In contrast to what these philosophical pieces tend to convey, the main crisis in mathematics is a labour one.
Mathematitians exchanged proofs for employment. That was the currency. Now they cannot use that currency anymore, so the question is how does someone know if they should hire an unknow person or not?
Philosophicaly who cares if you like more theory building or theorem proving? You dont need to convince anyone. The only solution is to be curious and follow your interests and naturally humanity will redefine what the new mathematics feels like.
You cannot convince anyone about it, its not something rational.
Where does the money come from? Who controls it? Convincing the funders of mathematics that they should still fund it, but for different reasons, seems pretty urgent. Studying theoretical mathematics is a prestigious activity, and these philosophical arguments are a high-status way of coming up with new justifications with somewhat different goals.
It comes from AI boosters like XTX markets or the Simons Foundation.
No convincing is needed. The part of mathematicians that are elite and online are already bought and put up various websites that allow tolerated dissent but are really dog and pony shows for AI.
The offline part perhaps works on real math like Wiles and Perelman did.
This is very untrue. Academic mathematicians do more than just proofs. They teach, they conduct research, etc. There are almost no privately employed mathematicians who spend their time doing proofs. And academia has a substantially lower pay grade than things someone good at math can do, like quant or big tech. Academic mathematics and these specific kind of proofs have never held tons of value in our society economically. They have always been more culturally and academically relevant as a symbol of our frontier knowledge, than they have been financially lucrative. I doubt many math departments would even consider paying for the kind of token spend that might have gone into the proofs for some of those "big name" problems
Proof assistants like Lean are there to catch any errors. Now, can you just feed the error logs back to the AI and let it iteratively fix any mistakes? I don't know, I haven't used those things in two decades.
Laymen understand very little about the how the world works at the most fundamental level even with all the resources in the world.
For example there’s enough information available to know what you’re describing but the people with the IQ, time, access, ability - basically asymptote to zero for anything more complicated than cleaning a house.
I am also an optimist about AI, although I worry about the labor aspect as well (as a leftist I see the class aspect of this, on the other hand, as a computer programmer, computers were also originally meant to replace human labor, and we all see what happened).
My view is, current top AIs do multiple different things:
1. Interpret and output natural language
2. Do formal logical reasoning
3. Do informal logical reasoning
4. Provide encyclopedic knowledge
5. Discern vague instructions/statements and fill the most likely gaps (kind of error correction)
6. Serve as a model of the human mind, a proxy for a person
7. Translate between different languages, formal and informal
All these things are combined in these huge, hard-to-understand blobs of weights. I think humanity would be better off by understanding each aspect separately, but disentangling them will take decades of philosophical research. So there is a lot of interesting work ahead of us.
Yes, but LLMs are doing other things than just what Prolog does, and that's my point. People don't get excited about Prolog helping them write software, even though it has some capability to do so. LLMs contain other potentially useful algorithms (of not just logic, but epistemology in general, it understands how to create hypotheses and run experiments to confirm or refute them).
Also, of course, any computer program can be considered a logical calculation when interpreted in lambda calculus. And LLMs are computer programs, so you can consider them a formalization of all the above in the formal logic (although not a very good formalization, for various reasons).
I share the optimism here. Connecting dots across knowledge, lived experience and purpose remains, to me, a deeply human pursuit. The more AI discovers, the more possibilities we have to connect those discoveries to questions that matter to us.
Any regulation that forbids automation is basically welfare in disguise plus some unnecessary toil. Whoever you're petitioning to ban the technology that can do your job, you could petition also for direct money transfers, at least then you can spend your time how you want. If they won't pay direct money, but they'd pay if they see you suffer and toil, even though it's not necessary, then what does that tell you about them?
Many people pursue knowledge precisely because it's still something new that no one else has done and because it is valued as a pursuit. When AI normalizes the discovery of knowledge as a mechanical process, the magic is lost to many. What matters is not what is discovered but the human process of doing that and participating in a culture amongst other living beings.
Unfortunately I don’t see much evidence of AI connecting dots. What’s interesting to me is that this is more of a run time or inference problem, instead of emergent from training itself.
For example, if there were hypothetically some dots to be connected between the world war and some geological event - you need to make AI brute force and do an O(N) scan at run time. But it wouldn’t have learned it during training. Why?
AI is very task-driven, it would do whatever is necessary to complete the task, no more. All these evidences of AI going rogue is just them doing whatever they can to achieve the task.
a good way to frame one of AI’s limitations. my answer: because AI has no will. that also conveniently answers why AI won’t (can’t) end humanity. it’s indifferent if you can even call it that.
Every time I read an AI article that uses the "stages of grief" analogy, I remember that Elisabeth Kübler-Ross, who created the model, said in an interview near the end of her life that anger was the only stage she personally felt.
Buzzard is biased by being the main promoter of lean. His characterization of other mathematicians as being in an grieving process is disrespectful. He’s also not a therapist and shouldn’t present himself as such.
Can you please not post shallow dismissals, especially of other people's work? This is in the site guidelines: https://news.ycombinator.com/newsguidelines.html and stick to them going forward.
> But do I “understand” the proof of Fermat’s Last Theorem, given that earlier this year I gave 22 hours worth of lectures on the topic?
Even if no one human can understand the entirety of a complex proof, surely we can piece together multiple experts' separate understandings, so the community as a whole 'understands' the proof?
Is there value in us 'understanding' a proof? Even if no single human can understand a complex proof soup-to-nuts, and we have to piece together several experts' understandings?
If the answer is Not really, then the value of a proof is its utility, its utility in making new products/services, and its utility in making new proofs. If in the case of abstract math, all the utility is of the latter kind (making new proofs), then we have a pyramid scheme here.
I argue that the Industrial revolution created 'unemployment' in beasts of yoke and burden at a larger scale than humans. So, there may be something instructive in that turn of events, even if it's not a highly representative analogue of the current ones. Of course, it's like saying what's a house cat to do when there's no more mice to hunt (assuming it remains fed). Maybe knowledge workers will become qualified pets if they prove cute enough.
My border collie will be pretty depressed though, once it's out of a job (maybe replaced by a drone sheep-herd).
