creative expressive human thing that is machine legible will be replaced by a torrent of machine slop. It's not "benefiting humanity." These mathematicians are telling you it's not benefiting humanity. It sucks.
Alignment problem.
That is fine to say when it is not your field. I guarantee you feel different when it is the thing you care about, that gives you joy, that defines your status. Think about how many sheldon-equivalents insist on being called Dr. (non medical)
It is part of what people use to define themselves. Its going to hurt. There may even be a Bulterian Jihad
It is clear to me that any competent person with a little patience can now build software better than what I used to build by hand.
Why do physicians insist on calling themselves Dr. (medical)?
Whole sections of the economy are being upheaved by AI, and there is no reason to make a special case for the mathematicians anymore than for the illustrators, developers, translators, HR, etc.
Of course; but it's very hypocritical to raise these feelings only when mathematicians are affected, whereas all the above professions are just told to adapt to the new way of things.
For sure though, translators don't have the same clout and social status as mathematicians do.
Mathematicians do a terrible job here. They use inconsistent symbols they don't even explain. They often obfuscate the main idea just to make the paper longer. If you are not part of a small club you are not meant to understand it. I think this is a terrible approach and I am eagerly waiting for AI to do a better job!
It just seems that this class of mathematicians is being "disrupted".
The field is changing and a new class of mathematicians will take their place.
This happens all the time in fields as technology disrupts them.
A new class of individuals, with different motivations, take the place of the old guard.
I'm sure the motivations of individuals involved in designing and manufacturing cars changed as Henry Ford introduced the factor line.
But that old crop of humans either adapted or retired.
But, plenty of humans took their place with new motivations and automotive technology continued to progress.
I personally feel math will indeed move faster as a result of these breakthroughs. And the humans that take the place of the old guard will have different passions and motivations than the current group.
Maybe the new group will be productivity motivated rather than motivated by the love of tinkering with a single problem for years.
Sounds like salaries for mathematicians need to start going up if we stop paying them with fun.
https://proofsandprompts.com/2026/09/10/open-letter-about-th...
>Participation in an event so closely associated with Anthropic and OpenAI could plausibly negatively impact the future reputations of participants.
Given how much power advisors etc have over students in academia, interpret it as you wish.
Science isn’t some passive busywork thing where you tie your hands behind your back because it isn’t fair on others to solve all the neat problems - or at least it shouldn’t be.
If your idea of science is leather patches on tweed suits and the quiet ticking of a clock while you do crosswords, then this is an argument in favour of letting the AI do the work so you can focus on your sudoku book in your slippers.
The picture I have in mind is OpenAI running their most advanced model in a loop over all the open mathematical problems they can find, just to verify that the model is indeed very smart. Neither the company nor the model actually care about the problems, it's just a cheap exercise machine for them, but the problems get solved and mathematicians don't even get to participate.
Like, even those who accepted the "centaur" thinking, man + machine, won't benefit because by the time they get their hands on good enough models, everything is already done.
It's an emotional thing first and foremost - people who care about the thing can't do the thing, because it's already been done by those who couldn't care less about it.
And before someone goes "poor mathematicians", a food for thought: this is just an early instance of what looks like our shared destiny.
I said here before: given the economics of progress in AI and robotics, it's obvious what the natural division of labor is: computers do the thinking, humans do the menial, manual labor. AI will do politics and philosophy, so you have more time to fold laundry and scrub the toilet.
Are we gonna get the same pushback from medical researchers if the models cure xyz diseases?
I absolutely understand the emotional connection to their work and the heartbreak, but mathematics doesn't exist for their pleasure, it exists to provide tools to solve humanitie's problems.
Some of it, yes. Much like physics. Both have a track record of producing technological breakthroughs every now and then, but it's not why people are doing it.
> Are we gonna get the same pushback from medical researchers if the models cure xyz diseases?
For better or worse, yes. We already are. In my country, there's a big spat between radiologists and cardiologists right now, that boils down to the progress of technology allowing the former to answer questions that, before, involved a procedure that was a big money-maker for the latter.
The general body of research points that more doctors lowers all cause mortality ( with diminishing returns) but Tunisia is still far lower than the Eu average.
Yet Doctors and med Student unions do lobby very heavily against expanding admission to the public uni or allowing private unis.
So we have the weird situation where people go and study in Romania ( making Tunisia lose hard currency that it really needs).
