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Unsolved Problem by Fields Medalist Breached by Two High School Students
- Xcelerate 19d agoI sort of wonder if effectively using AI to solve math problems is a skill in its own right, distinct from traditional mathematical skills. I don’t just mean “prompt engineering” either. More so figuring out how to combine agents with other tools and approaches in an effective way.
- firesteelrain 19d agoAgree this is a broad statement for any use of AI for any purpose. Open ended prompts / requests are bound to lead to misleading results, hallucinated responses, waste of tokens, etc
- breezybottom 19d agoYou still have to be able to verify the solution to say that it's solved, so I'd say no.
- perching_aix 19d agoI'm not sure that makes sense? Having the expertise to verify the completion of a given task is a usually necessary but not sufficient requirement to what they're describing. I don't think they even disagree. You seem to be imagining completely independent areas of competence, but I don't think that's a reasonable interpretation of what they wrote.
- stabbles 19d agoIf it is a skill, it's something that can be learned by both humans and LLMs.
- threethirtytwo 19d agoI guess the better question is, can this skill be learned without being an extreme expert in mathematics? Can I be a sort of intelligence highschool student (not incredibly exceptional at all) and have the LLM teach me the required math for a specific problem and guide it towards a solution? I think the answer to this question is becoming, in general, a big yes. LLMs can arrive at a solution via two paths. The first one is via heavy guidance by an adept expert in the domain. The other path is via brute force... multiple agents (the more the faster it can arrive at a solution). The later path is what enables anybody to do this.
- empath75 19d agoIMO, it _currently_ requires a lot of skill because it will frequently take wrong turns and dead ends and needs suggestions and steering to get there. You do need to understand what it is doing at least a little bit and to understand the general landscape of the problem, and to at least have a sense of whether and why the problem is tractable at all.
- htrp 19d agothe fact that you have to encourage these models and tell them that they can solve these problems and warm up on easier problems seems to indicate that there's something to AI pairing above and beyond prompt
- bananaflag 19d agoYeah it s because they have a strong prior on unsolved problems being unsolvable. Once the idea of AI routinely solving conjectures enters the training data this encouragement will disappear like 2023-era prompt engineering did.
- arscan 19d agoI would think this type of behavior (ugh, or dare I say default mindset) by consumer-facing LLMs will always be desirable for ‘hard’ problems (things previously unsolved) because it’s a bit like having saftey mechanisms in place to prevent hallucinations for users incapable of verifying correctness of the output. You’ve got to do a little work to prove you understand that it’s hard but it’s still something the LLM might be able to accomplish.
- rowanG077 19d agoI think this is also a healthy mindset for a person to have in many cases. If my boss asks me "go solve P = NP", as extreme example, I would also give some pushback.
- skybrian 19d agoIt will likely burn a lot of tokens, take a long time, and might not work, so hopefully they'll still ask if you really want to spend the money on the attempt.
- empath75 19d agoI spent about a month walking through proving something with Claude a few months ago and it _constantly_ told me that it was impossible and I should stop working on it, right up until it proved it.
- sp-ti-en-ma-in 19d agopaper: Title: BOUNDED RATIOS FOR LORENTZIAN POLYNOMIALS https://arxiv.org/pdf/2609.05341 https://arxiv.org/pdf/2609.05341
- catpower 19d agoGreat short term achievement but humanity is better served by these kids doing it without AI. The ideas have to come from the next generation (eg would we be worried if a 5 year old wrote the great American novel with AI or not?)
- measurablefunc 19d agoAI is not going away so people will have to get used to it just like they will have to get used to it in software engineering. The alternative is being less productive than people who are happy to use AI to write software & do mathematical research.
- oasisaimlessly 19d agoIt is still an unknown whether an unqualified increase in productivity in the long-term for software engineering is a given.
- qarl 19d agoReally? OK - then let me stand up and vouch that I am at least 20X more productive with AI.
- dermacentor 19d agoIn the long term.
- qarl 19d agoFair enough - it will take some time before the science comes back. But I feel the need to point out - the goalposts for "does AI work" shift daily.
- tom_ 19d agoIn the long term, it'll be at least be the year 2030. Let's not get ahead of ourselves.
- no-name-here 19d agoReal title includes: > Unsolved Problem by Fields Medalist Breached by Two High School Students with AI My title recommendation: Fields Medalist Problem Solved With AI They used AI for “computation, proof idea generation, and editing assistance”. It’s a bit odd how they list the AIs used - “Claude Opus 5, Anthropic and ChatGPT Sol5.6 were used for calculations, proof ideas, and editorial assistance.”
- shafyy 19d ago[flagged]
- random3 19d agonote HEAVILY > The students heavily utilized AI assistants, specifically Claude Opus 5 and GPT-5.6 Sol, for computational exploration, proof idea generation, and editing. this is a bit like Enhanced Olympics(https://www.enhanced.com https://www.enhanced.com), except that you have someone else compete for you. My issue is that it makes it hard to distinguish real insight/work etc. from effectively null one. An old instance of the same issue was with what was called "script kiddie" back in the 90-00s
- gus_massa 18d agoFor short problems the LLM are just too good now, but for long problems they still get in trouble. It's like bicycle or F1 race. It goes faster, but you still have to steer the boat to reach somewhere. (Or probably something in between, like a motorcycle race.) Also, the "kids" were guide by a postdoc, not completely on their own.
- karmakaze 18d agoDifference being anyone can be a "script kiddie". I don't think anyone could direct an AI to proofs like this one.
- dist-epoch 18d ago> 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. ... 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. https://www.anthropic.com/research/riemann-zeta https://www.anthropic.com/research/riemann-zeta
- dataflow 19d agoWhat I'm curious about is how far they would've gotten without the postdoc.
- srean 19d agoThis is a common pattern ahead of admissions season. Now admissions are mostly done I suppose.
- 1299348 19d agoNot peer reviewed. UCLA seems to be full of AI boosters who perform circus tricks.
- Aargau 19d agoWorking backwards from the Navier-Stokes solution, I was able to walk Astra through the path used to solve it. It took some formulation, starting with the problem, then challenging it to look closer at the specific path, and iterating when it got stuck, it was able to reach the solution.
- Founderarcstone 19d agoGreat to see high school students getting attention on this.
- robotpepi 19d agoi wonder if anyone is going to read that.
- axionbraid 19d ago[flagged]
- esafak 19d agoThis looks like a graduate-level proof. Did these high school students really understand what they were doing? I'd like to see what they have to say. https://arxiv.org/pdf/2609.05341 https://arxiv.org/pdf/2609.05341
- thrill 19d agoHaven't you heard? Fields Medalists believe it only counts when they do the solving - not the unwashed.