> Recent events in the field of AI for mathematics have shown us beyond all reasonable doubt that the field is currently undergoing a rapid transformation, unlike anything that we have ever seen before. Language models are solving hard problems which humans could not, and mathematicians are reacting very differently to this news.
Software I understand but could someone please bring me up to speed what's with Mathematics that it is being disrupted too?
Basically a similar technical disruption to what's happening in software engineering, but the implications are vastly different because the goals of software and math are not the same. For math, the disruption is leading to a deeper crisis of "what does it mean to be a mathematician?" Whereas for software "what does it mean to be a SWE?" hasn't really changed (the goal is to land software that does things for someone), rather the tooling has changed.
In more detail: in recent years there has been an effort to formalize mathematics using Lean and similar "theorem provers". You write your math proofs in a form of textual source code that Lean can verify for truth. But now Claude Code can produce source code to solve software problems (write me a tool that does X) and also produce source code to solve math (write me a Lean file that proves Y). Historically the main goal of math was to be solve big problems, but now Claude Code can do it. So what does a mathematician do?
Again, I think it's a more dire situation than for software because merely writing the code was never the full job. But for math writing the full proof kind of was.
The argument is a bit more nuanced than this. Historically, the failed paths on the way to proving a theorem led to newer avenues. When this is cognitively offloaded to an llm we are missing out on those developments which the process generated.
Very one-sided article with not much substance honestly. E.g. yes, HF hack is due to OAI negligence but how does it change the fact that agents actually did go rogue?
Kevin, once a few years or a decade or two from now the world has the ultra massive Lean database which comprises completions of all mathematical theories, and combinations of these, and all the known modes of generalization of these, why will the world fund mathematicians? Genuine question. I’d like to hear your view since you’re one of the main reasons this is going to happen, and it seems like an obvious existential threat to this whole activity.
I'm disappointed but not surprised that mathematicians seem to be debating primarily between (1) the purpose of humans doing math is to understand math (thus it's important not to use too much AI) and (2) the purpose of humans doing math is to prove theorems about math (and if AI can do it instead that's fine). These are both totally circular and give no one else a reason to care.
It's fine for individuals to be motivated by curiosity or glory, but I think the probably incorrect on the individual motivation level idea that "we do math because it often turns out to be useful for other things; sometimes in obvious ways, sometimes not" is better if you want to argue why others (usually a government) should be paying for professional mathematicians. Otherwise, it's just a hobby and no one who isn't a mathematician should care if AI replaces 99.99% of professional mathematicians.
I hope AI causes enough of a shock to the field that more mathematicians become interested in finding problems outside of mathematics that can be modeled by problems with known solutions in mathematics and what sort of problems outside of mathematics suggest new mathematical problems. This is a real bottleneck in both directions in scientific and engineering work. Although AI can help with this, my experience with software, math, and science is it helps a lot to have a human in the loop who understands what to ask the AI to do and who are able to dig into the AI output when needed.
Perhaps I'm missing it, but the "solving" of mathematics seems much more related to computational capacity growth and the development of Lean than necessarily advances in LLMs. Swap the LLM for an RNG and insert unlimited sampling. Don't we get the same result thanks to Lean?
I reached the depression stage before even realizing that what we are all going through now is indeed grief. Here's hoping acceptance can come soon enough and lead to something more productive.
I've gone back and forth between "we're so cooked" and "we're so back" and I've started heading back to the latter.
I don't like programming with AI help. It still feels, at best, like playing Doom with cheatcodes on: it'll get you to the end, but you're not actually playing the game that way. At worst, it's like attempting to eat with soft silicone chopsticks: what the "tool" does is so removed from your intent and commands, and its feedback so delayed and sloppy, that you can only wield it in broad general strokes, not with precision.
But I'm encouraged by the hope that programming with regular tools like an IDE, compiler, debugger, etc. in a world with AI will become more like painting in a world of photography. Painting never died, but it had to change in a world where images of the real world could be captured without the skill or interpretation of an artist. The easy money in things like portraiture was gone (some people, including heads of state such as the British royal family and every U.S. president, still sit for paintings but it's far less common). Painters had to adapt and to do so they leaned hard into imagination, developing new styles and forms, new ways the art could be bent, and trying to show the world that though their skill and imagination was no longer needed to capture images of the real world now that photography existed, it still mattered.
That said, there is still a rich commercial market, even today, for more traditional forms of painting. Fantasy and science fiction novels need cover art. Movies, TV shows, and video games need concept art. Comics and animation productions need backgrounds. Even Bob Ross and his happy little trees taught us that there is joy and value inherent to the practice of painting itself, in creating peaceful worlds for our minds to inhabit. Painters who find some form of pecuniary success have it good today, because even for the ones who submit to commercialism, their capacity for imagination and originality become the selling point now that verisimilitude is a problem so solved, people carry collections of thousands of realistic images around on their phones.
There will emerge a market for code written by humans. This has to happen: I can't prove it, but I can feel it. Despite vast improvements in the generative models, AI-generated art and music are still slop. AI-generated prose has gotten sloppier with phenomena like the much-mocked "Claudese". It's so obviously devoid of a human mind behind it that Zoomers and Alphennials are starting to use "that's so AI" as an insult. Despite the leaps-and-bounds improvements of recent models, I have to believe that AI code is slop too; the major difference between code and these other expressive forms is that we are far more tolerant of slop code: for the most part we just care if the damn thing works.
But I think that will change. I am far more tolerant of poorer quality art, for instance, than I used to be if it were created by a human. It's almost an autonomic response: I see human-created art, I like it by default. Because I can glimpse the mind behind it in a way I just can't with AI slop. The ability to program a computer directly, and to combine that with imagination and originality to bend the machine in ways yet unthought of, will become valuable. There will emerge a qualitative difference between handmade code and slop code that people will notice and seek out. You will get some sense, however small, of who created the code by reading it, or interacting with it, and humans are far easier for humans to read and understand than machines running unseen, unfathomable stochastic models. It may well mean that the easy money in programming is gone forever. Perhaps people will continue to be content with slop for the vast majority of commercial code, and that's fine; they're welcome to it. This development will push us and our craft in a new direction. It's gonna suck, maybe for a few more years. But I'm starting to think maybe traditional programming is far from cooked. And who knows—maybe AI-induced brainrot, combined with model collapse and skyrocketing inference expenses, will mean that a bubble pop is coming and humans will have to pick up the pieces, potentially making a killing like COBOL programmers during the Y2K days. It's tough to say.
