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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:Tell them to piss off (Score 1) 195

He's only bound by the fundamental laws of the universe and/or biology. SCOTUS finally found their spine a year and change too late, and they're just being disregarded. "Fuck you, I'm increasing the tariffs you told me I can't have at all". Why should we reasonably expect any other behavior at this point?

But one of the fundamental laws is "you can't compel something to exist just because you want it to". If there is no product to deliver, then a government could attempt to strong-arm them economically—but demanding they provide a product they don't have is just going to backfire the way Russia's absurd fine on Google has. Funny how businesses that get screwed over by a government make a point of assisting (or at least tolerating) the enemies of that government.

Comment Re:Much of it should have happened pre-AI (Score 1) 85

And I got tired of spending all day writing the same report every two weeks, so I also turned it into an Excel spreadsheet. Then rather than working up a full presentation of that report, I automated sending it to Word where it could be prettied up in under an hour. Once it got to that point, I was compelled to share it with everyone else but I had never intended to accommodate everyone else's workflow, and next thing I know, supporting the tool I developed for myself had become half my job.

And then the company got sold to a much larger competitor, in part because of that tool making everyone look better than they actually were. I knew people who had been run into the ground by said larger company and chose to leave. Maybe I should have kept a lid on that tool and others I'd created, but I didn't just want to make my job easier. I wanted to make *the* job easier. It probably wouldn't have mattered, the company was either going to sell or fold whether they adopted my tools or not.

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