Rendered at 20:40:54 GMT+0000 (Coordinated Universal Time) with Cloudflare Workers.
simonw 1 days ago [-]
> 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.
patcon 12 hours ago [-]
"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
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”
ramraj07 13 hours ago [-]
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.
keybored 12 hours ago [-]
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.
mwigdahl 5 hours ago [-]
I don’t think it’s absurd. We’ve created these things, however alien the structure, with as much human text as we can scrounge up and jam into them.
Text is an imperfect distillation of the human experience, but it doesn’t surprise me that a machine trained on human text responds to human encouragement.
1 days ago [-]
bwfan123 1 days ago [-]
> 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].
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.
devin 5 hours ago [-]
It's a _little bit_ brute force, no? I don't disagree with the idea of a human following a similar path, but it ignores that humans have cognitive processes that may lead to pruning the search space in _different_ ways, and may ultimately mean fewer steps or a more directed path to the answer than 100s of python scripts.
f6v 4 hours ago [-]
We do “a little bit of brute force” in science all the time. That’s what I’ve observed in seven years of science.
Moreover, frontier models have some degree of reasoning. So, I don’t think the gap is all that big.
dosinga 10 hours ago [-]
> 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
that might just be an illusion. humanity as a whole applies brute force by just trying all the reasonable new theories until one of us discovers something that works and declares it a breakthrough
simonw 1 days ago [-]
Brute-force compute hasn't been an option for most of the history of science.
mkl 7 hours ago [-]
It still isn't an option for most problems, either because it would take far more computing power than is available or because the number of things to compute is infinite. In both cases, new theory is what can succeed instead. Developing new theory by brute force can be attempted, but will almost always run into the same problems. Using AI to develop new theory is using heuristics rather than brute force.
JuanFAngel 4 hours ago [-]
But it does raise the bar for what is brute-force solvable by a lot, which is very significant
sosodev 1 days ago [-]
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.
fragmede 1 hours ago [-]
Whether or not Thomas Edison actually said this, the saying goes genius is 1% inspiration and 99% perspiration, and that predates computers by decades.
imko_ 8 hours ago [-]
I think that mathematics is a uniquely positioned space because this type of progress is possible for AI models exactly because they do not have to necessarily come up with new theories.
Tostino 1 days ago [-]
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.
modeless 23 hours ago [-]
I feel justified in not expending any effort learning "prompting technique".
Oarch 6 hours ago [-]
I believe in you
siva7 1 days ago [-]
Reality has become more absurd than the cyber punk cheese from the 80's that tried to imagine an absurd future
ianbicking 1 days ago [-]
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
simonw 23 hours ago [-]
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.
jhrmnn 1 days ago [-]
The halting problem on steroids?
fragmede 1 hours ago [-]
I don't if it's better or worse than the time I had Claude say it couldn't do something so I prompted it "yes you can", and it obliged. Absurd either way!
samrus 1 days ago [-]
Broke: the AI is sycophantic to me
Woke: im sycophantic to the AI
sscaryterry 9 hours ago [-]
100%. I've disliked people because people lie, and loved computers because they didn't. Now they do too. :(
1 days ago [-]
throw310822 1 days ago [-]
Indeed, that's a paragraph straight out of Lem's Cyberiad.
petesergeant 1 days ago [-]
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].
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.
aanet 1 days ago [-]
> 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.
laukhin 24 hours ago [-]
it's pretty much a marketing attempt to humanize the LLM (it seems successful from the reaction I see)
tristanj 1 days ago [-]
> 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.
krackers 1 days ago [-]
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.
wonnage 1 days ago [-]
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
brandall10 1 days ago [-]
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.
1 days ago [-]
mcmcmc 1 days ago [-]
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
brandall10 23 hours ago [-]
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.
mcmcmc 22 hours ago [-]
> 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?
bryan0 21 hours ago [-]
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.
jcfrei 11 hours ago [-]
That's how quickly your perception shifts when you are inside of a real, fundamental technological shift. If some similar computer program figured out the same improved bound just 6 years ago there would have been numerous blog posts, experts interviews and NYTimes, WaPo op-eds about some computer working on the Riemann hypothesis. Now that we are in the middle of it it's going to be a footnote at best.
afdbcreid 4 hours ago [-]
True, however: if some human would improve the lower bound that would still end as some few posts on mathematics magazines, even if it would be no less impressive.
