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> 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
> 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].
In meme form: https://imgur.com/a/rlmZuU1
(I hope this is ok to post on HN!)
$2M TC. Job: AI cheerleader.
I feel justified in not expending any effort learning "prompting technique".
Reality has become more absurd than the cyber punk cheese from the 80's that tried to imagine an absurd future
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
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].
Broke: the AI is sycophantic to me
Woke: im sycophantic to the AI
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!
Indeed, that's a paragraph straight out of Lem's Cyberiad.
> 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.
it's pretty much a marketing attempt to humanize the LLM (it seems successful from the reaction I see)
> 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.
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.
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.
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
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.
This is a beyond remarkable achievement. Finding this lower bound within a few days of prompting is absolutely crazy.
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]
[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...
> 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%.
60 subagents for a day and a half. I guess he's not on the same plan I am on.
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.
> 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.
> 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
> 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?
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.
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).
> 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.
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".
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.
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.
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.
IANAM but this might be unexplored territory because Jensen polynomials are no longer considered a "plausible route" to proving the Riemann Hypothesis.
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.
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.
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.
>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”.
I wonder how much it cost(s)
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.
No more "stochastic parrots" and "LLM's can never produce anything novel, just regurgitate" comments anymore huh?