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Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem
Knuth Claude's Cycles note update: problem now fully solved, by LLMs - https://news.ycombinator.com/item?id=47306926 - March 2026 (2 comments)
https://chatgpt.com/share/69aaab4b-888c-8003-9a02-d1df80f9c7...
Claude's Cycles [pdf] - https://news.ycombinator.com/item?id=47230710 - March 2026 (362 comments)
I've always said this but AI will win a fields medal before being able to manage a McDonald's.
Math seems difficult to us because it's like using a hammer (the brain) to twist in a screw (math).
LLMs are discovering a lot of new math because they are great at low depth high breadth situations.
I predict that in the future people will ditch LLMs in favor of AlphaGo style RL done on Lean syntax trees. These should be able to think on much larger timescales.
Any professional mathematician will tell you that their arsenal is ~ 10 tricks. If we can codify those tricks as latent vectors it's GG
Tricks are nothing but patterns in the logical formulae we reduce.
Ergo these are latent vectors in our brain. We use analogies like geometry in order to use Algebraic Geometry to solve problems in Number Theory.
An AI trained on Lean Syntax trees might develop it's own weird versions of intuition that might actually properly contain ours.
If this sounds far fetched, look at Chess. I wonder if anyone has dug into StockFish using mechanistic interpretability
Stockfish's power comes from mostly search, and the ML techniques it uses are mainly about better search, i.e. pruning branches more efficiently.
The weights must still have some understanding of the chess board. Though there is always the chance that it makes no sense to us
Why must it involve understanding? I feel like you’re operating under the assumption that functionalism is the “correct” philosophical framework without considering alternative views.
Does Stockfish have weights or use a neural net? I know older versions did not.
yes
Even that is probably too much. It has no understanding of what "chess" is, or what a chess board is, or even what a game is. And yet it crushes every human with ease. It's pretty nuts haha.
Actually, the neural net itself is fairly imprecise. Search is required for it to achieve good play. Here's an example of me beating Stockfish 18 at depth 1: https://lichess.org/XmITiqmi
chess is just a simple mathematical construct so that's not surprising
The ML techniques it uses are only about evaluation, but you were close
> I've always said this but AI will win a fields medal before being able to manage a McDonald's.
I love this and have a corollary saying: the last job to be automated will be QA.
This wave of technology has triggered more discussion about the types of knowledge work that exist than any other, and I think we will be sharper for it.
The ownership class will be sharper. They will know how to exploit capital and turn it into more capital with vastly increased efficiency. Everybody else will be hosed.
I've never seen you say that
You will have to take my word that I started saying this in Dec 2024 lol
I think this is mostly about existing legislature, not about technology.
In any other context than when your paycheck depends on it, you would probably not be following orders from a random manager. If your paycheck depended on following the instructions of an AI robot, the world might start to look pretty scary real soon.
There's a lot to being a manager
- Coherent customer interaction
- Common sense judgements
- Scheduling
- Quality control
All which are baked into humans but not so much into LLMs
Even if it were legal to have an LLM as a GM, I think it would fair poorly
> AI will win a fields medal before being able to manage a McDonald's
Of course, because it takes multi-modal intelligence to manage a McDonalds. I.e. it requires human intelligence.
> I predict that in the future people will ditch LLMs in favor of AlphaGo style RL
Same for coding as well. LLM's might be the interface we use with other forms of AI though.
Something like building Linux is more akin to managing a McDonald's than it is to a 10 page technical proof in Algebraic Groups.
Programming is more multimodal than math.
Something like performance engineering might be free lunch though
But LLMs have proven themselves better at programming than most professional programmers.
Don't argue. If you think Hackernews is a representative sample of the field then you haven't been in the field long enough.
What LLMs have actually done is put the dream of software engineering within reach. Creativity is inimical to software engineering; the goal has long been to provide a universal set of reusable components which can then be adapted and integrated into any system. The hard part was always providing libraries of such components, and then integrating them. LLMs have largely solved these problems. Their training data contains vast amounts of solved programming problems, and they are able to adapt these in vector space to whatever the situation calls for.
We are already there. Software engineering as it was long envisioned is now possible. And if you're not doing it with LLMs, you're going to be left behind. Multimodal human-level thinking need only be undertaken at the highest levels: deciding what to build and maybe choosing the components to build it. LLMs will take care of the rest.
Yeah, it's hard to compare management and programming but they're both multimodal in very different ways. But there's gonna be entire domains in which AI dominates much like stockfish, but stockfish isn't managing franchises and there is no reason to expect that anytime soon.
I feel like something people miss when they talk about intelligence is that humans have incredible breadth. This is really what differentiates us from artificial forms of intelligence as well as other animals. Plus we have agency, the ability to learn, the ability to critically think, from first principles, etc.
Exactly. It's what the execs are missing.
Also animals thrive in underspecified environments, while AIs like very specific environments. Math is the most specified field there is lol
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When I was younger I remember a point of demarcation for me was learning the 4chan adage “trolls trolling trolls”, and approaching all internet interactions with skepticism. While I have been sure that Reddit for a while has succumbed to being “dead internet”. This thread is another moment for me- I can no longer recognize who is a bot, and who has honest intentions.