These doctors have taken an oath and the direct consequence of their lobbying is literally more deaths.
Obviously this is often coming from folks who act in same ways as they criticize and usually don't contribute even a fraction back to society compared to doctors. Folks who do mistakes in their lives all the time yet thats fine since we are all humans or similar, right.
So please stop this cheap framing and accusations. If Tunisia wants more doctors and keep them there are ways to do it, society as a whole needs to decide what they want and act upon it. Otherwise, smart skilled folks will keep going for better lives elsewhere, just like everybody else.
Everyone (near enough) has some degree of self-interest. If you apply for a job and discover that some other applicant is about as well fitted to it as you and in more need of money, do you withdraw? If you see a $20 note on the ground and no one else around who might have dropped it, do you refrain from picking it up if you think you're better-off than the median person who might walk past next? If you see something you want going for a very good price on eBay, do you contact the seller and say "I think you should be making me pay more for this"?
Unless you are an extremely unusual person, the answers to those questions are somewhere between "no" and "of course not, and why would you even ask?".
If someone is working as a doctor, their work is already benefiting others substantially more than the typical person's. (At least, I think it is; it's certainly doing so more directly.) Being a doctor doesn't put them under some unique obligation never to give any priority to their own interests when, e.g., choosing what job to take where.
If they can save 0.2 lives per day for $50k/year in one place and save 0.19 lives per day for $200k/year in another, it would be virtuous for them to do the former but I can't see that it's obligatory. In the case we're talking about, it might actually be 0.2 lives per day for $50k/year versus 0.21 lives per day for $200k/year, because somewhere that can afford to pay them more can probably also afford better equipment, more ambulances, etc. (In case it isn't obvious, all actual numbers here are made up and nothing I'm saying depends on exactly what they are, only on the rough relationships between them.)
It seems to me like any principle that would oblige them to pick the first of those options over the second would e.g. also oblige all of us who have well paid jobs to give most of what we earn to life-saving charities. Some people do that. It's a virtuous and commendable thing. It would doubtless be better if more people did. But, as you might have noticed, very very few people do that and by and large we don't consider it outrageous that they don't, and I don't see why doctors in particular should be condemned when they don't do it.
(Since clearly unassisted human nature isn't going to make everyone behave in such a way, it seems to me that if we wanted that sort of thing then it would need to be imposed by force. Which in fact everyone might be OK with, in the same sort of way as players of high-level sports are OK with having externally-imposed safety rules so that we don't get everyone playing in increasingly dangerous ways for the sake of a small advantage over people who are being more careful. And, in fact, we do have that sort of thing and it is imposed by force; it's called taxation, and actually I think it's a beautiful thing even though there's plenty to dislike about every actually-existing regime of taxes and benefits. This is mostly a digression, but note that it means that if a doctor chooses to go somewhere where they're paid better it probably also means that they're contributing more to the general welfare in taxes. There are plenty of nits one could pick with this remark, but it still seems worth making.)
Most doctors aren't running departments in major hospitals, or advising government on policy. They don't earn the big bucks. And even hospitals themselves tend to run in the red all the time; it's sometimes hard to disentangle where greed ends, and longer-term interests of patients begin, as you have multiple people and organizations pulling in different directions for different reasons.
RE private medical universities, N=1 but in Poland we have a private provider pushing hard for training their own doctors "because public system is too slow and limited", and it's hard to tell whether they have a point, or whether it's a private-driven attempt at privatizing national healthcare, or a mix of both.
The risk here is that this does do fundamental long-term damage to mathematics as a viable field.
Virtually no one is going to want to take on the risk of PhD-level math work, studying a narrow problem for four years or so to arrive at an impressive incremental result, when there's a sword of damocles hanging over their head every day that an internal system held by an oracle they don't have access to may scoop their results and turn those four years into dust.
To some extent, that sword of damocles always existed in a de minimus sense in the form of other mathematicians. But everyone was playing the same game, coming to the game with the same arsenal limited by human cognition.
If the game board becomes irrevocably tilted, new entrants have no incentive to play except as a hobby. But few hobbyists can devote years of work to understanding and pushing the frontier. It could well mean existential damage to mathematics as a field.
Whether that might undermine math's ability to solve humanity's problems in the long term is almost an economics problem, not unlike the question of whether and when the existence of monopolies ultimately restricts long-term economic growth. Much probably depends on whether intellectual monopolies or oligopolies are being created that will supplant the existing mathematics "economy".