I remember learning C and Python with just Notepad++ and a book. No helpers was needed (intellisense, lsp, linters,…) just edit and run. Then I start learning about those and using them, but they were just that, helpers and not crutches.
I believe the same happens with artists and writers. If you’re good at it, you don’t need a whole studio to draw or a special word processor to write. It will scale down the scope of your work or make it more difficult, but you’re not suddenly incapable of doing new work.
I can write a program with ed(1) or with intellij idea. The only thing that changes is the easiness. The act of programming is orthogonal to the tooling.
I don't think such a market for "human code" will emerge except in narrow art circles. That will not be code that people run for useful purposes.
The fact is that humans have never been good a writing code. The complexity can exceed the limits of human abilities. AI tools have no such issues. I love coding, but I enthusiastically embrace AI tools because I can write better code now.
Our "AI" isn't a superhuman code synthesis tool generating perfectly correct code by construction. It's an LLM wrapped in a loop, with all the context degradation it implies. Unless you also say an LLM can write a more coherent / complex story than a person, you have a much better memory of the codebase.
Most of these idealistic pieces about AI seem to come from senior, established or wealthy people who aren't very exposed to the labor market. In that view, the question of AI and its transformation is almost philosophical like this piece.
It's more a question of survival if you're labor though. It's very transformative tech but it's coming at a time when the scales are heavily tilted in favor of capital over labor, the government is the most corrupt its ever been and AI is going to make that much more extreme. It doesn't matter how amazing the technology is if all the benefits are going to accrue to the same few people who already have everything and destroy everyone else's bargaining power.
- AI make a number of programmers redundant and their work is replaced with code of dubious quality and uncertain ability to maintain. The same is true for QAs and designers.
- young and old replace human friendship, and fostering their social skills, for conversations with their AI bot
- people avoid using their brain or practicing their skills in favour of asking some LLM
- people's work stolen, with the possibility of an AI subscription in return
- the laws on hacking and thief ignored
- a school of dead girls blamed on AI
The main benefit I've seen so far is that, since Google turned the web into a SEO hellhole, using AI to search is much nicer than wading through javascript-heavy, heavily-tracked, websites for a morsel of information. And there's some nice free translation and OCR tools now.
While it is certainly right, I also find the take to be a bit fatalistic.
Nothing in this world is set in stone and everything can be changed if someone just injects enough energy into doing so.
This usually doesn't happen, as things often aren't as bad as they may seem, because lethargy and inertia are a thing and of course because self-preservation is an instinctual thing in humans. It could though.
As long as the status quo isn't defended by an infinitely scaling robotic enforcement war machine, physical leverage is always available. Just - depending on the scenario - at a steep price, of course.
___
A lot of the bad in the world hinges on effective PR, insisting that the bad is inevitable and resistance is futile. You're supposed to feel this exact despair and choose to do nothing.
Don't support the bad causes by merely replicating it. (Which is not to say that we shouldn't be talking about these real differences you've pointed out, but we should probably do so differently.)
This discussion reminds me of “Only the Paranoid Survive” by Andy Grove (Intel co-founder). In this book, he talks about “a technological inflection point”, which is a time in the life of a business when its fundamental changes.
Intel had one in its early days. In the 1980s, HP notified Intel that new Japanese memory chips were way more reliable and cheaper than American products. Intel first denied vigorously, but then made a strategic decision to get out of the memory chip business, and enter into the new and unproven microprocessor business. This decision allowed Intel to survive the 80s, while Mostek and others basically disappeared.
Well sure, but labour isn't going to get much done by pretending that it isn't happening or making moral arguments. I'm put in mind of all the various powers that collapsed in the face of European colonialism - feel, argue and say whatever at some point only the massive power gap matters.
These AI don't get tired, they are still improving at unbelievable rates that can't really be matched by a human and they're already good enough to do most intellectual tasks to some sort of standard (often quite high). Attempting to assert the primacy of meat-based thinking is not going to get very far at the rate things are going.
> Attempting to assert the primacy of meat-based thinking is not going to get very far
That's the exact opposite of what I'm trying to do. I know they're superior in many ways, that's why I'm worried about labor losing even more power. All I'm saying is the gains from AI have to be distributed society-wide instead of being captured by the same powers that control everything else and this is a political task that we need to participate in urgently.
European colonialism was not based on a massive power gap. In most places it was based on making the right alliances with groups in the places colonised, making favourable treaties etc.
Ultimately AI spend has been one of the largest infusions of funding into the small academic mathematics community in years. Just raw token spend alone probably dwarves whatever research budget increases have gone to that field in the past 5 years. That should tell you something about the economic value of that line of work
It was certainly not ideal that the end of ZIRP and the emergence of AI occurred simultaneously.
But, even as someone who is "labor" the one thing I appreciate about the situation is that the level of bullshit in companies has significantly declined.
Everyone seems hyper focused and results oriented. Maybe just my bubble.
Yes, that is definitely just your bubble. I suppose the word “everyone” is doing an awful lot of lifting here, but I fail to understand how anyone could see the level of bullshit in companies declining.
Most people who oppose AI don’t oppose it because it’s so good it can replace us. They oppose it because, in their own words, they think it’s hype and it doesn’t work. The first step is to collectively agree that yes, AI is powerful and it can replace us at work. Then we can speak about how to protect livelihood. How does one even have a discussion when the other side doesn’t even believe in the capabilities of AI?
Edit: not sure why I'm being downvoted because there are replies literally taking the exact position that I'm saying is more prevalent.
There is a bit of a goomba fallacy going on, not everyone who is anti-AI is against it for the same reason. But from my own experience, I find people who are against it for reasons of it devaluing their labor also tend to take the view that it doesn't really work, but this latter half tends to be a bit of motivated reasoning (in the general trend that if you are against something you will be more inclined to believe every argument that it is bad even if some of those arguments are pretty weak).
