An Amateur Just Solved a 60-Year-Old Math Problem - by Asking AI

Slashdot reader 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 was 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...

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.

The new wave

[Anonymous Coward]

This is what a lot of people get wrong about "AI". The AI itself isn't the special thing on its own. It may not be real AGI but honestly you don't want that because then it wouldn't be a tool. It's the way it can wrap huge volumes of information in a way that is easily manipulated by a human. It's a search engine connected directly to your brain. With a little creativity and an AI you would be astounded as to what's possible with careful use.

It's not that different from any other work, just more advanced. L

Re:

[Cthefuture]

Futures generations will look back at these times and how "simple" and "awesome" they were. You're part of something bigger and you have a front row seat.

Not sure future generations will look back at all

[rsilvergun]

I think we are at the end of History. I think we're going to go into a permanent dark age in the form of techno feudalism. Other that or going to handle launch codes to some religious lunatics and they're going to wipe us all off the face of the Earth.

I don't see a third option and I hope I'm dead before the worst of it.

Like there is a huge automation push going on right now it is almost guaranteed the cause of minimum 25% permanent unemployment and our civilization is still hung up on if you don't

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[dfghjk]

Correct, those in charge seek to turn us all into mulch, they view people as property that they haven't yet stolen. They seek to replace you, deny you an ability to earn a wage, take everything you own, enslave you and have you starve to death homeless, voteless, and without rights or healthcare. This is capitalism in its purest form, only with a few people capable of taking everything with the aid of machines that we collectively pay for. And they are in league with religious freaks that seek to bring ab

Levels of abstraction matter

[shanen]

[Overlooking the nameless BF.]

Most relevant recent citation is Stolen Focus by Johann Hari, but my use of "level of abstraction" goes back many years and the more modern label is probably "reference frame". Also related to contextual meaning.

Fundamental problem is the accumulation of too much information, so we have to attack problems by reframing them at the right level and by using the correct tools to manipulate them within that appropriate frame. Not at all surprised that someone who hasn't mastered a

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[dfghjk]

"This is what a lot of people get wrong about "AI""
What is "this"? And who gets it wrong?

"The AI itself isn't the special thing on its own."
Which AI is "the AI"? It's not one thing, but it is a "special thing on its own".

"...because then it wouldn't be a tool."
Is your brain a tool? Are workers a tool? What makes AGI not a tool? AGI is merely a nebulous goalpost. a talking point to get money.

"It's a search engine connected directly to your brain"
So is your brain. And different AI works differently. Tra

Erds

[602]

lol

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[shanen]

Yeah, it's funny on its face, but when I asked a generative AI about "AI for Erds" and it hallucinated an answer involving ye olde Entity Relationship Diagrams.

Is there a new job category for people who are good at asking questions the generative AIs can't answer properly? I'm pretty sure my batting average against Gemini is way over .300. Combination of nasty questions and wording questions in ways that suggest I might be expecting a particular wrong answer. I'm also considering the possibility that the AI

Just means none of the experts cared enough

[gweihir]

Likely because they have other things to do that are more important. Seriously, digging though old stuff will occasionally lead to some discovery. That is all that happened here.

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[jd]

Whilst you're almost certainly correct (AI would be unlikely to conquer a problem requiring any meaningful original thinking, even with help), this gives the aforementioned student an Erdos number (which is not quite as exciting as a Fields medal, but nothing to sneeze at either) and it's entirely possible that the conjecture will turn out to actually be useful in some area.

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[dfghjk]

"AI would be unlikely to conquer a problem requiring any meaningful original thinking, even with help"

You have no reason to believe that, and I don't think it's true. The human brain does not work on magic, "original thinking" may be beyond us currently but there's no reason to think it will remain unsolved.

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[JoshuaZ]

Mathematician here, and in the same area of research (number theory). This is not a problem where no one one cared. While there are some Erdos problems in this category, this problem is one which was well known enough that I was already familiar with. This is also a problem where multiple people, including Jared Lichtman, who is an up and coming well respected young number theorist, have thought about. And if you go to the page for problem 1196 on the general Erdos Problem data base, you'll see three refere

Ahem

[fubarrr]

Since all it can output is whatever it managed to Google in the internet, then it mens some already had a speculative solution to the problem, which he, or she never properly pushed into the scholarly society.

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[Tablizer]

How easy is it to back-track through the model to find the main source(s) of the answer?

No, that's not how gen AI works

[shanen]

But I don't have the math skills to explain properly, so I'll resort to a kind of metaphor. The real "talent" of AIs is in sounding plausible based on lots of examples of "what sounds good". In this case, it turned out that Occam's Razor worked, and an explanation that sounded plausible turned out to be a valid proof.

But I speculate there were many failures, some of them hilarious, though the human "author" only published the good guess.

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[JoshuaZ]

Mathematician here. This is highly unlikely to be the case. This was a moderately well known Erdos problem (not one of the famous ones but well known enough that I had seen it before this). If there were a solution on the internet we would likely have already found it, especially because there's been a concerted effort to track down what is happening with all the Erdos problems in the last few years. Moreover, even after this problem was solved, people then went and tried hard to find a copy of the solution

We know

[nospam007]

Somebody already told us.

Unfortunately we still don't have an anti-dupe AI.

"Do you like apples?"

[realmojo]

"I solved it. How you like them apples?"