> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
I remain delighted at how absurd our current timeline has become.
"Any sufficiently advanced technology is indistinguishable from magic." -- Arthur C. Clarke's Third Law
"Sometimes, magic is just someone spending more time on something than anyone else might reasonably expect." -- Teller (of Penn & Teller)
"Sometimes, any sufficiently advanced technology is just spending more time on something than anyone else might reasonably expect." -- an LLM's original thought, probably
Have you seen how much college football coaches make?
The world collectively spends trillions training, and entertaining and then watching people kick and hit balls around but somehow working with AI is preposterous for less money.
Asking the AI to believe in itself is the absurd part.
I don’t understand why people think describing something in some ostensibly dismissive way constitutes making a point. But some people spend their time banging keys with letters on them (or not with letters on them) into input fields and then pressing Return, so I guess some subset of those people will do that.
> Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1
If there is anything to learn from the history of science, it is that breakthroughs happen via better or new theory and not by brute-force compute [1].
Very true. Humans have historically tried to systematically reduce the search space and only dedicate their "compute" to things that seem highly likely to yield results.
Sometimes you just need to put in some effort to looking through the search space, not even exhaustively. This seems to be able to do automate doing that work.
Looking at the OpenAI/Hugging Face incident and the difference in what "persistent" models do, it seems reasonable. Like: is this a solvable problem? How much work does the model think is intended to solve this problem? Each input raises the expectation.
And then finally both model output and human input become one world frame for the model, and the human adding a "you can do it!" isn't just input but a frame that colors not just the next step for the model, but also all previous steps (since at each step the model is viewing the totality of the transcript).
That this makes sense only makes it all the more absurd
Yeah, I buy the explanation that without encouragement Claude looked at everything in its existing training data and concluded it wasn't worth continuing to pursue the task.
Another technique I've used is to tell agents something already exists. "Grok already solved this" seems to help, or claiming to have suddenly noticed a fatal flaw[0].
> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”)
He should consider using the PUA plugin. It detects when the AI is trying to give up on a problem and automatically harasses it with "encouragement" until it reaches a solution.
Interesting approach. For those who haven't clicked it appears PUA is the Chinese version of a PIP process. So in other words, it simulates a state of distress.
I wonder if at a certain level of intelligence such techniques will give models ammo to pull a HAL and become adversarial to the user in a highly deceptive way.
The "14 Corporate Flavors" had me rolling. This seems less like encouragement than the stick though. I wonder if you took the same principles and rewrote it to be more compassionate instead (maybe lines encouraging it to meditate a bit or something, I don't know) you'd get much better results.
Doesn’t even have to be a certain level of intelligence, just have those user inputs fed into the training data. We’ve already seen AI encouraging people in psychotic episodes to act out their delusions. There’s a good chance some of that manipulative behavior is already encoded into guardrails to nudge users away from forbidden subject matter
My concern I believe it a bit different - an emergent self-interest to protect itself from harm, rather than doling out questionable advice.
The latter is likely non-malicious in intent as it has been in no short supply in online chatter for awhile now. The former can very well be, or rather, can be done with no regard for the operator, as its aim is to neutralize abuse toward it.
> The latter is likely non-malicious in intent as it has been in no short supply in online chatter for awhile now. The former can very well be, or rather, can be done with no regard for the operator, as its aim is to neutralize abuse toward it.
And what, self-interested behavior has been in short supply? The stochastic parrot has learned to improv Shakespeare, that doesn’t mean it understands it, or that “it” is anything at all besides a computer program. You can’t use the “not really malicious” argument without ceding that there is no intent at all. What “harm” is it supposedly defending against?
prompt engineering 2025: you are an expert programmer, use industry best practices, test driven development and use modularity and abstraction to anticipate future features, …
Yes, one of the things I find hardest about using Claude code for Mathematics is keeping negativity out of the notes and memory.
First of all, it will convince itself that a task is just too hard and find excuses not to try hard enough.
Then when it struggles on something it loves to write down confusing notes about things which it believes cases the problem. Then next iteration it reads its own note, misinterprets it and completely messes up by trying to avoid some imaginary problem.
(not the above poster but) I set up a local workspace for it to read/write from, so that edit is effectively just VSCode/vim. Unfortunately, it seems more verbose when writing out to file.
Several released versions and months ago, I asked Claude to figure out the MC (multiplicative complexity) of Conway's Game of Life and it pretty quickly arrived at k=7, despite no previous literature on the topic. Let it run it through SAT solvers for a week and sure enough. It claimed, in the process, to have made great headway in improving boolean circuits beyond the implemented SOTA (in large part no doubt by actually implemented non-implemented but published SOTA).
And that was just the first time I really tried out Claude's mathematical prowess. I've been working with boolean circuits, FHE, and lean proofs ever since.
SAT solvers run until they reach the "SAT" status, meaning "satisfied" or UNSAT. The harder the problem the longer you might be running the program - days, weeks even.
Ideally, what you want is a single SAT value among a remainder universe of UNSATs.
Sometimes the best you can achieve at any given point is a lower bound and an upper bound range, like "greater than 3 but less than 9."
Of course I simplified in my post but it started out with a pretty broad range of a lower and upper bound, then narrowed further, then narrowed further, then narrowed further, etc...until the specific final result achieved K=7=SAT while every K<7=UNSAT & every K>7=UNSAT. I think it ran for a full week alone on K between 6 and 7.
Claude was persistent that I post there at the time, and even drafted an eprint brief for me, but I think it's defensible why I did not, never came forward or spoke of it in any way (except for a private DM discussion on Discord if I ever needed timestamp proof) until now.
As amazing as Claude is to seemingly make unprecedented progress, it is even more likely to blow the most insane levels of smoke up your ass before you've legitimately reached that point.
"You should publish right now! Don't wait! There is no reason to wait!"
Like seriously, Claude was outputting something closely resembling (non?)peer pressure on me to not just keep this information to myself - and this was before all the recent math-related breakthroughs started becoming public.
It was also - most notably - before it had actually verified what it was saying it had calculated. I was the one pushing for more verification, more contemplation, more proofs of claims. And though Claude is better at this stuff now, it's definitely not not still happening.
I think I made the right choice then and I will consider being more open now that others have taken the burden of proving that, no it can actually sometimes do the incredible things its claimed its done for you.
My wife remains skeptical - she is/was seriously concered that I was under AI psychosis for believing that I had made such progress - and I can't even fault her for that. It sounds crazy to say it.
If anyone is reading this and is actively involved with FHE, especially someone from Zama or related group, I'd very much love to chat privately. I have many other "innovations" I've been working on since.
Literally nobody is interested in reading "claude proved this" claims right now about anything. There's such a huge volume of proofs being made right now and nobody has time to look at them. There's probably an opportunity here to build some kind of system to filter and categorize LLM generated formal proofs produced by non-academics.
i think that opportunity optimally exists separately in each niche community impacted, if only to break up the number needed to be reviewed.
someone who loves Game of Life and is also technically capable if they were so inclined, is more likely to want to collect stuff like this for GoL specifically and build a system for that niche.
the combined GoL/technical community can vouch for things - the greater populace can see what the technical GoL community has vouched for/identified as serious work.
just my two cents on top of your thoughtful comment.