All the commotion evens out: It's much easier to learn maths than ever before; you don't need to go to lectures any more; you don't need to learn from a specialist (advisor, lecturer) any more; it all costs much less than it used to.
So mathematics will continue to advance, albeit differently from before. The social structures will not survive however.
There's probably a loose and deeply imperfect analogy with computing: via democratization hobbyists have made a big impact in applied operating systems development (Linux/OpenBSD) but have been less successful/impactful in OS research (whither Hurd...) or in cost-heavy fields like microprocessor design.
Lol. As long as the process aka trials is respected not many would complain.
The feedback loop required to make progress is very different in medicine compared to math.
While AI has definitely helped quite a bit I am wondering how much all this research and treatments cost. Not sure the current health systems could sustain this for _everyone affected_. If ai enables it all the better.
My understanding of what Sid's describing is that you do RNA sequencing, a whole genome sequencing, feed that into frontier AI (if it will still let you), and somewhere along the way give the information the AI finds to people who can use it make a personalized mRNA vaccine, specifically for you and your cancer.
Another link here about Sid's case, it explains it didn't go through trials: "made possible through a compassionate use allowance from the U.S. Food and Drug Administration (FDA)".
https://www.houstonmethodist.org/newsroom/houston-methodist-...
I am not medical, so I'm happy for someone who understands better to come in and explain all the myriad ways I am wrong.
It's tempting to say "both", but that misses that AI is now forcing us to pick one.
As 'ogogmad said upthread:
> mathematics will continue to advance, albeit differently from before. The social structures will not survive however.
Who decreed that? Mathematics predates capitalism and publish-or-perish by a couple of millennia. Euclid’s Elements were not written to benefit the weapons or medical industry.
Maybe this hurts more than it should do because of publish-or-perish.
But humanity is not going to sit around and wait for solutions just so hobbyists can have a moment of glory.
Incredibly delusional and disconnected from the vast majority of people who are voters.
If only.
They certainly can't do them worse than humans.
In this instance however, it's openAI and Anthropic that are pushing people out of the field by running secret models that take the interesting work away and leaves the persons having to review endless slop proofs.
What you didn't make is the AI training process and resulting model. Extremely hard working people built that, and it has value in itself.
Without the AI training process, the model is useless. Otherwise we'd already have been here at GPT-3.
That's an incredibly generous take. If I'd pulled a fraction of the shenanigans prominent companies have to obtain data I'd be thrown under a prison to the thunderous applause of those who have, and are, doing much worse.
I’m interested in how you can support this assertion as it seems at odds with established copyright law
Who knows what they are up to.
This sort of happened at various times in the past, because they hired and/or funded so many mathematicians, and especially before the late 1970s they had many of them working in areas where academic mathematicians weren't working at all, so they were learning more math, or more math that they especially cared about, than the public was. (I was going to write a note here just a few days ago about how NSA has had a "Classified Mathematics Library" for many years.)
For vulnerability scanning, I think the new-capabilities trajectory is good (in the sense of "it will help defenders win") even if governments find ways to get more of it, because there are finitely many bugs and classes of bugs, so at some point more capable models' or longer runs' advantage over less capable models and shorter runs should stop helping them outcompete the less-well-funded defenders, because the defenders will still have learned most of the information that's relevant to achieving successful defenses.
So if NSA gets 5000 units of vulnerability scanning and the public only gets 4000 units, we might still just wipe out all of the pure software vulnerabilities and then go back to worrying about physical supply chain security or side channels or something.
For math, I'm not quite sure! For one thing, there may be things that have no feasibly deployable defense at all even when you understand the underlying mathematics (I'm especially worried about traffic analysis here, because understanding in detail how traffic analysis is done, or how powerful particular techniques are, does not necessarily always or usually make defending against it more convenient or less costly). In a more science fiction scenario, there might also not be any efficient secure cryptographic primitives of some kind, like if it turns out P=NP with reasonably small exponents and reasonably small constant factors.
Would that impact their own ability of solving Mathematics problems? I mean as a programmer I'm already seeing that impact on the programmers -- sure the best of us can leverage AI to achieve unimaginable things, but many of us are simply vibe coding.
