31–40 of 189 posts
> A good sign that LLMs have reached human level for a much wider class of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. They should also be methods that are difficult to stumble on by accident. It is hard to say precisely what would count as such a proof, but I think…
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> Try some context engineering. Try customizing your harness. Try having the harness improve itself. These are AI 101 lessons If AI is really that complicated, it sounds like it would be easier to write an ordinary computer program to aggregate job boards.
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You can easily test this yourself with the SOTA models....or read the corroborating literature... "General365: Benchmarking General Reasoning in Large Language Models Across Diverse and Challenging Tasks" https://arxiv.org/abs/2604.11778 "...General365, a benchmark specifically designed to assess general reasoning in LLMs. By restricting background knowledge to a K-12 level, General365 explicitly decouples reasoning…
What proportion of the human population could answer the example from that paper? Question: Strangers A, B, C, D, and E line up from youngest on the left to oldest on the right. Their clothing colors and shoe colors all differ, and they come from five different regions. Known facts: 1. A is from Morocco. 2. D is five years older than B. 3. E is older than A. 4. C stands next to D. 5. A stands next to B. 6. The person…
It means that it is possible for someone to be wearing a white shirt and yellow pants (say), but the person in green shoes came from the set of a Wes Anderson film.
A thoughtful and measured post, as usual from Gowers. The final note is neat and worth pasting out here in full: > A good sign that LLMs have reached human level for a much wider class of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. They should also be methods that ar…
>>A good sign that LLMs have reached human level for a much wider class >> of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. I must be taking crazy pills and the AGI surely will pass me by... But TODAY, middle August 2026...And in the context of testing and evaluating t…
Why do you think there's such a thing as too long for an LLM prompt? You'll run into context window limits at some point, but the more verbose you are with what you ask of it, the better the results will be.
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Its the tools. Sell those RSUs while they last. Most of these are 2026.... Frontier LLMs Still Struggle with Simple Reasoning Tasks - https://arxiv.org/abs/2507.07313 General365: Benchmarking General Reasoning in Large Language Models Across Diverse and Challenging Tasks - https://arxiv.org/abs/2604.11778 LLMEval-Logic: A Solver-Verified Chinese Benchmark for Logical Reasoning of LLMs with Adversarial Hardening - htt…
What a sloppy reply. You've hijacked a thread on mathematics first to complain that your incompetent attempt to use ChatGPT to find a job failed, but it seems now that this was a ruse to instead begin arguments unrelated to the article at all where you just spam arxiv links you've never read to "prove" that AI is a scam. This comes across, frankly, as either Dunning-Kruger (classic illusory superiority), or potential…
A thoughtful and measured post, as usual from Gowers. The final note is neat and worth pasting out here in full: > A good sign that LLMs have reached human level for a much wider class of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. They should also be methods that ar…
>>A good sign that LLMs have reached human level for a much wider class >> of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. I must be taking crazy pills and the AGI surely will pass me by... But TODAY, middle August 2026...And in the context of testing and evaluating t…
I don't know your prompt and setup, but my claude had no problems doing that task. The search index isn't live, so it can't find current gigs, but that is a tooling problem.
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What proportion of the human population could answer the example from that paper? Question: Strangers A, B, C, D, and E line up from youngest on the left to oldest on the right. Their clothing colors and shoe colors all differ, and they come from five different regions. Known facts: 1. A is from Morocco. 2. D is five years older than B. 3. E is older than A. 4. C stands next to D. 5. A stands next to B. 6. The person…
> What does [ 13 ] even mean? It means that it is possible for someone to be wearing a white shirt and yellow pants (say), but the person in green shoes came from the set of a Wes Anderson film.
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> Try some context engineering. Try customizing your harness. Try having the harness improve itself. These are AI 101 lessons If AI is really that complicated, it sounds like it would be easier to write an ordinary computer program to aggregate job boards.
Yes, one of the obvious ways to me to use these models is to tell them to write such a program. It can then go figure out data extraction and normalization. This is "the harness improving itself". Have it write tools to do its tasks.
When I say "write an ordinary computer program". I mean just writing the program, in a programming language. Your comment expresses disagreement with me, so should have started with "No", not "Yes".
We have just got some very strong evidence about the way in which LLM-based systems solve mathematical problems and this evidence supports what many have already suspected including myself.
Here's what I'm talking about. On 10 August Anthropic released an article [1] claiming that:
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%.
The same article describes the methodology followed by Anthropic's employee, Jarred Sumner, who prompted Claude, as follows:
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.
Jarred got Claude to throw stuff at the wall repeatedly (650 initial "ideas" plus unspecified more by "60 Claude subagents" ... running "2400 shell commands" and "hundreds of Python scripts") and then kept whatever happened to stick. In this case, by happy accident, what stuck was an improved bound of the zeroes of the zeta function etc.
This is how every single mathematical result reported by an AI company has ever been generated. They throw stuff at the wall and take whatever happens to stick.
This approach works. Not only it works, it is, in principle, a universal problem solver. "Millions of monkeys on typewriters" will eventually produce a proof of the Riemann hypothesis; or a disproof of it.
The key point being "eventually". Is this a way to do mathematics research? Can that replace mathematicians?
In AI, this method is well-known as the "generate-and-test" method. It is ancient, basal to AI if I may be so bold. It first appeared to my knowledge in the Logic Theorist, the proof-finding program that Simon and Newell presented in the 1956 Dartmouth convention that named "Artificial Intelligence", to such luminaries of AI and CS as John McCarthy (the real "godfather of AI" who named the field), Marvin Minsky, Claude Shannon and others.
We've had the ability to brute-force all of mathematics "eventually", given "enough" compute for nearing a century now. Why haven't we solved all of mathematics? Are LLMs really so special that they can out-brute force search every previous brute force searcher?
Well, you tell me, HN. I say: no.
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