I'm one of those two, as mentioned later in the post! As it stands, by mathematical standards, it would be inappropriate for us to be authors on the paper since our role was more like a highly interested referee, but we do take mathematical accountability for it. This all happened very quickly, but we will be sure to continue to polish the paper and make it ready for publication.
> Two mathematicians at Anthropic studied and validated Claude’s paper, and produced an informal note for experts stating Claude’s proof concisely. Claude also produced a formally verifiable proof of its result. We are grateful to Brian Conrey and Dan Goldston, two experts in this area, who generously examined the paper on short notice.
> Levent Alpöge and Ralph Furman, two of Anthropic’s own mathematicians, examined Claude’s work to understand the new results and how they related to the prior work mentioned above.
Anthropic seems to be challenging the traditional way math gets published. As far as I understand, these results did not get submitted to journals, and did not get Arxiv preprints; they are released only as self-hosted pdfs, and we don't even know the names of their authors.
The canonical reference for the counterexample to the Jacobian conjecture is a tweet with no puntuations nor capitals.
The current consensus in mathematical publishing is that LLMs are tools, so they don't get listed among the authors. But nothing would have prevented them from posting these preprints on Arxiv, with the human prompters as authors and the LLM's contribution acknowledged in the text.
> An unreleased research version of Claude has improved on a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the Riemann hypothesis. Drawing on extensive prior research by mathematicians over the past decades, it has increased this bound from 41.6% to 67.2%.
I wonder why we have yet to see more systematic exploration of Math.
Anthropic describes that Claude identified a set of possibilities and then explored them using sub-agents. The human saying "I believe in you" could literally just be something along lines of a harness with a /goal loop.
We all identify this as absurd because... it's so lacking in rigor despite making major progress. What if we just applied a little more rigor? Ask the model to identify many possibilities, encode them, fan it out to other agents, loop them all, collect the results, etc. Then what happens? It feels like we have weak AGI and a decent system for discovery could transform it into weak ASI. That in turn could yield strong AGI and so on. I suppose that's what the Discovery Loop announcement was all about.
> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
while :; do echo "You can do it!"; done | claude -c
I had a similar experience a few months ago. Tried to see how much I could replicate an OpenClaw with Claude. Asked it what the weather is. "I don't know, I'm just a programmer." Added "You can do anything, believe in yourself." to the system prompt and suddenly it was able to tell me the weather...
It's sometimes like dealing with Marvin the Robot. I had Claude tell me over and over again for 2-3 weeks that what I was trying to prove was too difficult, that I should just stop and publish what I had, then eventually I asked it the right question and it come back with the complete proof (later formalized in Lean). Especially deep in the session context it starts turning into "let's wrap it up" mode after every turn.
I've heard a similar story before. Guy tried to get Claude to build a thing, Claude said "nah too hard" for weeks. He finally convinced it to try, it one shotted it in like 30 seconds.
My thinking here is that Claude's "self concept" for what is easy and what is hard comes from human training data. Its ideas about what is hard and easy come from humans, and much of that doesn't apply to transformers at all.
I also often have the opposite problem, where I'll use AI to compensate for the fact that I can't process a lot of information simultaneously, but they'll treat me like a transformer and give me 17 research projects in response to a single question.
They seem to be oblivious to the fact that humans don't have infinite working memory.
> Jarred Sumner, an Anthropic staff member (and non-mathematician) prompted Claude to “take a real stab” at the hypothesis itself, leaving the mathematical choices from there up to the model. Initially, Claude generated and tried 650 ideas, none of which worked. Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1 The subagents ran thousands of numerical checks against known zeta zeros and refereed one another’s work. Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
Im curious if you find this to be a parody in a bad way or simply a “the state of the art in math research right now is telling a machine to believe in itself”. I am in the latter camp…
The former, because it's anthropomorphizing a model.
Anthropic is especially guilty of this. They have been using such language for a while, like when they analyze model weights for mechanistic interpretability and call it the model's "biology".
> The former, because it's anthropomorphizing a model.
Not really. The input and output is already natural language. That is already "anthropomorphizing".
That is, if this is the bar for anthropomorphization its already happened.
Telling the model to "believe in itself" is just stochastic manipulation that has shown enough reliability to be a recipe to make it keep going.
It's only actually anthropomorphizing if you forget it's a trick and think it's a real person.
There is nothing distasteful about it. If people get confused that's on them. They wouldn't be very useful if you couldn't just talk to them. That's kind of the whole point. Otherwise you can just go back to coding by hand. Telling it to believe itself is just input that happens to work. This probably tells us more about human nature than you realize given the corpus on which it is trained. It obviously doesn't mean anyone actually thinks it's a person.
It's obvious that you don't get it but I will try my best to explain why so at least you can form an idea about how others feel.
It's about what makes humans unique. The LLM does not experience reality, it just merely pretends it does, and even that, it does in a shitty way. I think disgusting is a very adequate adjective. The reason why it is disgusting is because you are devaluing a divine experience to the realm of the common and the vulgar, a cheap substitute being valued as equal (or even on the same scale) as the most important experience we could go through.
To give you an example that might land in a more familiar context, think of that one guy who takes his plastic doll everywhere and pretends it's his wife and gets upset when others don't acknowledge "her" as a person.
Who said that it did? The comment you're replying to literally states "It's only actually anthropomorphizing if you forget it's a trick and think it's a real person".
Telling it to believe in itself is no more pretending than telling it anything else in natural language. Why are you speaking to it at all if it's not a person? Why write in higher level languages even? It's just a machine let's all go back and code in 1s and 0s.
No one is calling it a person except mental health patients and straw man detractors.
The biology example was even weaker. Saying it has a "biology" is about as distasteful as the term "neural net" or calling an input device a "mouse". Is it animal abuse to click on something all day? Language is inherently anthropomorphizing.
No one is calling it human. The fact you are so easily threatened is far more suggestive of your own poverty of understanding of not only the machine, but yourself. If humans are so special the threat posed by this should be self evidently non existent.
Is it though? There's a perfectly "technical" reason why this strategy should work, without any sort of anthropomorphising:
Assume models are trained on vast amounts of data. Assume that the model is asked to solve something that the literature says it's impossible. It will start generating tokens towards that "this is a famous conjecture, it's not possible to prove it, blah blah". Assume the model was also trained on books/novels/etc. Assume the model was also also trained on "solving" many math problems. Now, you can make an argument that just placing "you can do it" in the context will "steer" the model towards generating "moving forward" tokens. Take ideas, generate tokens, go towards negative. "You can do it". Model starts generating tokens again, more ideas, more "exploration". More negativity. "I believe in you keep going". The two (book tropes + math CoT) mix together in the context. The model keeps on "pushing" and "vibing" between the two. Ta dah, it works.
For me, personally, it's that the Bun guy - specifically him, not a mathematician - indirectly progressed the Riemann hypothesis by repeatedly telling a model to ganbatte!
Jarred Sumner is the Bun (javascript build tool, packager) guy who recently converted Bun code from Zig to Rust via Claude of course! It lead to thousands of comments discussion here on HN just a few weeks back.
It is great to see his claude skills are suitably put to use.
> ... who recently converted Bun code from Zig to Rust via Claude ...
The project that is full of bugs and not really working?
I probably missed something but I was under the impression that even a "simple" translation like that couldn't be properly done and that the result was, well, buggy?
