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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.

      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...
    by andai
  • 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.
    by empath75
  • > 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.

    by Philpax
  • It's literally just brute forcing lol
    by johnnienaked
  • 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?
    by mahogany
  • I mean people beat diseases by encouragement and some sugar water (placebo)
    by whatever1
  • 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…
    by astro1234
  • 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.

    by geodel
  • 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.

    by sosodev
  • > I wonder why we have yet to see more systematic exploration of Math.

    > 60 Claude subagents

    by gessha
  • 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
    by johnnienaked
  • 60 subagents for a day and a half. I guess he's not on the same plan I am on.
    by laszlojamf
  • 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.
    by jrflo
  • 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.
    by lukevp
  • > 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%.
    by lorenzohess
  • 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]
    [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...

    by rvz
  • The acknowledgements section in the paper is so bizarre. We have an LLM thanking individual humans for their contributions.
    by bspammer
  • This is a beyond remarkable achievement. Finding this lower bound within a few days of prompting is absolutely crazy.
    by coffeeaddict1
  • 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.

    by MWil
  • Claude is underrated in math. The 10 problems that openai solved? They needed an internal version. Fable 5 solved 5 of those.
    by llelouch
  • 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.
    by DroneBetter
  • Sounds really cool, were you able to verify the correctness of the results?
    by bauldursdev
  • 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

    by tosh
  • 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.

    by black_knight
  • 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.
    by bryan0
  • 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.

    by magneticnorth
  • 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.
    by jcfrei
  • > Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”)

    He should consider using the PUA plugin. It detects when the AI is trying to give up on a problem and automatically harasses it with "encouragement" until it reaches a solution.

    https://github.com/tanweai/pua

    by tristanj
  • 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.

    by brandall10
  • > 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.

    by simonw