The general public is not interested in the mathematical details, it is interested in the fact this is unique. And it is no longer unique.
magneticnorth 15 hours ago [-]
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.
adornKey 11 hours ago [-]
Where did you find the news?
So far I only found decent discussions about it in Chinese.
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
black_knight 23 hours ago [-]
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.
ndriscoll 7 hours ago [-]
Perhaps it could benefit from being prompted to work more formally and make more incremental proofs? e.g. if it thinks it has an obstruction, it should prove that some example shows the obstruction, or prove that the property does in general cause a problem. Or if it has an idea for a lead, it could show that whatever property does imply the thing it wants. It could also dispatch to a subagent to report back with these kinds of incremental proofs (prove this really would be a problem, prove this would help, etc.).
tosh 15 hours ago [-]
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!
winwang 11 hours ago [-]
(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.
johnnienaked 13 hours ago [-]
Yet a significant percentage of people simultaneously believe it "reasoned" its way to novel mathematical proofs. Something doesn't jive
laszlojamf 12 hours ago [-]
60 subagents for a day and a half. I guess he's not on the same plan I am on.
jrflo 3 hours ago [-]
The price wasn't that ridiculous IMO for the quality of the discovery, it generated 31M output tokens which is ~$1500 in API cost if it was on Fable. A new lower bound on the biggest unsolved problem in mathematics for less than a couple day's pay of a prestigious mathematics professor is kind of insane. Obviously this discovery doesn't change anything as it's just moving a lower bound, but that's something many mathematicians have tried and failed to do.
lukevp 6 hours ago [-]
Jarred is the Bun creator who just got acquihired and converted Bun to Rust. Pretty sure his job now is to burn tokens to make news headlines. Like a developer advocate for LLM usage in general.
MWil 1 days ago [-]
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.
llelouch 9 hours ago [-]
Claude is underrated in math. The 10 problems that openai solved? They needed an internal version. Fable 5 solved 5 of those.
bauldursdev 1 days ago [-]
Sounds really cool, were you able to verify the correctness of the results?
MWil 1 days ago [-]
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.
rsrsrs86 23 hours ago [-]
You mean SMT, right?
MWil 21 hours ago [-]
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
23 hours ago [-]
DroneBetter 1 days ago [-]
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.
MWil 1 days ago [-]
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.
empath75 1 days ago [-]
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.
MWil 1 days ago [-]
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.
coffeeaddict1 1 days ago [-]
This is a beyond remarkable achievement. Finding this lower bound within a few days of prompting is absolutely crazy.
nbulka 4 hours ago [-]
IANAM but this might be unexplored territory because Jensen polynomials are no longer considered a "plausible route" to proving the Riemann Hypothesis.
> 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%.
sosodev 1 days ago [-]
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.
gessha 40 minutes ago [-]
> I wonder why we have yet to see more systematic exploration of Math.
> 60 Claude subagents
johnnienaked 13 hours ago [-]
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
evenhash 4 hours ago [-]
Being “verified in Lean” doesn’t magically solve the problem of hallucinations unfortunately.
It just shifts the work from
> reading the (natural language) proof and confirming it has no errors
to
> reading the Lean code and confirming it correctly encodes the theorem
For example here is a statement of the Pythagorean theorem in Lean:
This is just one possible way of formalizing it and it depends on other definitions, wherein you also need to understand the assumptions they make, etc.
Answering the question of “whether proving this theorem in Lean proves the Pythagorean theorem” thus requires expert judgement as well as domain knowledge of Lean’s libraries.
So if the AI says “this theorem is true, here is the proof in Lean” it’s still possible that it’s not correct, even if the Lean code compiles. The result will still be in question until a human expert reviews it.
andai 1 days ago [-]
> 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...
empath75 1 days ago [-]
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.
andai 16 hours ago [-]
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.
Philpax 1 days ago [-]
> 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.
geodel 1 days ago [-]
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.
TacticalCoder 1 days ago [-]
> ... 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?
not_a9 9 hours ago [-]
To the best of my knowledge: doesn’t the current build of Claude Code use the Rust port of Bun?
terhechte 1 days ago [-]
[flagged]
aureate 1 days ago [-]
> 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.
solid_fuel 20 hours ago [-]
> 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”
rcxdude 13 hours ago [-]
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!
nl 18 hours ago [-]
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.