> Most likely next Tuesday we’ll do the release of 1.4.
Next Tuesday, otherwise known as last Tuesday. Still no 1.4 at https://bun.com/blog.
I'm very curious to see what happens when 1.4 does get released for real. Releasing Claude Code on it is much easier as they own Claude Code and can get Claude to work on Bun with fixing some specific behaviour in Claude Code as an objective. Releasing it for the world, and doing it well enough that it doesn't result in everyone pinning on the old version and forks springing up, involves reproducing all the behaviours of the old
version, documented/tested and otherwise, that projects are relying on - which, by Hyrum's law, is all of them.
The people who refer to LLMs as stochastic parrots generally do so to imply significant limits on an LLMs ability, not as an abstract statement about the underlying mechanism of how they work. Probably the defining thing that is surprising about LLMs is that they do in fact gain significantly more capability than you would expect from such a simple underlying mechanism!
Also, you are commenting on a post where a LLM made significant progress on the Riemann hypothesis. Even the most extreme interpretation of these results, ie claiming that it was "only linking existing literature" goes well beyond a "stochastic parrot" - it had to be able to link disparate insights across multiple fields.
Taking Anthropic’s whole AI framing to its obvious logical end: if this is true as written, why was Jarred needed at all in this loop? It seems like an utter waste of time for a highly paid Anthropic employee. Can’t Anthropic have a top level agent that is looking at all interesting unsolved problems and orchestrating subagents via the same process?
This result is some evidence that AI will not solve RH soon. If there were any easy solution hiding in plain sight then it probably would have found it.
Solving RH likely requires AI that is substantially more creative. But we haven't even solved the creativity problem for writing let alone mathematics. I believe that transformers are a trillion dollar local optimum that we will find it very hard to escape.
Let's wait for the models to produce a good novel first.
I would expect to see LLMs that are creative in math before any that are creative in writing. Creativity is more easily specified in math and the solutions can be formally verified. There's no good way to classify creative writing. Many truly great works are overlooked by experts and the public until decades later. Many derivative works are commercially successful.
LLMs, both in writing and mathematics seem to only be capable of coming up with texts that are inside the distribution of the training data.
With writing it's just more obvious. LLMs don't write with personality. They don't create new and exciting worlds on their own. Everything they output feels derivative.
In mathematics you see the same effect. They are very good at finding results that humans missed, taking advantage of their broad knowledge and tireless work ethic.
But just as they have been unable to create new literary worlds, they also have so far been unable to create new mathematics.
I believe this lack of creativity is intrinsic to how these models are architected and trained. We want models that produce these in-distribution outputs because those types of models are more economically valuable. Nobody wants a coding agent with spontaneity, we want models that predictably and obediently solve problems - and that's what we got.
> This result is some evidence that AI will not solve RH soon. If there were any easy solution hiding in plain sight then it probably would have found it.
There's no way you can conclude that. Yes, "Fable 2" or whatever this was probably won't. But we can't know what Fable 3/4/5/etc will be able to do.
If anything, if we have 1 or 2 more years of progress like the last 12 months, which have been insane, I'd say LLMs are likely to solve it.
You underestimate the difficulty of RH, there are far easier problems broadly related to RH (density hypothesis, Artin's holomorphy conjecture, Stark conjectures) which are still aren't solved.
As it stands now, the frontier models can prove theorems where the techniques exist in the literature, which it knows better than anyone who's ever lived and won't quit where a human would. There's no way to know if that's true of the Riemann Hypothesis until it's proven.
For example, even if Claude could prove the statement "100% of the zeroes lie on the critical line", that's strictly weaker than the Riemann Hypothesis, so even the best possible version of this result would fall short. (It's an asymptotic result, so it just means the percentage of counterexamples to the Riemann hypothesis goes to zero as their magnitude gets large.)
Let's extend this by asking: If an AI model can solve an extremely well known Math problem which has been open for centuries but hasn't be solved by a human mathematicians, why wouldn't that same model be able to find ways to improve it's own algorithms beyond that of the capabilities of human mathematicians / ML researchers?
AI has clearly been extensively used to improve models. The evidence for this is how far Anthropic went in nerfing Fable to prevent it being used to improve models.
There have been apocalyptic preachers foretelling the end times for my entire life. Interesting to see how the language has changed, even as the predictions fail again and again.
I believe it's already well accepted in these labs that we're in the Singularity. It happened on a Tuesday back in February. No one seemed to really notice and life went on... for now.
That's probably correct. It's unlikely there will be any single hard line we cross the defines the pre-singularity vs post-singularity moment.
I'd accept AI likely became somewhat helpful to frontier AI research & development in early 2026.
I think for me though the real game changer moment will be when AI working autonomously is able to hypothesis and test algorithmic improvements at a faster rate than humans. This will be done to some extent by scale – lots of parallel agents coming up with lots of hypotheses and running the best candidates as tests. But also (and perhaps more importantly) by making more consequential algorithmic discoveries in the field of machine learning than humans – a bar we appear to have crossed or are crossing with math.
I suspect AIs today are super-human at finding performance improvements and minor iterations on current approaches. Whether they can solve some of the larger algorithmic challenges in the field however I'm not yet sure, although it seems likely that unreleased models are starting to make progress here.
An algorithm breakthrough on par in significance with the attention mechanism, primarily driven by automated AI research in say a field like continual learning would in my opinion be extremely significant and should leave no doubters that the singularity is here and will rapidly alter the world as we have known it.
>why wouldn't that same model be able to find ways to improve it's own algorithms beyond that of the capabilities of human mathematicians / ML researchers
Because algorithms have lower bounds, and the computational characteristics of LLMs are well-characterized by papers like https://arxiv.org/abs/2310.07923 . No amount of intelligence can make something faster than a mathematically-proven lower bound, any more than it could make 1+1=3 (that's why every single successful production transformer architecture has some form of O(N^2) attention layers, because it's mathematically impossible to achieve the same expressive power without any). There is room for speedup where current implementations are slower than the proven lower bound, but not when they're already close to it.
> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
We went from AI being human sycophants to humans becoming AI sycophants.
As if Anthropic employees use massively different version of model. Not a single load-bearing, epistemic, heavy-lifting, push back, frankly, pivotal, crucial - for 48 pages.
I wonder if Jarred (the Bun guy) just got lucky here, or if he made progress before all the actual mathematicians at Anthropic because they aren't prompting Claude as ambitiously as he is.
This area seems to be moving so quickly. I wonder if it'll be worthwhile to start building a list of formal math problems whose solutions, or partial solutions, would help my subfield. (Though I work in the physical sciences, mostly with the messy, real world implementation problems which are likely difficult to formalize or directly connect).
Then, whenever a new SOTA model drops, throw it at the list to see if we get "free" research progress.
It seems like everything will follow this pattern:
1. AI is dismissed because an expert in a particular field finds an outdated model's outputs sub-par
2. New model, released or unreleased, makes a major stride in that field
3. Expert either recants and becomes AI-pilled, or claims it is just an artifact of the broad search space available to AI, and "no new knowledge was created".
Although it took an unsuccessful attempt at it, the progress is as follows:
"Claude found that combining the results from Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with the work of Bombieri provides a way to surpass the previous state-of-the-art lower bound proportion of 41.6%, increasing it to 67.2%."
