> 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.”
Working 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.
the 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
They are relying on training data of humans talking about how hard these problems are. Same way an un-reminded Claude gives estimates for work that are as if a human is doing it by hand, but then will drop them by 20x if you remind them it’s going to do the work.
I 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.
I 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.
Agree 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
I'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.
You seem to be imagining completely independent areas of competence, but I don't think that's a reasonable interpretation of what they wrote.
Great 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?)
AI 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.
Real 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.”
They also used a computer, the internet, electricity and many other technologies. Why single out LLMs?
Great to see high school students getting attention on this.
Working 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.
paper:
Title: BOUNDED RATIOS FOR LORENTZIAN POLYNOMIALS
https://arxiv.org/pdf/2609.05341
If you replace "pdf" with "abs" the link sends you to the arXiv landing site.
Like so: https://arxiv.org/abs/2609.05341
the 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
They are relying on training data of humans talking about how hard these problems are. Same way an un-reminded Claude gives estimates for work that are as if a human is doing it by hand, but then will drop them by 20x if you remind them it’s going to do the work.
Yeah 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.
I 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.
What I'm curious about is how far they would've gotten without the postdoc.
This is a common pattern ahead of admissions season. Now admissions are mostly done I suppose.
I 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.
If it is a skill, it's something that can be learned by both humans and LLMs.
Agree 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
You still have to be able to verify the solution to say that it's solved, so I'd say no.
I'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.
You seem to be imagining completely independent areas of competence, but I don't think that's a reasonable interpretation of what they wrote.
Not peer reviewed. UCLA seems to be full of AI boosters who perform circus tricks.
Great 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?)
AI 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.
It is still an unknown whether an unqualified increase in productivity in the long-term for software engineering is a given.
Really? OK - then let me stand up and vouch that I am at least 20X more productive with AI.