> 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.”
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 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.
It 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.
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.
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?)
I think it's more like how anyone learning to play chess is going to use chess engines, but you can't learn to play by always asking the chess engine for the answer.
I expect that all mathematicians are going to be working with power tools, so they might as well learn about that. They will still need to do math exercises by hand to learn the material.
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.
Would I be wrong to assume that you are building end-user applications?
If people use AI for libraries, OSs, and mission critical software, the apparent productivity gains would have to be weighed against the reliability and performance hits that bubble up to the things that are built on them and rely on them.
In my experience - a robust testing harness will get you the safety you need. And most software you describe has such testing.
I think the Bun port is a great example where testing enabled a very successful implementation. (Both the original tests themselves and runtime comparisons to the previous implementation.)
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 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.
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. 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.
> 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.”
Title: BOUNDED RATIOS FOR LORENTZIAN POLYNOMIALS
https://arxiv.org/pdf/2609.05341
Once the idea of AI routinely solving conjectures enters the training data this encouragement will disappear like 2023-era prompt engineering did.
I expect that all mathematicians are going to be working with power tools, so they might as well learn about that. They will still need to do math exercises by hand to learn the material.
"Corruption is not going away so people will have to get used to it. The alternative is making less money than people who are happy to take bribes."
If people use AI for libraries, OSs, and mission critical software, the apparent productivity gains would have to be weighed against the reliability and performance hits that bubble up to the things that are built on them and rely on them.
I think the Bun port is a great example where testing enabled a very successful implementation. (Both the original tests themselves and runtime comparisons to the previous implementation.)
But I feel the need to point out - the goalposts for "does AI work" shift daily.
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.
You seem to be imagining completely independent areas of competence, but I don't think that's a reasonable interpretation of what they wrote.