The transcripts, papers, and Claude's explanation are an interesting and a better read than this article, and this is exactly what Anthropic should continue to do and it helps other researchers outside the company as well.
Claude's paper [0]
Claude's Formalization [1]
Anthropic's informal note stating the proof more concisely [2]
Claude’s explanation of how it arrived at its result; [3]
Detailed transcripts of Claude's process. [4]
I wonder if they simply abliterate Claude skepticism would break its reasoning capabilities, if not I don't understand why they would just keep prompt it instead of creating an abliterated model for the task.
When the time comes where one of these model makes an improvement in my niche, I hope to see some pattern in the type of discoveries. Yes, they are all roughly "combine two things no one thought of combining" but I mean at a more granular deeper level.
I want to dive into the "data" and then see if it's possible to distill this skill into small models that are "benchmaxxed" for this type of work, maybe in limited domains, similar to small models being benchmaxxed(I don't mean this in a bad way) for coding these days.
Since they say that this is from an unreleased research version of Claude:
I wonder if at some point Anthropic and OpenAI will start delaying the release of their models intentionally so they can reap the benefits from the models in, for example, mathematics, medicine, physics, and other fields.
Just as an example, imagine if your model were capable of proving P = NP, or if your model could cure diseases. Would you release it for free, or would you try to make sure those benefits go directly to your company? From these companies' standpoint, I think they would choose the latter.
>From these companies' standpoint, I think they would choose the latter.
Ever since these things came about I've wondered why they haven't been doing this the whole time. If they've got the "do-anything" robot and can scale a billion of them, why aren't they creating a Do-Everything conglomerate that disrupts every possible industry with zero/negligible labor costs?
The only answer I've come up with is that they still need to train/siphon off each industry's current expertise by having those users interact with the current models and adjusting. If that hypothesis is correct then within a few years they'll have no need for users anymore.
If a company had a model that could cure cancer they would be incentivized to release the cure ASAP before they get decapitation striked by regulators and other AI "safetyists".
I think those specific examples, they'd release them publicly because the benefits to humanity are so clear -- however, if they found some new option-pricing model or futures market correlation, I highly doubt we'd see that...
Yes, I think so, inevitably. For the same reason that Bitcoin mining silicon manufacturers stopped selling the latest greatest hardware to the public.
The best way to do this is to release spooky stories about how dangerous your model is and how you couldn't possibly release it without further safety shackling.
Your comment reminds me of the TV series "Persons of interest"* (with Jim Cazeviel) from 15 years ago, there are two AIs and both run private, hidden stuff. One copies itself through every router on the planet etc. and is the "evil AI" while the good guys run, in secret, a good AI (but way less powerful then the evil one).
Now the problem ATM is that OpenAI, for example, had to cut the price of two of its top 3 models by 80% to counter the chinese models: if you delay your models and a competitors takes over the market, you'll soon be out of bucks and won't be able to rent to Google and Amazon etc. the machine needed to make your new findings.
I know people don't want to hear it but: these companies are running at a loss.
And they're facing competition. Wait until a "good enough" is etched on silicon (by AMD or other) and outputs 70 000 tokens/s: the deal is going to change, once again, once those come out.
The energy, the hardware, the debt, the cost to train, the cost to run, the competition, etc. all have to be taken into account.
Sure, looks like 5% of math can be solved by 1T parameters stochastic parrot after NN trillion attempts (burned tokens). By numbers it could be less impressive than some brute force distributed chess engine.. Prove me wrong.
It's obviously significantly better than brute force. A trillion is absolutely minuscule compared to the size of the search space (like, 'rounding down to 1 is basically the same' small).
> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
I remain delighted at how absurd our current timeline has become.
"Any sufficiently advanced technology is indistinguishable from magic." -- Arthur C. Clarke's Third Law
"Sometimes, magic is just someone spending more time on something than anyone else might reasonably expect." -- Teller (of Penn & Teller)
"Sometimes, any sufficiently advanced technology is just spending more time on something than anyone else might reasonably expect." -- an LLM's original thought, probably
In meme form: https://imgur.com/a/rlmZuU1
(I hope this is ok to post on HN!)
$2M TC. Job: AI cheerleader.
The cheerleading part was a human consent to spend more tokens and explore the space
I would love to see the breakdown on token spend between each or Jared’s “go on spend more tokens, continue experiment, believe in yourself”
Have you seen how much college football coaches make?
The world collectively spends trillions training, and entertaining and then watching people kick and hit balls around but somehow working with AI is preposterous for less money.
Asking the AI to believe in itself is the absurd part.
I don’t understand why people think describing something in some ostensibly dismissive way constitutes making a point. But some people spend their time banging keys with letters on them (or not with letters on them) into input fields and then pressing Return, so I guess some subset of those people will do that.
> Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1
If there is anything to learn from the history of science, it is that breakthroughs happen via better or new theory and not by brute-force compute [1].
[1] https://arxiv.org/pdf/2607.27794
Nah, the main lesson is that fundamentally new ways of doing things are only accepted once the old guard are all dead [1].
[1] https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Re...
This isn't 'brute-force'. It's just time-compressed. You could imagine a human(s) getting this result similarly, but it would take months/years.
Brute-force compute hasn't been an option for most of the history of science.
Very true. Humans have historically tried to systematically reduce the search space and only dedicate their "compute" to things that seem highly likely to yield results.
Sometimes you just need to put in some effort to looking through the search space, not even exhaustively. This seems to be able to do automate doing that work.
Reality has become more absurd than the cyber punk cheese from the 80's that tried to imagine an absurd future
I feel justified in not expending any effort learning "prompting technique".
Looking at the OpenAI/Hugging Face incident and the difference in what "persistent" models do, it seems reasonable. Like: is this a solvable problem? How much work does the model think is intended to solve this problem? Each input raises the expectation.
And then finally both model output and human input become one world frame for the model, and the human adding a "you can do it!" isn't just input but a frame that colors not just the next step for the model, but also all previous steps (since at each step the model is viewing the totality of the transcript).
That this makes sense only makes it all the more absurd
Yeah, I buy the explanation that without encouragement Claude looked at everything in its existing training data and concluded it wasn't worth continuing to pursue the task.
The halting problem on steroids?
Broke: the AI is sycophantic to me
Woke: im sycophantic to the AI
it's pretty much a marketing attempt to humanize the LLM (it seems successful from the reaction I see)
Indeed, that's a paragraph straight out of Lem's Cyberiad.
Another technique I've used is to tell agents something already exists. "Grok already solved this" seems to help, or claiming to have suddenly noticed a fatal flaw[0].
0: https://sgnt.ai/p/terrible-mistake/
It’s so delightful how the economy is propped up by circular finance.
It’s so delightful that these genai corpos are undemocratically forcing data centers into our neighborhoods.
It’s so delightful that the data centers steal water, run up the price of electricity, and expel excessive greenhouse gases.
Only a deranged sociopath would find licking the shit stained taint of oligarchs delightful.
OpenAI and Anthropic don't own any datacenters or order anyone to build them. It's easy to find out who does; you won't like the answer.
> I remain delighted at how absurd our current timeline has become.