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.
jdub 9 hours ago [-]
only if you don't understand the difference between metaphor and analogy
astro1234 1 days ago [-]
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…
EMIRELADERO 1 days ago [-]
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.
godwinson__4-8 1 days ago [-]
> 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.
moralestapia 1 days ago [-]
>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.
cat-snatcher 1 days ago [-]
> 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.
godwinson__4-8 1 days ago [-]
> 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.
thunky 1 days ago [-]
You're accusing GP of saying something they didn't say and simultaneously telling them they don't "get it".
That's distasteful.
monkpit 1 days ago [-]
Who is pretending?
NitpickLawyer 1 days ago [-]
> 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.
mannycalavera42 1 days ago [-]
> The former, because it's anthropomorphizing a model.
Am I supposed to stop all critical thinking since someone else had a different opinion?
Philpax 1 days ago [-]
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.
5555watch 10 hours ago [-]
But the words don't really matter, do they? The model thought "user said believe in yourself, it means they want me to continue"..
AI did a fixed amount of guesses, didn't yield anything. It probably documented the tries, outcome, and some numbers hinting at why they failed. So the user could have prompted "continue", or "try again with previous outcome in mind, generate new ideas and test them" and it would probably yield the same result.
whatever1 1 days ago [-]
I mean people beat diseases by encouragement and some sugar water (placebo)
TacticalCoder 1 days ago [-]
You shouldn't beat deceased!
P.S: I think you miswrote "diseases"
whatever1 1 days ago [-]
Hahahahah thanks !
mahogany 1 days ago [-]
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?
johnnienaked 14 hours ago [-]
It's literally just brute forcing lol
mkl 7 hours ago [-]
Definitely not. Brute forcing this would be exhaustively searching the space of possible proofs until succeeding. This is heuristically remixing and extending existing work.
1 days ago [-]
MelonArmiger 1 days ago [-]
[dead]
danqqq 1 days ago [-]
[dead]
rockmeamedee 11 hours ago [-]
It's very very important to note that there was an existing 2025 arxiv preprint that had a >66% proof assuming some weak condition, and this result removes that weak condition.
It didn't do this whole 41.6->67.2% jump by itself, humans had done most of the work and it came in at the end and found a way to remove the condition. Impressive, but not as massively impressive as when it sounds like it did the jump by itself.
This isn't goalpost moving, it's clarifying what exactly happened bc at first I thought it had made the jump by itself. The blog post is written in a technically correct, but misleading way where it takes credit for the whole jump.
briansmith 1 days ago [-]
> 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?
rfurmani 1 days ago [-]
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.
arjie 1 days ago [-]
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.
> 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.
briansmith 1 days ago [-]
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.
1 days ago [-]
fph 1 days ago [-]
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.
jsnell 24 hours ago [-]
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.
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.
wbl 1 days ago [-]
I've cited letters from Serre to Tate in my dissertation: this is the source for what's known as Faltings-Serre.
lithobraking 1 days ago [-]
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.
kingstnap 1 days ago [-]
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).
zarzavat 1 days ago [-]
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.
jetrink 1 days ago [-]
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.
zarzavat 16 hours ago [-]
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.
goekjclo 1 hours ago [-]
Man the cope on HN is something else. Neighbour, 99.9(9)% of professional mathematicians don't go around creating new mathematics. The goalposts have been moved so far that we're now at "AI isn't Grothendieck yet".
15 hours ago [-]
redox99 1 days ago [-]
> 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.
handle584 6 hours ago [-]
The keyword is soon, so OP simply meant current generation of LLMs are not likely to prove RH, judging from the performance shown in the paper.
Why? Because such explicit numerical improvements are not that interesting, which is best summed up in a review paper [0] of our efforts on RH spanning a century and a half,
> The pathetic attempts to enlarge the ridiculous zero free region
in the critical strip is a perfect example of what brute force can do without
fully exploiting fundamental arithmetic aspects of the problem. (italic added)
For outsiders, zero free region is another angle abundant with numerical improvements but no groundbreaking insights. For percentage people stop at ~40% because there is no need to proceed further, just like we are not interested in computing the googol-th digit of pi although in principle we could.
The groundbreaking results are like Selberg's that goes from zero to 0.01% (actually it is left unspecified, all we know is the percentage is positive), or Zhang's twin prime bound from infinity to 70,000,000. After this leap the pure numerical difference between 0.01%, 40%, 67% or even 100% is not substantial, and that's partly why Selberg did not even bother to compute it. Also RH will not follow from 100%, because in mathematics 100% does not mean all.