Of course we can assume that it is only the best of us that really matters, and the rest of us are not going to produce anything substantially useful ANYWAY, it might as well to replace the rest of us with AI, but my worry is -- does that really have ZERO impact on the human specie's ability to produce "the best of us"? After all, they don't grow on trees.
I imagine the same will be true of AI, but I'll say that in the short term AI is going to make mathematicians better because it solves the breadth problem. Again, I feel like this Barnette conjecture got solved (if it is solved) because of some clever partition function sums which are intellectually tractable but simply too far out of anything I'd seen before (I see the apparition of my GT combinatorics professor intoning gravely that "everyone knows that, Jake, you're an idiot"). Maybe AI will help identify common threads far greater than Google and journal search.
I think if I had ChatGPT when I was 20 and working on this problem for the first time I might not have solved it, but I would have learned every angle and facet of it far more quickly. But then again I would not have spent so many late nights staring at the Országház across the Danube and letting my mind drift and bump against the problem like spilled cargo in the river.
Now if we can prove this, expand it to the whole spectrum of academic studies, and somehow convince 99.99% of us that they are basically garbage and we don’t care about them — sure the elites will throw UBI around but that’s it — then maybe AI is very positive to the human specie.
Oh we better pick up the speed of cloning and artificial fertilization quickly, because people who are told to be garbage probably have no interests in boring children, and it is still a myth how genies are born and grown. We need that diversity.
BTW the whole scheme reads like the background of a Chinese net novel 赛博英雄传.
So far, it looks like open-weight models are lagging less than a year behind frontier capabilities. And I think one year diffusion of technology from "insider lab demo" to widely available is actually pretty fast?
There are lots of research fields which "normal citizen" has no access to - medical and biological research, particle physics. Some of it is somehow publicly controlled (LHC), some of it not at all (commercial pharma research, mostly secret until the final human trials). And most of it reaches "normal citizens" in way more than a year.
(and I'm talking about open-weight models. The availability of commercial AI models from private preview to included-in-your-$100-subscription is currently like 4 months)
It has been super helpful in delineating where the crucial concept came from. The proof is rather simple as graph theory proofs go, but it does seem to use some constructions that would only seem obvious if you had serious physics experience with partition function and calculating energy states that cancel out. It's not a wholly alien bolt from the heavens, but I can also see how there hasn't been a human being with the broad theoretical physics knowledge combined with the deep graph theory experience in planar graphs to come up with this idea. I don't know, I'm looking for precedents of this formulation and some old papers of Penrose counting the number of edge colorings of this same graph type are coming up, the line of argument at least rhymes.
But I agree with the thought that this sort of progress should not be siloed inside those companies. I propose a tax so that every slop cannon AI video pays for another hour of compute time for advancing mathematics.
I suspect that this might be one of the reasons people inside the labs are scared about AI.
What if they have asked AI how it would wipe out humanity and it came up with reasonable answers that they don’t want to publish unlike they do with these math problems?
I think those models and findings should be investigated.
Cure for aging? What do you reckon that'd be worth?
Replace “AI” with “supercomputer”.
(Super)computers have been solving many math problems that mathematicians can’t solve. Now they are capable of solving problem types that they weren’t able to solve before. (this applies to other fields as well)
Problem is it’s not clear if there is anything left for humans. Probably yes, since human mathematicians are still more economical.
I guess if you worked together with some people who all put some money into a fund, and by using very modern technologies like 3D printing and modern CAD modelling etc., it should be possible even for private people to build a jet airplane.
The problem rather is that the government does an insane amount of gatekeeping to prevent this from happening (enforcing expensive and time-consuming certifications on airplanes and pilots etc.).
The concern is about elite level researchers no longer being able to move the industry forward in a public way, and leaving potentially all major discoveries in private hands going forward.
Possible worst case scenario in your case, you personally miss out on a luxury item.
Possible worst case scenario in the topic case, an AI company controls the only intelligence that discovers and understands the most powerful tools / physics we know of.
Obviously the more intelligent the model, the smaller/more directed the search is. But they spoke about huge numbers of agents working on Navier-Stokes for example (I think it cost >$10m).
But to me it also signals (as if it didn't before!) a great need for the wider AI community to focus exclusively on researching and building AI algorithms and systems that are more humanistic: completely transparent in its workings and the representations they create, super efficient in terms of data and compute, componentised so that individual entities can plug in different bits and rapidly train on their own data, highly adaptive to individual needs, programmable in a real sense, largely independent of corporate influence, easily accessible to everyone across all social and economic strata, and enable individuals to grow/learn/reach their full potential.