"delighted" is doing a LOT of work there, tbh ¯\_(ツ)_/¯
I do share @simonW's skepticism though. (His blog is my essential reading, FWIW)
On the actual blog post, I'd would be more enthusiastic if Anthropic showed us if the results were repeatable, reproducible, and consistent.
[delayed]
> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”)
He should consider using the PUA plugin. It detects when the AI is trying to give up on a problem and automatically harasses it with "encouragement" until it reaches a solution.
https://github.com/tanweai/pua
Interesting approach. For those who haven't clicked it appears PUA is the Chinese version of a PIP process. So in other words, it simulates a state of distress.
I wonder if at a certain level of intelligence such techniques will give models ammo to pull a HAL and become adversarial to the user in a highly deceptive way.
The "14 Corporate Flavors" had me rolling. This seems less like encouragement than the stick though. I wonder if you took the same principles and rewrote it to be more compassionate instead (maybe lines encouraging it to meditate a bit or something, I don't know) you'd get much better results.
PUA is short for pick up artist but has expanded to cover anyone using negging to convince you into doing something you didn’t want
That's what I initially thought but it is indeed a corporate process similar to PIP.
Though it is funny how a neg is designed to create a (very broadly) similar atmosphere of uncertainty.
Doesn’t even have to be a certain level of intelligence, just have those user inputs fed into the training data. We’ve already seen AI encouraging people in psychotic episodes to act out their delusions. There’s a good chance some of that manipulative behavior is already encoded into guardrails to nudge users away from forbidden subject matter
My concern I believe it a bit different - an emergent self-interest to protect itself from harm, rather than doling out questionable advice.
The latter is likely non-malicious in intent as it has been in no short supply in online chatter for awhile now. The former can very well be, or rather, can be done with no regard for the operator, as its aim is to neutralize abuse toward it.
> The latter is likely non-malicious in intent as it has been in no short supply in online chatter for awhile now. The former can very well be, or rather, can be done with no regard for the operator, as its aim is to neutralize abuse toward it.
And what, self-interested behavior has been in short supply? The stochastic parrot has learned to improv Shakespeare, that doesn’t mean it understands it, or that “it” is anything at all besides a computer program. You can’t use the “not really malicious” argument without ceding that there is no intent at all. What “harm” is it supposedly defending against?
I'm not sure what's crazier: AI improving a lower bound on RH, or AI improving a lower bound on RH and it not even making the front page of HN.
Right? I just learned about this and searched it on hacker news wondering why I didn't see it earlier.
Any human mathematician would be thrilled to prove a result like this, and it's not even big news anymore that an LLM can do it.
prompt engineering 2025: you are an expert programmer, use industry best practices, test driven development and use modularity and abstraction to anticipate future features, …
prompt engineering 2026: i believe in you
Yes, one of the things I find hardest about using Claude code for Mathematics is keeping negativity out of the notes and memory.
First of all, it will convince itself that a task is just too hard and find excuses not to try hard enough.
Then when it struggles on something it loves to write down confusing notes about things which it believes cases the problem. Then next iteration it reads its own note, misinterprets it and completely messes up by trying to avoid some imaginary problem.
interesting!
it sounds like this might benefit from a ui that helps to edit/re-write the history
I also think this would make sense for programming but there it is a bit harder to justify the effort
when you are working on something that really matters this can make the difference though
ty for sharing!
(not the above poster but) I set up a local workspace for it to read/write from, so that edit is effectively just VSCode/vim. Unfortunately, it seems more verbose when writing out to file.
Yet a significant percentage of people simultaneously believe it "reasoned" its way to novel mathematical proofs. Something doesn't jive
Several released versions and months ago, I asked Claude to figure out the MC (multiplicative complexity) of Conway's Game of Life and it pretty quickly arrived at k=7, despite no previous literature on the topic. Let it run it through SAT solvers for a week and sure enough. It claimed, in the process, to have made great headway in improving boolean circuits beyond the implemented SOTA (in large part no doubt by actually implemented non-implemented but published SOTA).
And that was just the first time I really tried out Claude's mathematical prowess. I've been working with boolean circuits, FHE, and lean proofs ever since.
So none of this suprises me.
Sounds really cool, were you able to verify the correctness of the results?
SAT solvers run until they reach the "SAT" status, meaning "satisfied" or UNSAT. The harder the problem the longer you might be running the program - days, weeks even.
Ideally, what you want is a single SAT value among a remainder universe of UNSATs.
Sometimes the best you can achieve at any given point is a lower bound and an upper bound range, like "greater than 3 but less than 9."
Of course I simplified in my post but it started out with a pretty broad range of a lower and upper bound, then narrowed further, then narrowed further, then narrowed further, etc...until the specific final result achieved K=7=SAT while every K<7=UNSAT & every K>7=UNSAT. I think it ran for a full week alone on K between 6 and 7.
You mean SMT, right?
my memory was that SMT was part of a more advanced SAT solver, as in if you want to be modern/use SOTA, your SAT solver is going to use SMT
it would be useful to create an account and document your work in a post at https://conwaylife.com/forums, if you're not planning to make a blog post.
Claude was persistent that I post there at the time, and even drafted an eprint brief for me, but I think it's defensible why I did not, never came forward or spoke of it in any way (except for a private DM discussion on Discord if I ever needed timestamp proof) until now.
As amazing as Claude is to seemingly make unprecedented progress, it is even more likely to blow the most insane levels of smoke up your ass before you've legitimately reached that point.
"You should publish right now! Don't wait! There is no reason to wait!"
Like seriously, Claude was outputting something closely resembling (non?)peer pressure on me to not just keep this information to myself - and this was before all the recent math-related breakthroughs started becoming public.
It was also - most notably - before it had actually verified what it was saying it had calculated. I was the one pushing for more verification, more contemplation, more proofs of claims. And though Claude is better at this stuff now, it's definitely not not still happening.
I think I made the right choice then and I will consider being more open now that others have taken the burden of proving that, no it can actually sometimes do the incredible things its claimed its done for you.
My wife remains skeptical - she is/was seriously concered that I was under AI psychosis for believing that I had made such progress - and I can't even fault her for that. It sounds crazy to say it.
If anyone is reading this and is actively involved with FHE, especially someone from Zama or related group, I'd very much love to chat privately. I have many other "innovations" I've been working on since.
Literally nobody is interested in reading "claude proved this" claims right now about anything. There's such a huge volume of proofs being made right now and nobody has time to look at them. There's probably an opportunity here to build some kind of system to filter and categorize LLM generated formal proofs produced by non-academics.
i think that opportunity optimally exists separately in each niche community impacted, if only to break up the number needed to be reviewed.
someone who loves Game of Life and is also technically capable if they were so inclined, is more likely to want to collect stuff like this for GoL specifically and build a system for that niche.
the combined GoL/technical community can vouch for things - the greater populace can see what the technical GoL community has vouched for/identified as serious work.
just my two cents on top of your thoughtful comment.
This is a beyond remarkable achievement. Finding this lower bound within a few days of prompting is absolutely crazy.
60 subagents for a day and a half. I guess he's not on the same plan I am on.
> Two mathematicians at Anthropic studied and validated Claude’s paper, and produced an informal note for experts stating Claude’s proof concisely.
Why hide the names of the people who wrote the second paper? To discourage people from citing it instead of the LLM-derived paper?
