Unsolved Problem by Fields Medalist Breached by Two High School Students
htx.com
htx.com
> 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 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), 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
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.
Title: BOUNDED RATIOS FOR LORENTZIAN POLYNOMIALS
Once the idea of AI routinely solving conjectures enters the training data this encouragement will disappear like 2023-era prompt engineering did.
You seem to be imagining completely independent areas of competence, but I don't think that's a reasonable interpretation of what they wrote.
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.
But I feel the need to point out - the goalposts for "does AI work" shift daily.
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.)
Tests can show you problems, if you can find them, but they cannot show that there are no problems. Property based testing or fuzzing gets your more coverage, and is a good step, but it is still nothing compared to proving things or understanding how something is built and that it is solid. Testing works towards checking for reliability and robustness, but often it's only 10% (?) of the job.
I'm curious - is there any data on the Bun port error rate? I think that would be very indicative of how successful or not the testing is.
"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."
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.
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.