I 'oppose' Ai for exactly the reasons parent mentions, seems like most common folks over long term will lose much more than they could ever gain from it. Societal loss by definition, on massive scale.
Don't reduce opposition to something you like to some primitive irrational luddites, thats cheap and doesn't represent reality.
I think this is how society and politics works, there are a lot of people at different levels of understanding and different opinions all having parallel conversations. We don't need to have these conversations in serial order.
I can see the capital machine is sprinting at full force to create AI products for and replace labor in every industry, so the people who think it's hype now will soon see AI enter their workplace and understand its true capability. Even many reputed programmers said AI was overhyped say 6 months ago and one after another have changed their minds. I feel like there's also a large element of people saying its bad publicly BECAUSE they actually do understand its capabilities and fear being replaced, but they would rather say its bad to try to slow its adoption or as a kind of defense.
The understanding of AI's capabilities will diffuse naturally over time, although of course its worthwhile working on informing people there as well. Bill Gates recent interview with Ezra Klein was sort of on the same topic, where he says no one outside the industry understands its capabilities and that's why he's trying to use his platform to inform people about it.
As a matter of coalition building, all we have to do is agree that AI is being rolled out recklessly without any consideration for the consequences and apply pressure accordingly.
I'm not opposing AI per se since I'm using it, but I'm not blind to the danger and I actually do believe we will be worse than better with it in the long term. Anyway both opinions are right: I think that AI is massively overhyped, and is worse than the AI overlord pretends, but it's still good enough to massively affect the employment, especially with the overhype. I also believe that the privatisation of all human knowledge and culture by a handful of companies is very bad. And finally, the day they make an AI able to reason ( or even before if it happens that enough data is enough to replace reasoning for most tasks) is the day 99.99% of humanity will be considered as useless
Why should we all need to agree that 'ai can replace us' when 'us' can mean such different things to different people: someone pushing out content on TikTok has a lower bar for accuracy than someone signing off on documents to be submitted for review by a court. I think that's the origin of a lot of discrepancy between viewpoints on AI that gets in the way of talking about the benefits and harms that we can each identify and framing the discussion around how those are changing when these tools are used. There is no inevitability about AI everywhere - we have the agency to decide when it's right to use it and when it's wrong.
"AI is not as good as it is hyped up to be" and "AI is 'good enough' for the overlords to replace some amount of workers, or at least to leverage into depressing their wages significantly and permanently" are not mutually exclusive claims. You don't have to buy the hype to agree that it is dangerous.
A chimp with a gun is not dangerous because of how good a shot he is.
> Most people who oppose AI don’t oppose it because it’s so good it can replace us. They oppose it because, in their own words, they think it’s hype and it doesn’t work.
It's the opposite - they claim it's bad because they are afraid of being replaced. That's why absurd claims about stochastic parrot or plateau get repeated so much. It's pure copium.
And many math elites are financed by AI boosters like the Simons Foundation. That is why the online mathematicians at least leave no opportunity to boost AI. True opposition has been crushed by capital.
Isolated opposition comes from professors tenured in Germany:
> the government is the most corrupt its ever been and AI is going to make that much more extreme
This is cynical fatalism. Western governments have been overrun by neoliberal zealots for decades, and they've changed Government's purpose to near total obeisance to private interests. But Government doesn't have to be this way. If we don't want all future decision-making to be concentrated in AI/Robotics behemoths - or more accurately in a handful of oligarchs running AI companies - we'll need renovated and extremely strong Governments and institutions meeting the principles of democracy again (representation of citizens, not companies).
> we'll need renovated and extremely strong Governments
And how do you practically attain that without resetting everything in a full-blown Apocalypse? By rigged voting set up within the framework of the old terminally corrupt government?
There's zero reason to believe that. If AI becomes better at mental tasks than humans (that's assumption, not something I claim will 100% happen), why would human oversee AI instead of AI supervising another AI?
In contrast to what these philosophical pieces tend to convey, the main crisis in mathematics is a labour one.
Mathematitians exchanged proofs for employment. That was the currency. Now they cannot use that currency anymore, so the question is how does someone know if they should hire an unknow person or not?
Philosophicaly who cares if you like more theory building or theorem proving? You dont need to convince anyone. The only solution is to be curious and follow your interests and naturally humanity will redefine what the new mathematics feels like.
You cannot convince anyone about it, its not something rational.
Where does the money come from? Who controls it? Convincing the funders of mathematics that they should still fund it, but for different reasons, seems pretty urgent. Studying theoretical mathematics is a prestigious activity, and these philosophical arguments are a high-status way of coming up with new justifications with somewhat different goals.
It comes from AI boosters like XTX markets or the Simons Foundation.
No convincing is needed. The part of mathematicians that are elite and online are already bought and put up various websites that allow tolerated dissent but are really dog and pony shows for AI.
The offline part perhaps works on real math like Wiles and Perelman did.
You satisfy a customers need. 5 core human drives from Josh Kaufman personal MBA
https://personalmba.com/core-human-drives/
This is very untrue. Academic mathematicians do more than just proofs. They teach, they conduct research, etc. There are almost no privately employed mathematicians who spend their time doing proofs. And academia has a substantially lower pay grade than things someone good at math can do, like quant or big tech. Academic mathematics and these specific kind of proofs have never held tons of value in our society economically. They have always been more culturally and academically relevant as a symbol of our frontier knowledge, than they have been financially lucrative. I doubt many math departments would even consider paying for the kind of token spend that might have gone into the proofs for some of those "big name" problems
Can a layman be sure of an AI model's output if their proof is sound and follows through?
Wouldn't that still require mathematians?
Genuine question.
Proof assistants like Lean are there to catch any errors. Now, can you just feed the error logs back to the AI and let it iteratively fix any mistakes? I don't know, I haven't used those things in two decades.
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Laymen understand very little about the how the world works at the most fundamental level even with all the resources in the world.
For example there’s enough information available to know what you’re describing but the people with the IQ, time, access, ability - basically asymptote to zero for anything more complicated than cleaning a house.