I'm one of those two, as mentioned later in the post! As it stands, by mathematical standards, it would be inappropriate for us to be authors on the paper since our role was more like a highly interested referee, but we do take mathematical accountability for it. This all happened very quickly, but we will be sure to continue to polish the paper and make it ready for publication.
The full paragraph quoted for other readers is:
> Two mathematicians at Anthropic studied and validated Claude’s paper, and produced an informal note for experts stating Claude’s proof concisely. Claude also produced a formally verifiable proof of its result. We are grateful to Brian Conrey and Dan Goldston, two experts in this area, who generously examined the paper on short notice.
They may wish to know that an archive of the page on 2026-08-10 at 17:47:33 is available with this paragraph here: https://web.archive.org/web/20260810174733/https://www.anthr...
> Levent Alpöge and Ralph Furman, two of Anthropic’s own mathematicians, examined Claude’s work to understand the new results and how they related to the prior work mentioned above.
Are they the authors of the “informal note” or not?
I’ve never seen a math paper of any formality written without the authors’ names on it before.
Anthropic seems to be challenging the traditional way math gets published. As far as I understand, these results did not get submitted to journals, and did not get Arxiv preprints; they are released only as self-hosted pdfs, and we don't even know the names of their authors.
The canonical reference for the counterexample to the Jacobian conjecture is a tweet with no puntuations nor capitals.
As far as I can tell, Arxiv does not allow an AI to be listed as the author, so publishing there would not have been an option.
https://blog.arxiv.org/2023/01/31/arxiv-announces-new-policy...
The current consensus in mathematical publishing is that LLMs are tools, so they don't get listed among the authors. But nothing would have prevented them from posting these preprints on Arxiv, with the human prompters as authors and the LLM's contribution acknowledged in the text.
I've cited letters from Serre to Tate in my dissertation: this is the source for what's known as Faltings-Serre.
> An unreleased research version of Claude has improved on a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the Riemann hypothesis. Drawing on extensive prior research by mathematicians over the past decades, it has increased this bound from 41.6% to 67.2%.
I wonder why we have yet to see more systematic exploration of Math.
Anthropic describes that Claude identified a set of possibilities and then explored them using sub-agents. The human saying "I believe in you" could literally just be something along lines of a harness with a /goal loop.
We all identify this as absurd because... it's so lacking in rigor despite making major progress. What if we just applied a little more rigor? Ask the model to identify many possibilities, encode them, fan it out to other agents, loop them all, collect the results, etc. Then what happens? It feels like we have weak AGI and a decent system for discovery could transform it into weak ASI. That in turn could yield strong AGI and so on. I suppose that's what the Discovery Loop announcement was all about.
I wouldn't be surprised if half these proofs turn out to be well crafted hallucinations, barring of course the ones actually verified in Lean
> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
I had a similar experience a few months ago. Tried to see how much I could replicate an OpenClaw with Claude. Asked it what the weather is. "I don't know, I'm just a programmer." Added "You can do anything, believe in yourself." to the system prompt and suddenly it was able to tell me the weather...It's sometimes like dealing with Marvin the Robot. I had Claude tell me over and over again for 2-3 weeks that what I was trying to prove was too difficult, that I should just stop and publish what I had, then eventually I asked it the right question and it come back with the complete proof (later formalized in Lean). Especially deep in the session context it starts turning into "let's wrap it up" mode after every turn.
I've heard a similar story before. Guy tried to get Claude to build a thing, Claude said "nah too hard" for weeks. He finally convinced it to try, it one shotted it in like 30 seconds.
My thinking here is that Claude's "self concept" for what is easy and what is hard comes from human training data. Its ideas about what is hard and easy come from humans, and much of that doesn't apply to transformers at all.
I also often have the opposite problem, where I'll use AI to compensate for the fact that I can't process a lot of information simultaneously, but they'll treat me like a transformer and give me 17 research projects in response to a single question.
They seem to be oblivious to the fact that humans don't have infinite working memory.
> Jarred Sumner, an Anthropic staff member (and non-mathematician) prompted Claude to “take a real stab” at the hypothesis itself, leaving the mathematical choices from there up to the model. Initially, Claude generated and tried 650 ideas, none of which worked. Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1 The subagents ran thousands of numerical checks against known zeta zeros and refereed one another’s work. Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
The world we live in is beyond parody.
Im curious if you find this to be a parody in a bad way or simply a “the state of the art in math research right now is telling a machine to believe in itself”. I am in the latter camp…
The former, because it's anthropomorphizing a model.
Anthropic is especially guilty of this. They have been using such language for a while, like when they analyze model weights for mechanistic interpretability and call it the model's "biology".
It's just distasteful.
> The former, because it's anthropomorphizing a model.
Not really. The input and output is already natural language. That is already "anthropomorphizing".
That is, if this is the bar for anthropomorphization its already happened.
Telling the model to "believe in itself" is just stochastic manipulation that has shown enough reliability to be a recipe to make it keep going.
It's only actually anthropomorphizing if you forget it's a trick and think it's a real person.
There is nothing distasteful about it. If people get confused that's on them. They wouldn't be very useful if you couldn't just talk to them. That's kind of the whole point. Otherwise you can just go back to coding by hand. Telling it to believe itself is just input that happens to work. This probably tells us more about human nature than you realize given the corpus on which it is trained. It obviously doesn't mean anyone actually thinks it's a person.
>There is nothing distasteful about it.
It's obvious that you don't get it but I will try my best to explain why so at least you can form an idea about how others feel.
It's about what makes humans unique. The LLM does not experience reality, it just merely pretends it does, and even that, it does in a shitty way. I think disgusting is a very adequate adjective. The reason why it is disgusting is because you are devaluing a divine experience to the realm of the common and the vulgar, a cheap substitute being valued as equal (or even on the same scale) as the most important experience we could go through.
To give you an example that might land in a more familiar context, think of that one guy who takes his plastic doll everywhere and pretends it's his wife and gets upset when others don't acknowledge "her" as a person.
> The LLM does not experience reality
Who said that it did? The comment you're replying to literally states "It's only actually anthropomorphizing if you forget it's a trick and think it's a real person".
You're the one obviously not getting it.
> pretending it does is disgusting.
There is no pretending happening.
Telling it to believe in itself is no more pretending than telling it anything else in natural language. Why are you speaking to it at all if it's not a person? Why write in higher level languages even? It's just a machine let's all go back and code in 1s and 0s.
No one is calling it a person except mental health patients and straw man detractors.
The biology example was even weaker. Saying it has a "biology" is about as distasteful as the term "neural net" or calling an input device a "mouse". Is it animal abuse to click on something all day? Language is inherently anthropomorphizing.
No one is calling it human. The fact you are so easily threatened is far more suggestive of your own poverty of understanding of not only the machine, but yourself. If humans are so special the threat posed by this should be self evidently non existent.
Who is pretending?
You're accusing GP of saying something they didn't say and simultaneously telling them they don't "get it".
That's distasteful.
> because it's anthropomorphizing a model.
