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#https#human#llms#claude#org#llm#prompt#arxiv#abs#proof
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These days "test-time scaling" mostly means letting the model talk to itself for longer, but the first genuinely surprising results came from plain sampling. Google's AlphaCode generated millions of candidate programs and filtered them down to a handful of submissions, which beat the average human programmer in 2022, before ChatGPT even showed up.
Sampling is what AI is good at. Making examples and doing LeetCode are similar in that verification is clear and cheap. Compared to that, "proof" is still a vague concept, except where Lean works. See the fuss over the ABC conjecture. So humans are still needed.
The interesting question to me is what happens after enough learning from "sampling." Isn't AlphaGo's move 37 an AI's nose? If that happens in mathematics, we may end up with results that are correct, machine checkable, and not explainable in any way we find satisfying.
Wikipedia is maybe the narrow end of a wedge into this topic but the controversy revolves around a very large and very complex paper that few people are equipped to understand and some of those who are able believe the proof is false.
You can toss it at a task with a suitable machine for transforming that raw material into action and it'll rattle through and sample "plausible human behavior" at that endpoint.
There are more clever ways to use it, but a general tool here is to upgrade any sort of stochastic search to use this new form of random sampling. It'll be way more efficient, properly conditioned, because it just won't visit implausible things nearly as often as competing random sources.
I wanted to demonstrate capacity (how well it does a thing) instead of capability (which things it does, like drawing a pelican on a bicycle with SVG or solving a Rubik's Cube). To understand how LLMs solve math, look at the simplest case of multiplication. I deconstructed and classified the thinking token output. It is very important that model training yields thinking token output that structurally follows an observe, orient, decide, act (do the multiplication), and observe again loop.
[0] https://adamsohn.com/reasoning-grid/
> 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 we’ll recognise it when we see it.
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 the capabilities of current SOTA models to implement an Agentic application for job search, here is some simple inhouse built evals I run today, since I don´t trust LLM vendors published benchmarks...
Models tested: GPT-5.6 Sol in Extra High mode and Opus 4.8 Max.
TASK REQUEST: Clear, not too long not too short prompt, for LLMs to go out and research freelance consulting gigs for one specific IT domain, and in one specific country in Europe, including maybe opportunities driven from temp agencies based in geographically close countries.
RESULT: Models go out, fetch the data, and completely misunderstand the task...offering on first results, permanent roles instead of freelance, and based on the country where the agencies are, not in the one it was request for. Think for example IT jobs in Ireland, while freelance agency in London.
ANALYSIS: No intelligence I can call it shown by models, adding cognitive effort for human in the loop to detect subtle factors, and therefore totally useless for agentic app...Best practices would be I guess to add agents on top of agents but although in the p95 of cases that will reduce the errors...for the remaining 5% that could have hallucinations or logic hallucinations like these ones, compounding on top of other logic hallucinations.
I dont care about the theorems being proven. At the end we will found out what most mathematicians were doing, was just exploring the same combinatorial and abstraction patterns. And because of that I am sure LLMs will make mince meat of a lot of mathematical domains.
But right now, what we call intelligence is not existing where it matters, and Ed Zitron is right its a parlour trick.
Anything that can be verified mechanically should be code. Only use LLMs to fill in the gaps where things are fuzzy. Don't fall for the idea that those harnesses are general purpose, make your own fit to your task with the guards and verification steps you need. Make the LLM create the harness even.
There is no amount of markdown that can make a machine generating plausible text generate truthful text, it just happens to be truthful because of what it was trained on. Nothing coming out of an LLM should be taken at face value.
The propaganda about LLMs being intelligent and able to "reason" is only serving the companies selling you tokens to waste on "prompt engineering".
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.
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.
As a human, not an LLM, I could interpret "including maybe opportunities driven from temp agencies based in geographically close countries" as meaning "including opportunities in nearby countries outside of Ireland" (that happen to be driven by temp agencies).
Before writing off LLM as simply a "stochastic parrot" or a "parlour trick" remember it can't read your mind, not yet anyway.
So what happen is a prompt said for example, find freelance opportunities in Ireland but keep in mind some of these might be available via temp agencies in London.
If you offer me not freelance but permanent roles, and not in Ireland in London...that is a logic failure.
Its this type of complexity with the normal world, that these SOTA constructions so badly fail at, and so spectacularly fail at the margins... despite maxing all benchmarks...Parlour trick.
There is this persistent belief that AI is a great leveler and you just type "pls get me a job kthx" and it should perform literal miracles.
Try some context engineering. Try customizing your harness. Try having the harness improve itself. These are AI 101 lessons you can find in many tutorials. Anthropic has a great set of tutorials on how to use claude that go into a lot more depth for beginners.
This reminds me of how when Juniors use AI, they produce offensive slop, but when Principals use AI, they produce some truly beautiful systems.
AI is not a great leveler, it's a skill based tool. If your results suck, before you blame the tool, consider other possibilities.
But of course, bias confirmation that AI is just a big scam sounds a lot easier than admitting a skill deficit and spending real time and effort learning.
If AI is really that complicated, it sounds like it would be easier to write an ordinary computer program to aggregate job boards.
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 - https://arxiv.org/abs/2605.19597
LogicGraph: Benchmarking Multi-Path Logical Reasoning via Neuro-Symbolic Generation and Verification - https://arxiv.org/abs/2602.21044
Blind-Spots-Bench: Evaluating Blind Spots in Multimodal Models - https://arxiv.org/abs/2607.08317
Vision-Language Models Lag Human Performance on Physical Dynamics and Intent Reasoning - https://arxiv.org/abs/2601.01547
Do Vision-Language Models Understand 3D Scenes or Just Catalogue Objects? - https://arxiv.org/abs/2605.20448
The Reversal Curse: LLMs Trained on “A is B” Fail to Learn “B is A” - https://arxiv.org/abs/2309.12288
Large Language Model Reasoning Failures - https://arxiv.org/abs/2602.06176
Agreed. I find that after seeing these results from OpenAI we undeniably have a machine that has:
* General knowledge of nearly every subject humanity has ever learned
* The ability to simulate reasoning (albeit sometimes not very well) with that knowledge
* The ability to reference across the domains of knowledge
To me, this is more or less what I would think "Artificial General Intelligence" is. It's the cumulative knowledge of all general human intelligence, baked into an artificial form, which can then use that knowledge to achieve novel goals.
In many cases of mathematical breakthroughs there is an insight that comes from just happening to know a combination of already existing ideas and then combining them to solve that problem. This is where having that general knowledge seems particularly strong because we can run these machines for weeks on end effectively trying to brute force.
That being said, I could never imagine an LLM in its current form inventing something as elegant as the Fourier transform.
So then you need to explain ARC-AGI-3: https://arxiv.org/abs/2603.24621
"Our testing shows humans can solve 100% of the environments, in contrast to frontier AI systems which, as of March 2026, score below 1%."
Back 1996, EQP automatically solved the Robbins conjecture. But nobody concluded EQP was generally intelligent.
https://www.cs.unm.edu/~mccune/papers/robbins/
Step 1. LLM "brute forces" a search
Step 2. We train on this trace
Step 3. In the next model, LLM internally makes a "shortcut" for this path and "brute forces" it quicker (or one shots its in the best case)
And we want to ultimately show why that definitio evades this framework.
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.
___________
[1] https://www.anthropic.com/research/riemann-zeta
They are algebra, and yet kinda suck at it without training