Interesting but not surprising to me. Once a field expert guides the models, they most likely will reach a solution. The models are good at lazy work for experts. For hard or complicated questions, many a time the models have blind spots.
out of curiosity, i wonder if people are taking stabs at p!=np
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Super interesting but what does this mean for us mere mortals?
I got Claude to self reference and update its own instructions to solve making a typed proxy API of any website. After a week, scores of iterations, it can reverse engineer any website. The first few days I had to be deeply involved with each iteration loop. Domain knowledge is helpful. Each time I saw a problem I would ask Claude to update its instructions so it doesn't happen again. Then less and less. Eventually it got to the point it was updating and improving the metrics every iteration unsupervised.
Edit: This is going to have huge ramifications for the tech security industry as these systems will be able to break security systems as easily it solved the proof. The sooner the good guys, if there are any left, understand this the better it will be for everybody.
> Super interesting but what does this mean for us mere mortals?
I would go for a 2 or 3 hour walk with my phone using the remote control feature looking every 5 - 10 minutes to make sure it doesn't need human help. I went to the coffeeshop and drank very good coffee listening to music. Then at night I sat and had a beer thinking about T.S. Eliot's 'The Wasteland', the effect of industrialization in England at that time and his views of how ennui affected the aristocracy.
> I went to the coffeeshop and drank very good coffee listening to music. Then at night I sat and had a beer thinking about T.S. Eliot's 'The Wasteland', the effect of industrialization in England at that time and his views of how ennui affected the aristocracy.
Well, for those among us that are not aristocracy already, except for the vanishingly small number of people required to oversee such processes, we’re probably the closest we’re going to get to it. If they don’t need people to do the tech labor, we’ve got way more people than we need, so that’s a huge oversupply of tech skills, which means tech skills are rapidly becoming worthless. Glad to see how fast we’re moving in our very own race to the bottom!
Lol,a race to the bottom where too many tech savvy people are left unemployed while a few "privileged" get a decreasing buying power to maintain security of the digital tools that keep the whole digital dependent civilizations afloat?
Sounds like a great starting plot for an interesting story.
I kind of feel like software engineers working on improving AI are traitors working against other SE’s trying to make a living.
However…
I have to acknowledge my craft of SE has been putting people out of work for decades. I myself came up with business process improvement that directly let the company release about 20 people. I did this twice.
So… fair play.
In the grand scheme it's good to invent things that replace human labor. It frees up people to do more interesting things. The goal should be to put everyone out of a job.
> The goal should be to put everyone out of a job.
Yeah, but why does it need to take the fun jobs first, like painting, writing poems, coding, making music, ...
I want the AI to cook, do the dishes, take out the trash, etc.
>It frees up people to do more interesting things
Like beg on the corners and starve in the street? Trying to figure out how the basics of capitalism where labor is exchanged for money is not going to work well when the only jobs left are side gigs. Something will have to change and a lot of People will fight said change.
We will come up with new jobs, like we have for all of human history. I think even in an abundance utopia people will still work - we need purpose to sustain our existence.
The work will become even more fulfilling however.
I’ve thought about this myself. Couple of points:
1) It’s not my job to fix all the problems of Capitalism. It’s painful to try to fight the system without collective action. My family and I have to eat too.
2) We have had a solution all along for the particular problem of AI putting devs out of work. It’s called professional licensure, and you can see it in action in engineering and medical fields. Professional Software Engineers would assume a certain amount of liability and responsibility for the software they develop. That’s regardless of whether they develop it with LLM tools or something else.
For example, you let your tools write slop that you ship without even looking? And it goes on to wreak havoc? That’s professional malpractice. Bad engineer.
If we do this then Software Engineers become the responsible humans in the loop of so-called “AI” systems.
It’s not your job to fix capitalism. But it is your job to evaluate if your money making skill comes at too high a price for others.
Say you found a job shooting people in the head for money. Like if you work for ICE or something…
You need to feed your family. Is this job ok? You may decide yes. I decided no. I will find another way to feed my family.
You don’t get to escape consequences because you are a small cog in a large system.
In the bigger picture, automation should free people from labor. But that requires some very greedy people to relax their grip ever so slightly. I imagine they see automation as a way to reduce reliance on labor, and if they don’t need labor, they don’t need people. So let them starve and stop having kids.
Aren't the true traitors still the ones paying the SE to do that work? The managerial slave-master class?
You always have a choice to make. You make it everyday. Get up. Go to a legitimate job. Work.
You probably choose not to steal, rob, impersonate someone else, or generally make money illegally.
It can be traitors all the way down.
> Edit: This is going to have huge ramifications for the tech security industry as these systems will be able to break security systems as easily it solved the proof. The sooner the good guys, if there are any left, understand this the better it will be for everybody.