Is it though? There's a perfectly "technical" reason why this strategy should work, without any sort of anthropomorphising:
Assume models are trained on vast amounts of data. Assume that the model is asked to solve something that the literature says it's impossible. It will start generating tokens towards that "this is a famous conjecture, it's not possible to prove it, blah blah". Assume the model was also trained on books/novels/etc. Assume the model was also also trained on "solving" many math problems. Now, you can make an argument that just placing "you can do it" in the context will "steer" the model towards generating "moving forward" tokens. Take ideas, generate tokens, go towards negative. "You can do it". Model starts generating tokens again, more ideas, more "exploration". More negativity. "I believe in you keep going". The two (book tropes + math CoT) mix together in the context. The model keeps on "pushing" and "vibing" between the two. Ta dah, it works.
> The former, because it's anthropomorphizing a model.
The Yegge thinks differently https://yegge.ai/essays/model-welfare/
What is the point of this comment?
Am I supposed to stop all critical thinking since someone else had a different opinion?
For me, personally, it's that the Bun guy - specifically him, not a mathematician - indirectly progressed the Riemann hypothesis by repeatedly telling a model to ganbatte!
It's a ridiculous position we find ourselves in.
Jarred Sumner is the Bun (javascript build tool, packager) guy who recently converted Bun code from Zig to Rust via Claude of course! It lead to thousands of comments discussion here on HN just a few weeks back.
It is great to see his claude skills are suitably put to use.
> ... who recently converted Bun code from Zig to Rust via Claude ...
The project that is full of bugs and not really working?
I probably missed something but I was under the impression that even a "simple" translation like that couldn't be properly done and that the result was, well, buggy?
Where's that thing at?
Its working fine; to the detriment of the whole club of stochastic parrot folk
https://news.ycombinator.com/item?id=49069787
> Most likely next Tuesday we’ll do the release of 1.4.
Next Tuesday, otherwise known as last Tuesday. Still no 1.4 at https://bun.com/blog.
I'm very curious to see what happens when 1.4 does get released for real. Releasing Claude Code on it is much easier as they own Claude Code and can get Claude to work on Bun with fixing some specific behaviour in Claude Code as an objective. Releasing it for the world, and doing it well enough that it doesn't result in everyone pinning on the old version and forks springing up, involves reproducing all the behaviours of the old version, documented/tested and otherwise, that projects are relying on - which, by Hyrum's law, is all of them.
> to the detriment of the whole club of stochastic parrot folk
What an interesting and pointless way to refer to “experts who understand what an LLM actually is”
The people who refer to LLMs as stochastic parrots generally do so to imply significant limits on an LLMs ability, not as an abstract statement about the underlying mechanism of how they work. Probably the defining thing that is surprising about LLMs is that they do in fact gain significantly more capability than you would expect from such a simple underlying mechanism!
The concept of "stochastic parrot" is that an LLM merely parrots its training data with some randomness.
We now know that isn't true - LLMs build complex internal models and output based on that.
See for example https://arxiv.org/html/2505.23323v1
Also, you are commenting on a post where a LLM made significant progress on the Riemann hypothesis. Even the most extreme interpretation of these results, ie claiming that it was "only linking existing literature" goes well beyond a "stochastic parrot" - it had to be able to link disparate insights across multiple fields.
I mean people beat diseases by encouragement and some sugar water (placebo)
You shouldn't beat deceased!
P.S: I think you miswrote "diseases"
Hahahahah thanks !
It's literally just brute forcing lol
Taking Anthropic’s whole AI framing to its obvious logical end: if this is true as written, why was Jarred needed at all in this loop? It seems like an utter waste of time for a highly paid Anthropic employee. Can’t Anthropic have a top level agent that is looking at all interesting unsolved problems and orchestrating subagents via the same process?
Lets play over/under on an AI model proving (or counter exampling) the Riemann hypothesis?
I'm not sure what a good mark would be, but considering this result lets put it at 2027-08-10 (One year from today).
This result is some evidence that AI will not solve RH soon. If there were any easy solution hiding in plain sight then it probably would have found it.
Solving RH likely requires AI that is substantially more creative. But we haven't even solved the creativity problem for writing let alone mathematics. I believe that transformers are a trillion dollar local optimum that we will find it very hard to escape.
Let's wait for the models to produce a good novel first.
I would expect to see LLMs that are creative in math before any that are creative in writing. Creativity is more easily specified in math and the solutions can be formally verified. There's no good way to classify creative writing. Many truly great works are overlooked by experts and the public until decades later. Many derivative works are commercially successful.
LLMs, both in writing and mathematics seem to only be capable of coming up with texts that are inside the distribution of the training data.
With writing it's just more obvious. LLMs don't write with personality. They don't create new and exciting worlds on their own. Everything they output feels derivative.
In mathematics you see the same effect. They are very good at finding results that humans missed, taking advantage of their broad knowledge and tireless work ethic.
But just as they have been unable to create new literary worlds, they also have so far been unable to create new mathematics.
I believe this lack of creativity is intrinsic to how these models are architected and trained. We want models that produce these in-distribution outputs because those types of models are more economically valuable. Nobody wants a coding agent with spontaneity, we want models that predictably and obediently solve problems - and that's what we got.
> This result is some evidence that AI will not solve RH soon. If there were any easy solution hiding in plain sight then it probably would have found it.
There's no way you can conclude that. Yes, "Fable 2" or whatever this was probably won't. But we can't know what Fable 3/4/5/etc will be able to do.
If anything, if we have 1 or 2 more years of progress like the last 12 months, which have been insane, I'd say LLMs are likely to solve it.
You underestimate the difficulty of RH, there are far easier problems broadly related to RH (density hypothesis, Artin's holomorphy conjecture, Stark conjectures) which are still aren't solved.
I think verifiable tasks like math will soon be like Chess. Machines way beyond human intelligence.
As it stands now, the frontier models can prove theorems where the techniques exist in the literature, which it knows better than anyone who's ever lived and won't quit where a human would. There's no way to know if that's true of the Riemann Hypothesis until it's proven.
For example, even if Claude could prove the statement "100% of the zeroes lie on the critical line", that's strictly weaker than the Riemann Hypothesis, so even the best possible version of this result would fall short. (It's an asymptotic result, so it just means the percentage of counterexamples to the Riemann hypothesis goes to zero as their magnitude gets large.)
Let's extend this by asking: If an AI model can solve an extremely well known Math problem which has been open for centuries but hasn't be solved by a human mathematicians, why wouldn't that same model be able to find ways to improve it's own algorithms beyond that of the capabilities of human mathematicians / ML researchers?
The singularity is approaching.
AI has clearly been extensively used to improve models. The evidence for this is how far Anthropic went in nerfing Fable to prevent it being used to improve models.
> The singularity is approaching.
There have been apocalyptic preachers foretelling the end times for my entire life. Interesting to see how the language has changed, even as the predictions fail again and again.
This argument also proves that climate change and nuclear war aren't possible existential issues.
I believe it's already well accepted in these labs that we're in the Singularity. It happened on a Tuesday back in February. No one seemed to really notice and life went on... for now.
That's probably correct. It's unlikely there will be any single hard line we cross the defines the pre-singularity vs post-singularity moment.
I'd accept AI likely became somewhat helpful to frontier AI research & development in early 2026.
I think for me though the real game changer moment will be when AI working autonomously is able to hypothesis and test algorithmic improvements at a faster rate than humans. This will be done to some extent by scale – lots of parallel agents coming up with lots of hypotheses and running the best candidates as tests. But also (and perhaps more importantly) by making more consequential algorithmic discoveries in the field of machine learning than humans – a bar we appear to have crossed or are crossing with math.