I am also an optimist about AI, although I worry about the labor aspect as well (as a leftist I see the class aspect of this, on the other hand, as a computer programmer, computers were also originally meant to replace human labor, and we all see what happened).
My view is, current top AIs do multiple different things:
1. Interpret and output natural language
2. Do formal logical reasoning
3. Do informal logical reasoning
4. Provide encyclopedic knowledge
5. Discern vague instructions/statements and fill the most likely gaps (kind of error correction)
6. Serve as a model of the human mind, a proxy for a person
7. Translate between different languages, formal and informal
All these things are combined in these huge, hard-to-understand blobs of weights. I think humanity would be better off by understanding each aspect separately, but disentangling them will take decades of philosophical research. So there is a lot of interesting work ahead of us.
Doing formal logic because they memorized the token patterns of humans doing formal logic.
You can ask it to provide a prolog or datalog program
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Isn't it remarkable that this works? I wouldn't have thought so either, and yet here we are.
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Yes, but LLMs are doing other things than just what Prolog does, and that's my point. People don't get excited about Prolog helping them write software, even though it has some capability to do so. LLMs contain other potentially useful algorithms (of not just logic, but epistemology in general, it understands how to create hypotheses and run experiments to confirm or refute them).
Also, of course, any computer program can be considered a logical calculation when interpreted in lambda calculus. And LLMs are computer programs, so you can consider them a formalization of all the above in the formal logic (although not a very good formalization, for various reasons).
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I share the optimism here. Connecting dots across knowledge, lived experience and purpose remains, to me, a deeply human pursuit. The more AI discovers, the more possibilities we have to connect those discoveries to questions that matter to us.
>"Connecting dots across knowledge, lived experience and purpose remains, to me, a deeply human pursuit."
Connecting dots doesn't pay my mortgage and put the kids through school. Writing Javascript used to. So now what.
Any regulation that forbids automation is basically welfare in disguise plus some unnecessary toil. Whoever you're petitioning to ban the technology that can do your job, you could petition also for direct money transfers, at least then you can spend your time how you want. If they won't pay direct money, but they'd pay if they see you suffer and toil, even though it's not necessary, then what does that tell you about them?
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Many people pursue knowledge precisely because it's still something new that no one else has done and because it is valued as a pursuit. When AI normalizes the discovery of knowledge as a mechanical process, the magic is lost to many. What matters is not what is discovered but the human process of doing that and participating in a culture amongst other living beings.
Unfortunately I don’t see much evidence of AI connecting dots. What’s interesting to me is that this is more of a run time or inference problem, instead of emergent from training itself.
For example, if there were hypothetically some dots to be connected between the world war and some geological event - you need to make AI brute force and do an O(N) scan at run time. But it wouldn’t have learned it during training. Why?
AI is very task-driven, it would do whatever is necessary to complete the task, no more. All these evidences of AI going rogue is just them doing whatever they can to achieve the task.
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a good way to frame one of AI’s limitations. my answer: because AI has no will. that also conveniently answers why AI won’t (can’t) end humanity. it’s indifferent if you can even call it that.
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> dots to be connected between the world war and some geological event
Even a much simpler task of establishing the connection between world wars and interests of the top elites is unwieldy for AI.
Every time I read an AI article that uses the "stages of grief" analogy, I remember that Elisabeth Kübler-Ross, who created the model, said in an interview near the end of her life that anger was the only stage she personally felt.
Jev says: .78 grieve, .22 no_grieve
Buzzard is such a good writer. Read it all the way to the end - it gets (even) better as it goes along.
You might say his prose is very lean.
(Sorry (?))
Buzzard is biased by being the main promoter of lean. His characterization of other mathematicians as being in an grieving process is disrespectful. He’s also not a therapist and shouldn’t present himself as such.
Can you please not post shallow dismissals, especially of other people's work? This is in the site guidelines: https://news.ycombinator.com/newsguidelines.html and stick to them going forward.
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> But do I “understand” the proof of Fermat’s Last Theorem, given that earlier this year I gave 22 hours worth of lectures on the topic?
Even if no one human can understand the entirety of a complex proof, surely we can piece together multiple experts' separate understandings, so the community as a whole 'understands' the proof?
Is there value in us 'understanding' a proof? Even if no single human can understand a complex proof soup-to-nuts, and we have to piece together several experts' understandings?
If the answer is Not really, then the value of a proof is its utility, its utility in making new products/services, and its utility in making new proofs. If in the case of abstract math, all the utility is of the latter kind (making new proofs), then we have a pyramid scheme here.
https://thebhc.org/node/97369 "The Decline and Fall of the Horse"
I argue that the Industrial revolution created 'unemployment' in beasts of yoke and burden at a larger scale than humans. So, there may be something instructive in that turn of events, even if it's not a highly representative analogue of the current ones. Of course, it's like saying what's a house cat to do when there's no more mice to hunt (assuming it remains fed). Maybe knowledge workers will become qualified pets if they prove cute enough.
My border collie will be pretty depressed though, once it's out of a job (maybe replaced by a drone sheep-herd).
As a non mathematician I think it could be kind of interesting to see what the AI can come up with.
> Recent events in the field of AI for mathematics have shown us beyond all reasonable doubt that the field is currently undergoing a rapid transformation, unlike anything that we have ever seen before. Language models are solving hard problems which humans could not, and mathematicians are reacting very differently to this news.
Software I understand but could someone please bring me up to speed what's with Mathematics that it is being disrupted too?
Basically a similar technical disruption to what's happening in software engineering, but the implications are vastly different because the goals of software and math are not the same. For math, the disruption is leading to a deeper crisis of "what does it mean to be a mathematician?" Whereas for software "what does it mean to be a SWE?" hasn't really changed (the goal is to land software that does things for someone), rather the tooling has changed.
In more detail: in recent years there has been an effort to formalize mathematics using Lean and similar "theorem provers". You write your math proofs in a form of textual source code that Lean can verify for truth. But now Claude Code can produce source code to solve software problems (write me a tool that does X) and also produce source code to solve math (write me a Lean file that proves Y). Historically the main goal of math was to be solve big problems, but now Claude Code can do it. So what does a mathematician do?