Is this possible? I think so, but it will require ingenuity and bringing in ideas from (ironically enough) some of the deepest areas of modern mathematics such category theory, algebraic topology etc. which are largely about building abstractions that expose the underlying structure of complex mathematical objects and the relationships between them.
It's already happening to a degree, but the urgency has reached epic levels at this point and it needs to happen at scale.
Humans are the same way sometimes but I guess there's romance in that. If a human had solved it a la Kekulé and said "it came to me in a dream" I would at least understand that.
it's deeply problematic because they are building on open, public results yet they don't provide information on how people may build on it - its exploitative and exclusionary - at least they are consistent
I've seen more goalposts move in the last 3 years than maybe in my whole (lengthy) career up to that point.
> I suspect that this is in fact the source of much of the angst.
Your comment reveals that you absolutely did not read or understand the Field medalists' open letter... Please, why would you refer to their complaints and claim you disagree when you clearly aren't engaging with the arguments presented therein!?
Agree, and, to my mind - shows why the efforts of the Free Software Foundation have been worthwhile all along. We need software to be open / free / libre or the power elite controlling them will ruin the world.
Yes. They have already shown to have no scruples when it comes to making profit and to have little to no morals.
> If you worry about the government, isn't it better that than rando terrorists?
In my country the largest terrorist attack was almost certainly financed by Iran and caused roughly one hundred deaths. This number pales compared to the thousands who died during the latest, US-backed military coup, a move that relied on a doctrine that the US has never stopped asserting [1].
And those morals I mentioned earlier from AI companies? They do not apply to me because I'm not a US citizen. So no, I do not think the US government is the "seal of quality" you think it is.
I am currently in Germany. In the 21st Century roughly 60 people have been killed and 160 injured in ~40 terrorist attacks, most of them perpetrated with cars or knives [1]. In comparison, the US' war in Iran has costed Germany 2.781 billion dollars in fuel costs this year alone and the US government has publicly announced its plans to interfere in German politics partially by funding far-right activities [2].
My point being: the probabilities of terrorists shaking the world order with AI are rather low, seeing as even the most successful attacks in this century have been performed with the simplest of technologies. In contrast, the probability of the US flexing its power irresponsibly are rather high, seeing as they have been doing it for a couple years now and are, in fact, doing it right now.
As far as I'm concerned, and from an evidence-based, day-to-day point of view, the "AI in the hands of terrorists" is an irrelevant concern while "the US may abuse its power" is not.
[1] https://en.wikipedia.org/wiki/Terrorism_in_Germany
[2] https://www.theguardian.com/us-news/2026/jul/15/germany-warn...
Has the government stopped Google and Apple? https://news.ycombinator.com/item?id=49964791
"Math" is about uncovering the epistemological foundations of the universe.
Adding AI here does nothing and is probably a regression in that it diverts resources from actual "math" into some sort of LLM wankery that nobody wants.
Which depends on (1) whether there are actual good ideas in it, (2) whether as well as finding the proofs the AIs can explain their ideas in ways humans (and other AIs) can use, and (3) whether the results they prove are ones that really contribute to that rather than being isolated curiosities that don't go anywhere.
I am not expert enough in all these fields, and haven't looked enough at the papers, to assess #1, but in general the way mathematicians have bet is that if you can solve things regarded as important problems you'll usually do so in a way that contains more broadly useful ideas. Differences between how today's AI systems do mathematics and how humans do mathematics might make that less true when it's an AI that solves the problem, but I would still bet that way. I'd be surprised if OpenAI's big math dump didn't turn out to contain some ideas, and connections between ideas, that humans find useful.
At the moment the AIs are worse than good humans at #2. (But some humans are also really bad at #2, including some humans who are very good at proving theorems.) It looks to me as if they're getting better, and I would expect them to continue to do so. I also suspect (but this is only guesswork) that today's publicly-available frontier AIs may be able to answer questions along the lines of "please take a look at this AI-written paper, and tell me what key new ideas it contains and how they relate to other things in the field" well enough to be useful to human mathematicians. (Even when the paper itself was written by a proprietary AI that no one outside OpenAI or Anthropic or Hypothetical New AI Mathematics Lab has access to.)