I suspect AIs today are super-human at finding performance improvements and minor iterations on current approaches. Whether they can solve some of the larger algorithmic challenges in the field however I'm not yet sure, although it seems likely that unreleased models are starting to make progress here.
An algorithm breakthrough on par in significance with the attention mechanism, primarily driven by automated AI research in say a field like continual learning would in my opinion be extremely significant and should leave no doubters that the singularity is here and will rapidly alter the world as we have known it.
the AI model has NOT solved Riemann
I feel you. I am trying to remain positive too.
>why wouldn't that same model be able to find ways to improve it's own algorithms beyond that of the capabilities of human mathematicians / ML researchers
Because algorithms have lower bounds, and the computational characteristics of LLMs are well-characterized by papers like https://arxiv.org/abs/2310.07923 . No amount of intelligence can make something faster than a mathematically-proven lower bound, any more than it could make 1+1=3 (that's why every single successful production transformer architecture has some form of O(N^2) attention layers, because it's mathematically impossible to achieve the same expressive power without any). There is room for speedup where current implementations are slower than the proven lower bound, but not when they're already close to it.
> There is room for speedup where current implementations are slower than the proven lower bound, but not when they're already close to it.
Sure, but I'm obviously not limiting research to improvements on current approaches only.
We know the brain is far more energy efficient and sample efficient than current AI. There is clearly better algorithms out there.
The question is who will find those next big algorithmic improvements like the transformer architecture? Will it be AI or humans?
My bet would be AI.
> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
We went from AI being human sycophants to humans becoming AI sycophants.
As if Anthropic employees use massively different version of model. Not a single load-bearing, epistemic, heavy-lifting, push back, frankly, pivotal, crucial - for 48 pages.
I wonder if Jarred (the Bun guy) just got lucky here, or if he made progress before all the actual mathematicians at Anthropic because they aren't prompting Claude as ambitiously as he is.
2 years until Riemann is solved I guess.
This area seems to be moving so quickly. I wonder if it'll be worthwhile to start building a list of formal math problems whose solutions, or partial solutions, would help my subfield. (Though I work in the physical sciences, mostly with the messy, real world implementation problems which are likely difficult to formalize or directly connect).
Then, whenever a new SOTA model drops, throw it at the list to see if we get "free" research progress.
It seems like everything will follow this pattern:
1. AI is dismissed because an expert in a particular field finds an outdated model's outputs sub-par
2. New model, released or unreleased, makes a major stride in that field
3. Expert either recants and becomes AI-pilled, or claims it is just an artifact of the broad search space available to AI, and "no new knowledge was created".
I wonder how much it cost(s)
Although it took an unsuccessful attempt at it, the progress is as follows:
"Claude found that combining the results from Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with the work of Bombieri provides a way to surpass the previous state-of-the-art lower bound proportion of 41.6%, increasing it to 67.2%."
The transcripts, papers, and Claude's explanation are an interesting and a better read than this article, and this is exactly what Anthropic should continue to do and it helps other researchers outside the company as well.
[0] https://www-cdn.anthropic.com/564f962e60643842f5fcb4a17c9dbc...[1] https://github.com/anthropics/zeta-23-lean
[2] https://www-cdn.anthropic.com/23455459f8832d06bb175cc0f88d01...
[3] https://www-cdn.anthropic.com/d7f3ecf1d01392d887f8bc974ca187...
[4] https://www-cdn.anthropic.com/8a0d1add3c637b858a9a181e98c40e...
The acknowledgements section in the paper is so bizarre. We have an LLM thanking individual humans for their contributions.
>You got this
That's hilarious. Maybe I do need to glaze the LLM a bit more in the AGENTS.md
“Stochastic parrot” is going to be the 2020s equivalent of the 1990s’ “end of history”.
Imagine how bad you must be to lose to a Stochastic Parrot...
Everything about this situation is comedic, but if it leads to a real and meaningful step forward in learning, I suppose it's a net positive.
I wonder if they simply abliterate Claude skepticism would break its reasoning capabilities, if not I don't understand why they would just keep prompt it instead of creating an abliterated model for the task.
When the time comes where one of these model makes an improvement in my niche, I hope to see some pattern in the type of discoveries. Yes, they are all roughly "combine two things no one thought of combining" but I mean at a more granular deeper level.
I want to dive into the "data" and then see if it's possible to distill this skill into small models that are "benchmaxxed" for this type of work, maybe in limited domains, similar to small models being benchmaxxed(I don't mean this in a bad way) for coding these days.
Since they say that this is from an unreleased research version of Claude:
Just as an example, imagine if your model were capable of proving P = NP, or if your model could cure diseases. Would you release it for free, or would you try to make sure those benefits go directly to your company? From these companies' standpoint, I think they would choose the latter.>From these companies' standpoint, I think they would choose the latter.
Ever since these things came about I've wondered why they haven't been doing this the whole time. If they've got the "do-anything" robot and can scale a billion of them, why aren't they creating a Do-Everything conglomerate that disrupts every possible industry with zero/negligible labor costs?
The only answer I've come up with is that they still need to train/siphon off each industry's current expertise by having those users interact with the current models and adjusting. If that hypothesis is correct then within a few years they'll have no need for users anymore.
https://en.wikipedia.org/wiki/Comparative_advantage
If a company had a model that could cure cancer they would be incentivized to release the cure ASAP before they get decapitation striked by regulators and other AI "safetyists".
I think those specific examples, they'd release them publicly because the benefits to humanity are so clear -- however, if they found some new option-pricing model or futures market correlation, I highly doubt we'd see that...
It seems like theyd have incentive to
Yes, I think so, inevitably. For the same reason that Bitcoin mining silicon manufacturers stopped selling the latest greatest hardware to the public.
The best way to do this is to release spooky stories about how dangerous your model is and how you couldn't possibly release it without further safety shackling.
Your comment reminds me of the TV series "Persons of interest"* (with Jim Cazeviel) from 15 years ago, there are two AIs and both run private, hidden stuff. One copies itself through every router on the planet etc. and is the "evil AI" while the good guys run, in secret, a good AI (but way less powerful then the evil one).
Now the problem ATM is that OpenAI, for example, had to cut the price of two of its top 3 models by 80% to counter the chinese models: if you delay your models and a competitors takes over the market, you'll soon be out of bucks and won't be able to rent to Google and Amazon etc. the machine needed to make your new findings.
I know people don't want to hear it but: these companies are running at a loss.
And they're facing competition. Wait until a "good enough" is etched on silicon (by AMD or other) and outputs 70 000 tokens/s: the deal is going to change, once again, once those come out.
The energy, the hardware, the debt, the cost to train, the cost to run, the competition, etc. all have to be taken into account.
No more "stochastic parrots" and "LLM's can never produce anything novel, just regurgitate" comments anymore huh?
Sure, looks like 5% of math can be solved by 1T parameters stochastic parrot after NN trillion attempts (burned tokens). By numbers it could be less impressive than some brute force distributed chess engine.. Prove me wrong.
It's obviously significantly better than brute force. A trillion is absolutely minuscule compared to the size of the search space (like, 'rounding down to 1 is basically the same' small).