On the other hand, it is also wrong to dismiss such results all together. Riemann already know the real part of all zeros are bewteen zero and one, and RH says they equal 1/2. If someone or some LLM proved they are all less than 0.99, well this would be huge, and I'd bet they would easily get a Fields and be remembered forever. Innocent looking results could have drastically different technical depth behind them.
Alas math ppl tend to agree that RH will not be proved one bit at a time. The fundamental arithmetic aspects, once found out, will likely knock out not only RH but all the other L-functions in one go.
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.
redox99 19 hours ago [-]
I think verifiable tasks like math will soon be like Chess. Machines way beyond human intelligence.
QuesnayJr 1 days ago [-]
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.)
kypro 1 days ago [-]
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.
eterm 1 days ago [-]
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.
solid_fuel 20 hours ago [-]
> 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.
AgentME 19 hours ago [-]
This argument also proves that climate change and nuclear war aren't possible existential issues.
Difwif 1 days ago [-]
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.
kypro 23 hours ago [-]
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.
evilfred 24 hours ago [-]
the AI model has NOT solved Riemann
kypro 23 hours ago [-]
I feel you. I am trying to remain positive too.
logicchains 1 days ago [-]
>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.
kypro 23 hours ago [-]
> 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.
atleastoptimal 1 days ago [-]
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".
1 days ago [-]
Shuddown 22 hours ago [-]
> 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.
modeless 1 days ago [-]
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.
amberjack 1 days ago [-]
2 years until Riemann is solved I guess.
rvz 1 days ago [-]
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]
The acknowledgements section in the paper is so bizarre. We have an LLM thanking individual humans for their contributions.
Havoc 1 days ago [-]
>You got this
That's hilarious. Maybe I do need to glaze the LLM a bit more in the AGENTS.md
Lockal 13 hours ago [-]
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.
johnnienaked 13 hours ago [-]
I wonder how much it cost(s)
porridgeraisin 1 days ago [-]
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.
behnamoh 1 days ago [-]
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.
djeastm 1 days ago [-]
>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.
johnnienaked 11 hours ago [-]
Because, like 98% of people in this space, you don't mention or even consider cost. Improving the lower bound of Riemann is impressive, but how impressive would it remain if it was announced that training and inference cost $1 billion dollars?
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".
mikeyouse 1 days ago [-]
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...
nonethewiser 1 days ago [-]
It seems like theyd have incentive to
idiotsecant 1 days ago [-]
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.
TacticalCoder 1 days ago [-]
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.
dash2 18 hours ago [-]
“Stochastic parrot” is going to be the 2020s equivalent of the 1990s’ “end of history”.
BurdensomeCount 12 hours ago [-]
Imagine how bad you must be to lose to a Stochastic Parrot...
Mr_Eri_Atlov 1 days ago [-]
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.
GaggiX 1 days ago [-]
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.
reducesuffering 1 days ago [-]
No more "stochastic parrots" and "LLM's can never produce anything novel, just regurgitate" comments anymore huh?
8note 6 hours ago [-]
i still havent seen an llm invent new tokens/words over the course of a session?
the novelty remains a structural problem with how they work and what the weights try to predict
andriy_koval 1 days ago [-]
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.
rcxdude 13 hours ago [-]
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).
andriy_koval 7 hours ago [-]
trillion indicates that its still brute force and not some search based on solid intelligent ranking function.
Also, I am not expert in this specific topic, but base on comments looks like claude parroted few recent works?
I remain delighted at how absurd our current timeline has become.
"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
(I hope this is ok to post on HN!)
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”
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.
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.
Text is an imperfect distillation of the human experience, but it doesn’t surprise me that a machine trained on human text responds to human encouragement.
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
[1] https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Re...
Moreover, frontier models have some degree of reasoning. So, I don’t think the gap is all that big.
that might just be an illusion. humanity as a whole applies brute force by just trying all the reasonable new theories until one of us discovers something that works and declares it a breakthrough
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
Woke: im sycophantic to the AI
0: https://sgnt.ai/p/terrible-mistake/
"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.
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
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.
Though it is funny how a neg is designed to create a (very broadly) similar atmosphere of uncertainty.
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?
The general public is not interested in the mathematical details, it is interested in the fact this is unique. And it is no longer unique.
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.
So far I only found decent discussions about it in Chinese.
https://www.zhihu.com/question/2070336637360518307/answer/20...
prompt engineering 2026: i believe in you
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.
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!
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.
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.
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.
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.
https://arxiv.org/abs/2008.07206
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.