As for #3, that's always been something of a crapshoot. A lot of mathematicians' effort goes into proving things that approximately no one ever reads or builds on, just as a lot of industrial R&D goes into trying things that don't turn out to make good products. The recent OpenAI dump contains things that sure seem like important building blocks for future mathematics (e.g., the "quasi-Riemann-Hypothesis" thing) but it's hard to know for sure and also hard to know whether, if they do prove things that turn out to be useful, it's only because they've read the human-written literature and aimed at things human beings have said seem likely to be useful.
None of this seems to me like "adding AI here does nothing". Whether what AIs are doing to mathematics at the moment is good on balance is highly debatable, of course, but it's a matter of trading off costs and benefits, rather than there being costs and no benefits.
So basically nothing changes, Math was subject to gatekeeping and policing of the worst kind.
If you were not among the geniuses, and it didn't come to you automagically, you were simply supposed to leave it to the people who did get it and go do work for people of your intelligence. Smugness was too much to take.
Math people, like chess people never made any genuine attempt to help people understand the processes and methods that made math happen.
To me it should have been a field as teachable and ubiquitous as accounting.
The net result is once these methods and processes were worked out by AI, it was over for the human mathematicians.
The "aha" insight for this is actually f**ing wild, it involves a complex valued exponential sum on the edges. I've seen a lot of clever counting arguments before in graph theory but this is the first time I've seen complex roots and annihilating terms like this, the symbolic manipulation tricks in this look like things out of quantum physics. I don't understand where this trick originated, I need to really digest this.
I asked GPT here: https://chatgpt.com/share/6ac5fd7d-0390-83ed-a02a-6d80fc64f6... and it says:
> the exact Barnette argument appears quite novel, but nearly every ingredient in its cancellation trick has a recognizable ancestor.
> The closest precedent is much closer than I expected: in fully packed O(n) loop models, people have been assigning complex phases to the two orientations of a loop and making them cancel for decades. At n=0, the phases are literally +I and -I. And the n->0 limit has specifically been used to extract Hamiltonian cycles/walks.
You can judge better than me. But it's definitely worth it having a research assistant AI with you when reading these papers.
It makes solving advanced math problems feel like cracking a hash. If it's possible, it's just a matter of compute time.
I'm sympathetic to the mathematicians who are worried about the future of their field, but as an outsider I wonder if they couldn't learn from the go community's "recovery" after the introduction of an alien intelligence.
But also I am excited to be living through this new era of programming and new era of mathematics. I'm still saddened that I couldn't be the one to solve this old problem, but now I realize that my personal approaches were really solving a level of this problem even stronger than the original conjecture, and I'm energized to tackle those (in my free time between being a solo founder and father of 3, etc.).
If you can remember the content of any scientific publication and any book in the world, you are able to make use of this knowledge in every step of you proof.
However, this does now answer how the model came up with the specific route it has taken for the proof.
I'm fairly sure your understanding is not fully accurate.
And then they are for sure able to fill their context based on 'smart search on top' to actually progress further.
But obviously, it adds up to something greater than went in; in aggregate, our contributions are something to awe.
But my point is, if you zoom in at the marginal, incremental contributions of any individual human in this process, it's really hard for me to say LLMs are not at the same level already.
On this topic, people like to compare LLMs to Einstein, but as far as I know, Einstein did not zero-shot special relativity in an afternoon. He built it up incrementally over time, it took him three times longer than the time between first ChatGPT release and today, and it depended on centuries of prior art, culminating in the right observation and right notation being available to him in his moment of greatness.
At what level LLMs are is then an entirely separate discussion, I think.
Name three.
So your view is that everything was there at the creation of the universe (it's a possible view, of course)? Or are there any "things" that can create ideas from scratch?
I think it's not impossible that words evolved as adaptations of the environmental sounds with which our ancestors lived. The human creativity producing DNA is also a remix of preexisting molecules formed under evolutionary pressure, so the view that it's turtles all the way down, unintuitive as it is, may not be so indefensible after all.
They combine things, verify it and if it works and progresses the problem, they created something new.
Loaded question. A "brand-new insight" is still built off the work of others. A possibly better way to frame it would be in how many subjectively unintuitive logical leaps have been made from prior work.