What can the good guys do? Fire up Claude to improve their systems? Unless you have it working fully autonomously to counter-act abuse, I don't see how you can beat the "bad guys". There may be some industries where this is a solved problem (e.g. you can do all the validation server-sided, religiously follow best practices to prevent and mitigate abuse), but a lot of stuff like multiplayer video games will be doomed unless they move to a "you must use a locked down system we control" model. I honestly don't consider it liberating as someone that has various hobby projects, that now in addition to plain old DDoS I'll also have people spin up layer 7 attacks with just their credit card. It almost makes me want to give up instead of pushing forward in a world where the worst of the worst has access to the best of the best.
> I would go for a 2 or 3 hour walk with my phone using the remote control feature looking every 5 - 10 minutes to make sure it doesn't need human help.
That is a nightmarish scenario tbh
That nightmarish scenario is what T.S. Eliot was describing in "The Wasteland" which "portrays deep, existential ennui and boredom as defining symptoms of modern life following World War I."
Later this boredom was described by the Stones, "And though she’s not really ill / There’s a little yellow pill / She goes running for the shelter of a mother’s little helper".
It is a nightmare. Mostly what I'm thinking about while the agents are running is how bored I'm going to be. That is the joke, my deep thought on T.S. Eliot are about the wasteland this thing is going to create.
Nightmarish?! In comparison to the average person's actual job? I'm pretty sure that many people out there would sign up for a battle royale for a chance at such a job.
Would they? I'd love to get in touch
So sitting at a desk is nicer than a walk outside for you? Why would relaxation be a nightmare?
This type of slop comment is somehow worse than spam.
>After a week, scores of iterations, it can reverse engineer any website
Cool, let’s see the proof.
I posted a link but don't want to spam HN more than I have.
It is proof-of-concept. Seriously burns some tokens (~80k - ~200k) but doesn't require AI after to scrape and automate a website so if all the people at Browser Use, Browser Base, and every one pounding every website used it, I think, the net benefit would be in the billions. I would recommend using it in isolation. Nonetheless, it works very very well on my machine.
> This type of slop comment is somehow worse than spam.
Please don't be mean.
There is no proof, just a self-congratulatory word salad with dubious authenticity.
It’s insane how insufferable this place is now.
> I would go for a 2 or 3 hour walk with my phone using the remote control feature looking every 5 - 10 minutes
2-3 hours "walking" while having to check in every 5-10 minutes?
If I have to check in every 5-10 minutes, I won't taste coffee or hear that there's good music playing.
Just Claude code a push notification feature then
That's fucking insane. Thank you for sharing.
I had a bad feeling we were basically already there.
I have similar amounts of success (pretty good!) standing in line at a coffee shop talking to people who work for me through some action that needs to be taken and doing the same with AI.
However I do not trust AI anywhere near as much as I trust the humans. The AI is super capable but also occasionally a psychopath toddler. I sat in amused astonishment when faced with job 2 not running because job 1 was failing Claude went in to the database, changed the failure record to success, triggered job 2 which produced harmful garbage, and then claimed victory. Only the most troubled person would even think of doing that, but Claude thought it was the best solution.
My understanding is that, if confirmed, this demonstrates that AI can find novel solutions. This is a strong counterpoint to generative-AI-is-strictly-limited-to-training-data.
https://en.wikipedia.org/wiki/AlphaFold ...
we've had AlphaFold for a while. it's not a novel that we have ML solutions that can find, erm, novel solutions.
however, by and large, most LLMs as typically used by most individuals aren't solving novel problems. and in those scenarios, we often end up with regurgitated/most common/lowest common denominator outputs... it's a probability distribution thing.
Put in the hands of great mathematicians, pencil and paper proved able to write proofs of open problems.
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Another signal that we still have relevant progress in ai.
Also that it is now good enough to make researchers faster.
Learn plumbing
There is no reason why market for plumbing will get much larger than it is now (which is not too large)
Surely AI has to take a shit eventually. What's all this racket about water usage?
This is kindof the opposite? Man + AI > either man or AI. I'd say "learn to work with Claude" is the better lesson here.
For now. The term people use is "centaur", like the half-man-half-horse of mythology.
The AI CEO's are pointing out that when chess was "solved", in that Kasparov was famously beaten by deep blue, there was a window of time after that event where grandmasters + computers were the strongest players. The knowledge/experience of a grandmaster paired with the search/scoring of the engines was an unbeatable pair.
However, that was just a window in time. Eventually engines alone were capable of beating grandmaster + engine pairs. Think about that carefully. It implies something. The human involvement eventually became an impediment.
Whether you believe this will transfer to other domains is up to you to decide.
I know your reply was half joking, so please take this the same way, but ... are you sure about that? https://www.youtube.com/watch?v=p1ip68Vv7NE
This is truly amazing. Do people not really realize how amazing stuff like this is? I feel like I'm taking crazy pills here, but man, it certainly feels like we're on the edge of something quite amazing...
Autonomous robots murdering humans in warfare? That's at least the sense i got from reading this news site the past few days
Where I live it's bathroom and kitchen tiling
AI isn't replacing anything, get over yourself.
Arent you using Claude?
That llms in the middle of everything will continue until morale improve because llms can generate text on top of bullshit made up problems