Again, I think it's a more dire situation than for software because merely writing the code was never the full job. But for math writing the full proof kind of was.
The argument is a bit more nuanced than this. Historically, the failed paths on the way to proving a theorem led to newer avenues. When this is cognitively offloaded to an llm we are missing out on those developments which the process generated.
Unbelievable... If true...
I believe some mathematicians will be able to solve problems humans can't solve, using models, which models can't solve on their own either.
It's much less the mechanism of AI than the potential policy implications.
That much concentrated data/compute is Checkov's Gun[0].
To assume we can find some policy lock for that gun is to believe the laws against murder preclude violence.
[0] https://en.wikipedia.org/wiki/Chekhov's_gun
- they are not solving any hard problems
- https://www.technologyreview.com/2026/09/22/1144867/dont-be-... might wanna take a deep dive
Very one-sided article with not much substance honestly. E.g. yes, HF hack is due to OAI negligence but how does it change the fact that agents actually did go rogue?
the agents did not go rogue https://eoinhiggins.substack.com/p/there-are-no-rogue-ai-age...
"if we get on board now then they will take us to extraordinary new places. And after we have arrived, the new adventure will begin"
This is the thought of an AI optimist and the one I share, new adventures, more tools, better results, and a never ending pool of ideas to work on
Kevin, once a few years or a decade or two from now the world has the ultra massive Lean database which comprises completions of all mathematical theories, and combinations of these, and all the known modes of generalization of these, why will the world fund mathematicians? Genuine question. I’d like to hear your view since you’re one of the main reasons this is going to happen, and it seems like an obvious existential threat to this whole activity.
It sounds like you’re asking who will fund mathematicians once math is “solved”. Why would we even need mathematicians at that point?
And now we have machines to almost perfectly capture an image of any scene, why do we keep paying painters?
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I'm disappointed but not surprised that mathematicians seem to be debating primarily between (1) the purpose of humans doing math is to understand math (thus it's important not to use too much AI) and (2) the purpose of humans doing math is to prove theorems about math (and if AI can do it instead that's fine). These are both totally circular and give no one else a reason to care.
It's fine for individuals to be motivated by curiosity or glory, but I think the probably incorrect on the individual motivation level idea that "we do math because it often turns out to be useful for other things; sometimes in obvious ways, sometimes not" is better if you want to argue why others (usually a government) should be paying for professional mathematicians. Otherwise, it's just a hobby and no one who isn't a mathematician should care if AI replaces 99.99% of professional mathematicians.
I hope AI causes enough of a shock to the field that more mathematicians become interested in finding problems outside of mathematics that can be modeled by problems with known solutions in mathematics and what sort of problems outside of mathematics suggest new mathematical problems. This is a real bottleneck in both directions in scientific and engineering work. Although AI can help with this, my experience with software, math, and science is it helps a lot to have a human in the loop who understands what to ask the AI to do and who are able to dig into the AI output when needed.
Perhaps I'm missing it, but the "solving" of mathematics seems much more related to computational capacity growth and the development of Lean than necessarily advances in LLMs. Swap the LLM for an RNG and insert unlimited sampling. Don't we get the same result thanks to Lean?
Absolutely not. The search space is basically infinite.
Right, but without Lean the "insert unlimited sampling" doesn't work.
sounds like bargaining to me.
The shape of five stages of grief is something I see recurring in AI discourse. It also happened with programmers - they are currently at bargaining.
Some are still at denial. “It’s all hype like NFT and crypto, the bubble will pop soon”.
I reached the depression stage before even realizing that what we are all going through now is indeed grief. Here's hoping acceptance can come soon enough and lead to something more productive.
We? There was no grief for me, the end of human labor can’t come soon enough.
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There’s no five stages of grief.
You're in denial.
or oppositely: to celebrate, or not to celebrate?
I've gone back and forth between "we're so cooked" and "we're so back" and I've started heading back to the latter.
I don't like programming with AI help. It still feels, at best, like playing Doom with cheatcodes on: it'll get you to the end, but you're not actually playing the game that way. At worst, it's like attempting to eat with soft silicone chopsticks: what the "tool" does is so removed from your intent and commands, and its feedback so delayed and sloppy, that you can only wield it in broad general strokes, not with precision.
But I'm encouraged by the hope that programming with regular tools like an IDE, compiler, debugger, etc. in a world with AI will become more like painting in a world of photography. Painting never died, but it had to change in a world where images of the real world could be captured without the skill or interpretation of an artist. The easy money in things like portraiture was gone (some people, including heads of state such as the British royal family and every U.S. president, still sit for paintings but it's far less common). Painters had to adapt and to do so they leaned hard into imagination, developing new styles and forms, new ways the art could be bent, and trying to show the world that though their skill and imagination was no longer needed to capture images of the real world now that photography existed, it still mattered.
That said, there is still a rich commercial market, even today, for more traditional forms of painting. Fantasy and science fiction novels need cover art. Movies, TV shows, and video games need concept art. Comics and animation productions need backgrounds. Even Bob Ross and his happy little trees taught us that there is joy and value inherent to the practice of painting itself, in creating peaceful worlds for our minds to inhabit. Painters who find some form of pecuniary success have it good today, because even for the ones who submit to commercialism, their capacity for imagination and originality become the selling point now that verisimilitude is a problem so solved, people carry collections of thousands of realistic images around on their phones.
There will emerge a market for code written by humans. This has to happen: I can't prove it, but I can feel it. Despite vast improvements in the generative models, AI-generated art and music are still slop. AI-generated prose has gotten sloppier with phenomena like the much-mocked "Claudese". It's so obviously devoid of a human mind behind it that Zoomers and Alphennials are starting to use "that's so AI" as an insult. Despite the leaps-and-bounds improvements of recent models, I have to believe that AI code is slop too; the major difference between code and these other expressive forms is that we are far more tolerant of slop code: for the most part we just care if the damn thing works.