"it's a matrix-tree cancellation wearing Kasteleyn's planar signs, run as a Witten index over Penrose-lineage states, evaluated as a fugacity-zero loop gas in an infinitesimal magnetic field — and the reason it reads like physics is that every one of those tools was built for partition functions"
I thought this was pure slop when I read it but there are some clear analogues in these other areas of physics, really neat computational tricks, and a very interesting paper by Penrose calculating Tait colorings I never knew about previously (extremely relevant, actually related to a separate approach I had once taken on this problem). The problem is that the paper isn't saying "aha, we were inspired by the related problems of pairing excited states and creating spanning trees out of cancelled coefficients" it just defines the function apropos of nothing. Which is kind of like the Jacobian counterexample in that it works but doesn't really explain how exactly it got there.
I really think the load-bearing concept here is "prior work". If prior work is considered papers on this problem or graph theory, yes this has one huge subjectively unintuitive logical leap. If "prior work" is the entire corpus of neat computational tricks that physicists derived to make their equations spit out something other than zero or infinity, maybe it's not so crazy?
Makes me wonder how the patent space will be disrupted when that inventiveness step becomes obsolete because of LLMs. Given your example above, it seems like a combination of different methods from many different sources. This would be regarded as inventive, clearly. If eligible patents can now be brute-forced, the bottleneck becomes only selecting the most promising ones and paying for the patent.
Also, once upon a time I wanted to be a patent lawyer. It's incredibly hard to sit for the patent bar if you have a pure math degree and don't have an engineering degree. Thankfully New Hampshire lets anyone sit for the FE exam.
Are there no loads left to be borne?
I am not demotivated though, I have a great consumer privacy product coming out soon that I'm very excited about.
IMO that’s where AI is going: as soon as a problem can be formulated clearly enough, AI will trounce us humans. I have yet to see evidence that it can decide what problems are important at a remotely human level.
I think something like the Collatz conjecture will be solvable not as number theory or ergodic theory but some other completely wacky environment that humans haven't even sniffed at.
But I have an existential dread about it… I don’t see how it cannot, at least in the vast majority of cases. It seems like a grim new reality is emerging where humans can’t contribute any more, and beyond that being incredibly depressing, I also don’t see it playing out well for human relations.
I’d personally much rather risk dying of cancer or facing whatever other fate may await me that these AI labs allege they will fix (with zero evidence yet) than to risk whatever dystopian anti-human future this technology may very well produce. I’d rather my kids have a shot at something, and be guaranteed to die eventually, than to risk them being hopeless in a severely disordered world with a far off promise that they’ll live forever
But can it all survive and thrive under the boulder of an automated existence.
Just like there are talented software engineers driving the AI to create the software that "it" builds, and talented steel workers, teachers, nurses etc who use computers and other machines to create value all over the economy (without whom, the machines they use at work would be worthless).
Capital owners have always sought to minimise the value of the input that "workers" make in the process of creating value. Maybe now that information workers are on the wrong end of this deal, they might develop some empathy and solidarity with their fellow working class comrades and together, demand that people recapture the value that capital has stolen from them.
https://github.com/openai/math/blob/main/lean/ComparatorChal...
at least now you are one of the most qualified people to check the result, transform it into understandable (by humans) state and grow stuff on top of it
I would love to know the true unsubsidized cost of all of this. How many grad student-years did this cost?
Strange
but at least as a software engineer, i always knew my work was "never done" and so it was common to build a bunch of code that might be thrown away, either because it didn't serve our customers (the mvp or pilot fails to meet demand), or because we found a better way to do it and so we deprecate it.
some people got too attached to the code and honestly they were the types to be filtered out fast.. way too emotional and hard to work with. getting attached to code meant you actually don't advance (after all, in our case, we were a business serving customers and not a hobby artisan shop). attachment leads one to hold back due to some misplaced cognitive load.
isn't the goal of working on "advancing the field/product/whatever" to always be solving/selling/whatever?
maybe in your hands, with your knowledge and experience over the last 20+ years, you can use AI to make leaps and bounds by steering it properly towards whatever solution or goal?
Also there is a larger epistemic problem with the argument to "using AI to meet the goal or solution", which is that the goal is to mentor and train future mathematicians to advance the field.
There is a similar issue in software engineering too: if no one hires junior engineers because AI can do all the work then the upstream pipeline of engineers qualified to work on difficult architectural problems would dry up.