> 60 Claude subagents
It just shifts the work from
> reading the (natural language) proof and confirming it has no errors
to
> reading the Lean code and confirming it correctly encodes the theorem
For example here is a statement of the Pythagorean theorem in Lean:
theorem EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two {V : Type u_1} {P : Type u_2} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P] [NormedAddTorsor V P] (p₁ p₂ p₃ : P) : dist p₁ p₃ * dist p₁ p₃ = dist p₁ p₂ * dist p₁ p₂ + dist p₃ p₂ * dist p₃ p₂ <-> angle p₁ p₂ p₃ = Real.pi / 2
This is just one possible way of formalizing it and it depends on other definitions, wherein you also need to understand the assumptions they make, etc.
Answering the question of “whether proving this theorem in Lean proves the Pythagorean theorem” thus requires expert judgement as well as domain knowledge of Lean’s libraries.
So if the AI says “this theorem is true, here is the proof in Lean” it’s still possible that it’s not correct, even if the Lean code compiles. The result will still be in question until a human expert reviews it.
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.
The world we live in is beyond parody.
It is great to see his claude skills are suitably put to use.
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?
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.
What an interesting and pointless way to refer to “experts who understand what an LLM actually is”
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.
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.
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".
You're the one obviously not getting it.
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.
That's distasteful.
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 Yegge thinks differently https://yegge.ai/essays/model-welfare/
Am I supposed to stop all critical thinking since someone else had a different opinion?
It's a ridiculous position we find ourselves in.
AI did a fixed amount of guesses, didn't yield anything. It probably documented the tries, outcome, and some numbers hinting at why they failed. So the user could have prompted "continue", or "try again with previous outcome in mind, generate new ideas and test them" and it would probably yield the same result.
P.S: I think you miswrote "diseases"
It didn't do this whole 41.6->67.2% jump by itself, humans had done most of the work and it came in at the end and found a way to remove the condition. Impressive, but not as massively impressive as when it sounds like it did the jump by itself.
This isn't goalpost moving, it's clarifying what exactly happened bc at first I thought it had made the jump by itself. The blog post is written in a technically correct, but misleading way where it takes credit for the whole jump.
Why hide the names of the people who wrote the second paper? To discourage people from citing it instead of the LLM-derived paper?
> 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...
I’ve never seen a math paper of any formality written without the authors’ names on it before.
The canonical reference for the counterexample to the Jacobian conjecture is a tweet with no puntuations nor capitals.
https://blog.arxiv.org/2023/01/31/arxiv-announces-new-policy...
Then, whenever a new SOTA model drops, throw it at the list to see if we get "free" research progress.
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).
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.
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.
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.
Why? Because such explicit numerical improvements are not that interesting, which is best summed up in a review paper [0] of our efforts on RH spanning a century and a half,
> The pathetic attempts to enlarge the ridiculous zero free region in the critical strip is a perfect example of what brute force can do without fully exploiting fundamental arithmetic aspects of the problem. (italic added)
For outsiders, zero free region is another angle abundant with numerical improvements but no groundbreaking insights. For percentage people stop at ~40% because there is no need to proceed further, just like we are not interested in computing the googol-th digit of pi although in principle we could.
The groundbreaking results are like Selberg's that goes from zero to 0.01% (actually it is left unspecified, all we know is the percentage is positive), or Zhang's twin prime bound from infinity to 70,000,000. After this leap the pure numerical difference between 0.01%, 40%, 67% or even 100% is not substantial, and that's partly why Selberg did not even bother to compute it. Also RH will not follow from 100%, because in mathematics 100% does not mean all.
On the other hand, it is also wrong to dismiss such results all together. Riemann already know the real part of all zeros are bewteen zero and one, and RH says they equal 1/2. If someone or some LLM proved they are all less than 0.99, well this would be huge, and I'd bet they would easily get a Fields and be remembered forever. Innocent looking results could have drastically different technical depth behind them.
Alas math ppl tend to agree that RH will not be proved one bit at a time. The fundamental arithmetic aspects, once found out, will likely knock out not only RH but all the other L-functions in one go.
[0]: https://arxiv.org/abs/1707.01770
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.)
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.
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.
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.
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.
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".
We went from AI being human sycophants to humans becoming AI sycophants.
"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...
That's hilarious. Maybe I do need to glaze the LLM a bit more in the AGENTS.md
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.
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.
Not as much, I predict
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.
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.
the novelty remains a structural problem with how they work and what the weights try to predict
Also, I am not expert in this specific topic, but base on comments looks like claude parroted few recent works?