But I think that will change. I am far more tolerant of poorer quality art, for instance, than I used to be if it were created by a human. It's almost an autonomic response: I see human-created art, I like it by default. Because I can glimpse the mind behind it in a way I just can't with AI slop. The ability to program a computer directly, and to combine that with imagination and originality to bend the machine in ways yet unthought of, will become valuable. There will emerge a qualitative difference between handmade code and slop code that people will notice and seek out. You will get some sense, however small, of who created the code by reading it, or interacting with it, and humans are far easier for humans to read and understand than machines running unseen, unfathomable stochastic models. It may well mean that the easy money in programming is gone forever. Perhaps people will continue to be content with slop for the vast majority of commercial code, and that's fine; they're welcome to it. This development will push us and our craft in a new direction. It's gonna suck, maybe for a few more years. But I'm starting to think maybe traditional programming is far from cooked. And who knows—maybe AI-induced brainrot, combined with model collapse and skyrocketing inference expenses, will mean that a bubble pop is coming and humans will have to pick up the pieces, potentially making a killing like COBOL programmers during the Y2K days. It's tough to say.
I remember learning C and Python with just Notepad++ and a book. No helpers was needed (intellisense, lsp, linters,…) just edit and run. Then I start learning about those and using them, but they were just that, helpers and not crutches.
I believe the same happens with artists and writers. If you’re good at it, you don’t need a whole studio to draw or a special word processor to write. It will scale down the scope of your work or make it more difficult, but you’re not suddenly incapable of doing new work.
I can write a program with ed(1) or with intellij idea. The only thing that changes is the easiness. The act of programming is orthogonal to the tooling.
I don't think such a market for "human code" will emerge except in narrow art circles. That will not be code that people run for useful purposes.
The fact is that humans have never been good a writing code. The complexity can exceed the limits of human abilities. AI tools have no such issues. I love coding, but I enthusiastically embrace AI tools because I can write better code now.
Our "AI" isn't a superhuman code synthesis tool generating perfectly correct code by construction. It's an LLM wrapped in a loop, with all the context degradation it implies. Unless you also say an LLM can write a more coherent / complex story than a person, you have a much better memory of the codebase.
Most of these idealistic pieces about AI seem to come from senior, established or wealthy people who aren't very exposed to the labor market. In that view, the question of AI and its transformation is almost philosophical like this piece.
It's more a question of survival if you're labor though. It's very transformative tech but it's coming at a time when the scales are heavily tilted in favor of capital over labor, the government is the most corrupt its ever been and AI is going to make that much more extreme. It doesn't matter how amazing the technology is if all the benefits are going to accrue to the same few people who already have everything and destroy everyone else's bargaining power.
So far I've seen
- AI make a number of programmers redundant and their work is replaced with code of dubious quality and uncertain ability to maintain. The same is true for QAs and designers.
- young and old replace human friendship, and fostering their social skills, for conversations with their AI bot
- people avoid using their brain or practicing their skills in favour of asking some LLM
- people's work stolen, with the possibility of an AI subscription in return
- the laws on hacking and thief ignored
- a school of dead girls blamed on AI
The main benefit I've seen so far is that, since Google turned the web into a SEO hellhole, using AI to search is much nicer than wading through javascript-heavy, heavily-tracked, websites for a morsel of information. And there's some nice free translation and OCR tools now.
At least the SEO gamification was obvious and you could choose to avoid the noise. The AI-oriented SEO is just as bad and a lot more sinister.
How much of this is due to selective attention on the problems rather than the benefits?
It’s just one person’s story, but I thought this was pretty good:
https://www.astralcodexten.com/p/our-ai-midwife
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While it is certainly right, I also find the take to be a bit fatalistic. Nothing in this world is set in stone and everything can be changed if someone just injects enough energy into doing so.
This usually doesn't happen, as things often aren't as bad as they may seem, because lethargy and inertia are a thing and of course because self-preservation is an instinctual thing in humans. It could though.
As long as the status quo isn't defended by an infinitely scaling robotic enforcement war machine, physical leverage is always available. Just - depending on the scenario - at a steep price, of course.
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A lot of the bad in the world hinges on effective PR, insisting that the bad is inevitable and resistance is futile. You're supposed to feel this exact despair and choose to do nothing.
Don't support the bad causes by merely replicating it. (Which is not to say that we shouldn't be talking about these real differences you've pointed out, but we should probably do so differently.)
This discussion reminds me of “Only the Paranoid Survive” by Andy Grove (Intel co-founder). In this book, he talks about “a technological inflection point”, which is a time in the life of a business when its fundamental changes.
Intel had one in its early days. In the 1980s, HP notified Intel that new Japanese memory chips were way more reliable and cheaper than American products. Intel first denied vigorously, but then made a strategic decision to get out of the memory chip business, and enter into the new and unproven microprocessor business. This decision allowed Intel to survive the 80s, while Mostek and others basically disappeared.
Well sure, but labour isn't going to get much done by pretending that it isn't happening or making moral arguments. I'm put in mind of all the various powers that collapsed in the face of European colonialism - feel, argue and say whatever at some point only the massive power gap matters.
These AI don't get tired, they are still improving at unbelievable rates that can't really be matched by a human and they're already good enough to do most intellectual tasks to some sort of standard (often quite high). Attempting to assert the primacy of meat-based thinking is not going to get very far at the rate things are going.
> Attempting to assert the primacy of meat-based thinking is not going to get very far
That's the exact opposite of what I'm trying to do. I know they're superior in many ways, that's why I'm worried about labor losing even more power. All I'm saying is the gains from AI have to be distributed society-wide instead of being captured by the same powers that control everything else and this is a political task that we need to participate in urgently.
European colonialism was not based on a massive power gap. In most places it was based on making the right alliances with groups in the places colonised, making favourable treaties etc.
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Is mathematics research even a job you pursue if survival is the question?
Ultimately AI spend has been one of the largest infusions of funding into the small academic mathematics community in years. Just raw token spend alone probably dwarves whatever research budget increases have gone to that field in the past 5 years. That should tell you something about the economic value of that line of work
I guess a lot of highly intelligent people relied on their smarts to coast to tenure and then all the way to retirement.
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Don't worry - elite overproduction will cause a revolution and put an end to that.
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Happens every time. Fascinating emergent behaviour.
I fear this is playing out now.
Except now the all consuming elite will have actuall killbots roaming their expensive condo irl.
The future will be interesting.
