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Unsolved Problem by Fields Medalist Breached by Two High School Students

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Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#41

Post by empath75 »

kelseyfrog wrote: post #40
no-name-here wrote: post #7

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.”

It means that the solution is merely an interpolation of existing work and not fundamentally innovative as AI can only regurgitate, never creating something new.

This is such a silly thing to say in 2026

Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#43

Post by selectodude »

adamddev1 wrote: post #30
measurablefunc wrote: post #11

Earlier quoted context omitted.

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.

A similar line of thought is used to justify corruption: "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."

I can’t run a corruption racket in my basement.

Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#44

Post by empath75 »

bananaflag wrote: post #9
htrp wrote: post #3

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

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 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.

Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#45

Post by empath75 »

Xcelerate wrote: post #2

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.

IMO, 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.

Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#46

Post by measurablefunc »

adamddev1 wrote: post #30
measurablefunc wrote: post #11

Earlier quoted context omitted.

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.

A similar line of thought is used to justify corruption: "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."

People used to complain about compilers as well.

Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#47

Post by btilly »

adamddev1 wrote: post #30
measurablefunc wrote: post #11

Earlier quoted context omitted.

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.

A similar line of thought is used to justify corruption: "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."

The fact that a similar argument can be made does not mean that it is wrong.

Socrates famously made the opposing side of the argument against writing. Which is why we mostly know of him through Plato, who did believe in writing.

And to your corruption example. If you live in a society where corruption is normal and expected, you will be worse off if you are unwilling to be corrupt. It is indeed a local optima. But we are all, of course, better off if we live in a society where corruption is punished. To me, the worst thing about modern US politics, is that it's encouraging us to see ourselves as living in a world where corruption exists and is tolerated.

Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#48

Post by adamddev1 »

qarl wrote: post #36
adamddev1 wrote: post #31

Earlier quoted context omitted.

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.)

Testing is an extremely inadequate measure of reliability and robustness.

Re: Unsolved Problem by Fields Medalist Breached by Two High School Students

#49

Post by adamddev1 »

measurablefunc wrote: post #46
adamddev1 wrote: post #30

Earlier quoted context omitted.

A similar line of thought is used to justify corruption: "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."

People used to complain about compilers as well.

Compilers are deterministic.
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