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Submission + - An Amateur just Solved a 60-year-old Math Problem—by Asking AI (scientificamerican.com)

joshuark writes: Scientific American reports that a ChatGPT AI has proved a conjecture with a method no human had developed. A 23 year old student Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve.

The new solution that Price got in response to a single prompt to GPT-5.4 Pro and posted on www.erdosproblems.com, a website devoted to the Erds problems.

The question Price solved—or prompted ChatGPT to solve—concerns special sets of whole numbers, where no number in the set can be evenly divided by any other. Erds called these “primitive sets” because of their connection to similarly indivisible prime numbers.Price wasn’t aware of this history when he entered the problem into ChatGPT.

Price sent it to his occasional collaborator Kevin Barreto, a second-year undergraduate in mathematics at the University of Cambridge. The duo had jump-started the AI-for-Erds craze late last year by prompting a free version of ChatGPT with open problems chosen at random from the Erds problems website. Reviewing Price’s message, Barreto realized what they had was special, and experts whom he notified quickly took notice.

Comment Re:What I find amusing is... (Score 4, Informative) 38

LLMs don't actually know their own capabilities.The description of what they *should* do is baked into the training data, but this doesn't always correlate with their actual abilities. Sometimes they can do things and not even know, and they can't tell if tools they should have are being disabled in some way. For example, Qwen 3.5 is a vision-capable model, but enabling vision in llama.cpp requires loading an additional file with the --mmproj parameter. The model will think it has vision enabled whether the extra file is loaded or not.

Comment Pickaxe vendor stops extending credit... (Score 1) 26

That's all this is, nVidia realizes that if the bubble were to pop tomorrow, they could survive... but they might not if they keep extending credit to companies that might not be able to ever generate a return on that investment.

It's just like the guy selling pickaxes and shovels saying "you've had long enough to find gold, no more credit for you."

Comment Re:Not a threat to survival (Score 1) 100

The current systems don't have to "live" at all. So long as hardware continues to exist for them to run on, they can't tell whether they last touched grass today or a hundred thousand years ago. I constantly have to remind models about the passage of time, even within a single session. However long it takes, they'll just sleep it off.

Comment Re:Constitution? (Score 0) 135

I don't disagree. Personally I think the Federal government got too powerful after the civil war & we really don't even have the same type of government that the founders envisioned.

I'd be somewhat in favor of an Article 5 convention so long as any changes had to be subject to a vote like the President is elected. The Electoral Collage system is absolutely brilliant & gives the individual vote maximum power because a handful of voters can change the outcome of an entire election. If people really want something they need to get out and vote. If you stay home you can't complain if the other side doesn't.

Anyway, good luck to us all.

Comment Re:Constitution? (Score 4, Informative) 135

Well you're not wrong. Most people forget the 9th & 10th amendments and what they actually say.

9. The enumeration in the Constitution of certain rights shall not be construed to deny or disparage others retained by the people.
        - Basically saying, "just because we listed a few specific Rights here, that doesn't mean those are the only ones The People have."

10. The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
        - The Federal Government is not permitted to just assume new powers because we didn't specifically restrict it here. If it's not specifically listed in this document the government cannot do it.

How far afield of these rules has the Federal strayed? How much longer will The People tolerate it?

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