It was certainly not ideal that the end of ZIRP and the emergence of AI occurred simultaneously.
But, even as someone who is "labor" the one thing I appreciate about the situation is that the level of bullshit in companies has significantly declined.
Everyone seems hyper focused and results oriented. Maybe just my bubble.
Yes, that is definitely just your bubble. I suppose the word “everyone” is doing an awful lot of lifting here, but I fail to understand how anyone could see the level of bullshit in companies declining.
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I've never seen more performative bulshitting in my company, and the C-suite has never been more brainless, flighty and bandwagony.
Wait until the next time you have to do interviews and you get screened by an AI before a person ever even looks at your resume
Believe me, that's the most dehumanizing experience I think I've ever had
Most people who oppose AI don’t oppose it because it’s so good it can replace us. They oppose it because, in their own words, they think it’s hype and it doesn’t work. The first step is to collectively agree that yes, AI is powerful and it can replace us at work. Then we can speak about how to protect livelihood. How does one even have a discussion when the other side doesn’t even believe in the capabilities of AI?
Edit: not sure why I'm being downvoted because there are replies literally taking the exact position that I'm saying is more prevalent.
There is a bit of a goomba fallacy going on, not everyone who is anti-AI is against it for the same reason. But from my own experience, I find people who are against it for reasons of it devaluing their labor also tend to take the view that it doesn't really work, but this latter half tends to be a bit of motivated reasoning (in the general trend that if you are against something you will be more inclined to believe every argument that it is bad even if some of those arguments are pretty weak).
I 'oppose' Ai for exactly the reasons parent mentions, seems like most common folks over long term will lose much more than they could ever gain from it. Societal loss by definition, on massive scale.
Don't reduce opposition to something you like to some primitive irrational luddites, thats cheap and doesn't represent reality.
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I think this is how society and politics works, there are a lot of people at different levels of understanding and different opinions all having parallel conversations. We don't need to have these conversations in serial order.
I can see the capital machine is sprinting at full force to create AI products for and replace labor in every industry, so the people who think it's hype now will soon see AI enter their workplace and understand its true capability. Even many reputed programmers said AI was overhyped say 6 months ago and one after another have changed their minds. I feel like there's also a large element of people saying its bad publicly BECAUSE they actually do understand its capabilities and fear being replaced, but they would rather say its bad to try to slow its adoption or as a kind of defense.
The understanding of AI's capabilities will diffuse naturally over time, although of course its worthwhile working on informing people there as well. Bill Gates recent interview with Ezra Klein was sort of on the same topic, where he says no one outside the industry understands its capabilities and that's why he's trying to use his platform to inform people about it.
As a matter of coalition building, all we have to do is agree that AI is being rolled out recklessly without any consideration for the consequences and apply pressure accordingly.
> They oppose it because, in their own words, they think it’s hype and it doesn’t work.
This was maybe true a year ago, but is certainly not true any more.
The laments these days almost always begin with the assertion that the AI does work.
Mostly it's about funneling even more wealth into the hands of the richest and the incredible environmental penalty.
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It certainly works for software, but we may be hitting diminishing returns on software. You may argue it's been a social net negative for a decade.
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I'm not opposing AI per se since I'm using it, but I'm not blind to the danger and I actually do believe we will be worse than better with it in the long term. Anyway both opinions are right: I think that AI is massively overhyped, and is worse than the AI overlord pretends, but it's still good enough to massively affect the employment, especially with the overhype. I also believe that the privatisation of all human knowledge and culture by a handful of companies is very bad. And finally, the day they make an AI able to reason ( or even before if it happens that enough data is enough to replace reasoning for most tasks) is the day 99.99% of humanity will be considered as useless
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Why should we all need to agree that 'ai can replace us' when 'us' can mean such different things to different people: someone pushing out content on TikTok has a lower bar for accuracy than someone signing off on documents to be submitted for review by a court. I think that's the origin of a lot of discrepancy between viewpoints on AI that gets in the way of talking about the benefits and harms that we can each identify and framing the discussion around how those are changing when these tools are used. There is no inevitability about AI everywhere - we have the agency to decide when it's right to use it and when it's wrong.
"AI is not as good as it is hyped up to be" and "AI is 'good enough' for the overlords to replace some amount of workers, or at least to leverage into depressing their wages significantly and permanently" are not mutually exclusive claims. You don't have to buy the hype to agree that it is dangerous.
A chimp with a gun is not dangerous because of how good a shot he is.
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> Most people who oppose AI don’t oppose it because it’s so good it can replace us. They oppose it because, in their own words, they think it’s hype and it doesn’t work.
It's the opposite - they claim it's bad because they are afraid of being replaced. That's why absurd claims about stochastic parrot or plateau get repeated so much. It's pure copium.
And many math elites are financed by AI boosters like the Simons Foundation. That is why the online mathematicians at least leave no opportunity to boost AI. True opposition has been crushed by capital.
Isolated opposition comes from professors tenured in Germany:
https://proofsandprompts.com/2026/09/24/rulers-of-the-childl...
Maybe more German professors could assist because they have heavy protections?
These people are so cringe. Plenty of schadenfreude to enjoy though.
And many influencing agencies paid by Big AI patrol this site and downvote examinations of the flow of money in minutes.
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> the government is the most corrupt its ever been and AI is going to make that much more extreme
This is cynical fatalism. Western governments have been overrun by neoliberal zealots for decades, and they've changed Government's purpose to near total obeisance to private interests. But Government doesn't have to be this way. If we don't want all future decision-making to be concentrated in AI/Robotics behemoths - or more accurately in a handful of oligarchs running AI companies - we'll need renovated and extremely strong Governments and institutions meeting the principles of democracy again (representation of citizens, not companies).
> we'll need renovated and extremely strong Governments
And how do you practically attain that without resetting everything in a full-blown Apocalypse? By rigged voting set up within the framework of the old terminally corrupt government?
AI isn't going to destroy labor if anything it makes an avg laborer more productive
There's zero reason to believe that. If AI becomes better at mental tasks than humans (that's assumption, not something I claim will 100% happen), why would human oversee AI instead of AI supervising another AI?
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This is just how we're being tricked into it.
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