This importance of this is being felt by mathematicians more acutely because the field will collapse quickly if people refuse to join it.
I've been mentoring (or so I'd like to think) a very bright undergraduate mathematician, in fact he was the one who pointed out the final irreducible flaw in my proof last summer. And I am extremely curious to see what he does and if he even finishes his degree in mathematics. He had already expressed to me some dismay that his summer undergrad research program with several Ivy-league math majors got blown out of the water by a few hours of a frontier model. It's making everyone question what the future will look like and what education and training and certification will even look like.
But the future belongs to those who show up. Maybe this is the beginning of a mass democratization of scientific and math research, maybe we are going back to the gentleman-scholar model of amateur researchers and Twitter will be the new Journal of the Royal Society.
i hope so!
You may achieve far more than you plan on and it may come years and years after you think it should happen. You probably haven't met the right problem yet. You will.
I mean: if some reclusive Japanese genius had a breakthrough on your problem and published it, would you have felt the same?
And if not, why not?
I will never meet that person and I will never hold a real conversation with the "creator" of that proof. They will never tell me how they came up with the cancelling exponential summation that cracked the construction. It's just another enigma but one that is far more unknowable than the original problem.
Weavers don't have dibs on those intangibles.
You just made my day, beautifully said. Thank you Sir, for all your thoughts expressed in this thread. You put an human story behind the #180 number.
It’s probably distributed on so much compute that it would never be economical to serve it to you or I or anybody
It has no memory or experience of working on similar problems. Even if it made one of the foundational libraries that I use in a weather forecasting program, it still has no comprehension of the thought process it takes to understand the problem and build it from zero, and if I’m building on that library it just makes fresh assumptions about how things should work.
It’s not a human with experience or expertise, it’s a computer program that’s really good at turning English descriptions into functioning code
If it did it once, it can do it again from zero, and this time you can watch as it works and even it ask it questions. Many of the agents that worked on the problem did not have comprehension of the whole problem. I don't think you need that many tokens to be able to query it for the insights it had during the process.
Isn’t this the issue with using it the way you’re suggesting? At best the model can come up with an after-the-fact rationalization of how to get to the solution, but it doesn’t know what actual path it took to get there - what were interesting traps it fell into, where was a place it was close to the solution but didn’t realize at the time.
Those are things that are valuable to share between humans, those which teach us how to think better, and give us deeper understanding ourselves, and which a model doesn’t have any comprehension of.
Not that things like that can't happen with humans too (Salieri v. Mozart comes to mind).
Another possibility is that they have internal versions of the model with access to training data that is not provided to external users.
Don’t you feel any relief that you won’t obsess on this any longer and not lose more hours on this than you already have?
These are genuine questions. I know I spent a good amount of time thinking about P vs NP, and that sometimes I go back to it just to realize I’ll never solve it. I’d feel that knowing the proof would feel more like a liberation, a weight lifted off my shoulders than something being taken away from me.
What is this then, vibes? Without a machine-checkable proof I'm not sure what to think of any of this.
I think it helps that basically everyone thinks this conjecture is true, it's just been so darn weird to attack. There's this odd thing that the induction proofs of this problem kept running into, which is that the N+1 condition would work except for in one tiny case when it could fail, but it would be covered by a very slightly stronger version of the conjecture. But then that would fail on one tiny case in induction, but you could solve that with another slightly stronger version. Etc., etc. I almost wondered if there were some sort of structure to the increasingly strong conditions and wanted to prove something about the meta-induction between the stronger conditions and the N's that they needed the next level to remain true. But that failed after 5 steps I think (Fable actually helped me write a few hundred test cases to explicitly show that pattern didn't continue forever, thank God).
BTW my existing test suite from previous proof attempts jives with this new algorithm, so I haven't seen any evidence yet that it's incorrect. Waiting for a Lean proof obviously.
/-- Cubic bipartite three-vertex-connected plane graphs have a Hamiltonian cycle. -/ def MainStatement : Prop := ∀ (V : Type u) [Fintype V] [DecidableEq V] (G : SimpleGraph V) [DecidableRel G.Adj], G.IsRegularOfDegree 3 → G.IsBipartite → Planar G → ThreeVertexConnected G → HasHamiltonianCycle G
theorem main : MainStatement.{u} := by sorry
the proof is probably split over the constructions in the whole directory.
You mean you ran her over , or someone else ?