alt Hacker NewsLearning more about Claude's mathematical capabilities
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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
> 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.
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 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.
> 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?
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
This is a beyond remarkable achievement. Finding this lower bound within a few days of prompting is absolutely crazy.
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.
> 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%.
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".
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).
> 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.
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.
I wonder if Jarred (the Bun guy) just got lucky or if the mathematicians at Anthropic aren't prompting Claude as ambitiously as he is.
2 years until Riemann is solved I guess.
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.
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...
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.
I wonder if they simply abliterate Claude skepticism would break its reasoning capabilities, if not I don't understand why they would just keep prompt it instead of creating an abliterated model for the task.
When the time comes where one of these model makes an improvement in my niche, I hope to see some pattern in the type of discoveries. Yes, they are all roughly "combine two things no one thought of combining" but I mean at a more granular deeper level.
I want to dive into the "data" and then see if it's possible to distill this skill into small models that are "benchmaxxed" for this type of work, maybe in limited domains, similar to small models being benchmaxxed(I don't mean this in a bad way) for coding these days.
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No more "stochastic parrots" and "LLM's can never produce anything novel, just regurgitate" comments anymore huh?
> 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.