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Posted by pr337h4m 1 day ago

Amateur armed with ChatGPT solves an Erdős problem(www.scientificamerican.com)
https://www.erdosproblems.com/1196
653 points | 455 commentspage 6
brcmthrowaway 16 hours ago|
This is not a good Saturday night for humanity
homo__sapiens 17 hours ago||
Big if true.
tomlockwood 18 hours ago||
My big question with all these announcements is: How many other people were using the AI on problems like this, and, failing? Given the excitement around AI at the moment I think the answer is: a lot.

Then my second question is how much VC money did all those tokens cost.

ecshafer 17 hours ago||
I've tried my hand at a few of the Erdos problems and came up short, you didn't hear about them. But if a Mathematician at Harvard solved on, you would probably still hear about it a bit. Just the possibility that a pro subscription for 80 minutes solved an Erdos problem is astounding. Maybe we get some researchers to get a grant and burn a couple data centers worth of tokens for a day/week/month and see what it comes up with?
tomlockwood 15 hours ago||
The question is how many people tried to solve this Erdos problem with AI and how many total minutes have been spent on it.
gdhkgdhkvff 18 hours ago|||
Why do you care about either of those questions?
tomlockwood 17 hours ago||||
Because it could be a massive waste of time and money.
azan_ 11 hours ago|||
Why do you think it's a waste of time and money? I really can't see it.
komali2 16 hours ago|||
Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically? There's entire professions that are essentially worthless to society that exist only to perpetuate the inherent contradictions of this system, why not focus more on all that wasted human effort? Or the fact that everyone has to do some arbitrary sellable labor in order to justify their existence, rather than something they might truly enjoy or might make the world better?
azan_ 11 hours ago||
> Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically?

It's absolutely best allocator of human effort there is. It has some problems but compared to alternatives it's almost perfect.

yfee 8 hours ago|||
No it is the best of what we know.

There’s something else out there that nobody has the imagination to personally figure it out and get alignment toward it.

It can also be true that capitalism is transitory to get to a place where much of the capital one needs is invented.

azan_ 5 hours ago||
Well of course the discussion is only about systems that actually exist, not ones that not only not exist, but also can't be imagined by anyone.
komali2 10 hours ago|||
Looking around, the evidence doesn't seem to support this conclusion. 50% of food thrown away, yet people go hungry. Every privatized industry diminishes in quality and reach. Selects and optimizes for profit rather than for human need.
azan_ 9 hours ago||
> Looking around, the evidence doesn't seem to support this conclusion.

It absolutely does if you look at facts and not "vibes". There are less people starving now than ever now and it's a giant, giant difference. We are tackling more and more diseases thanks to big pharma. Even semi-socialist countries such as China have opened markets. Basically the only countries that do not implement capitalist solutions are the ones you'd never want to live in such as North Korea or Cuba (funny thing - even China urged Cuba to free their markets).

komali2 4 hours ago||
> There are less people starving now than ever now

I see no reason to attribute that to capitalism. Capitalist and non capitalist societies had famines, and capitalist and non capitalist societies industrialized and improved people's material conditions - by raw number of people, non capitalist societies did this for more people.

The PRC indeed has opened their markets, and now has capital allocation issues - their initial chip development programs failed because of market viability issues, and for whatever reason their government didn't put the communism hat on and just nationalize the entire industry like it's done for other ones. More evidence against the supposed increase efficiency and outcomes of privatization and market based R&D and incentives.

North Korea seems to be failing less because of its economic system and more because the entire nation is a cult with a horrifying political system.

It seems quite literally all economic strife in Cuba is due to American sanctions - and in spite of these they still have a lower infant mortality rate than the Americans and make breakthroug medical discoveries.

So again, given the evidence, it seems capitalism is, at best, equally viable to whatever the Soviets and PRC did, in terms of allocating resources and lifting people out of poverty.

Given that we probably all will run out of ways to justify our existence under capitalism through selling our labor within our lifetimes, it seems like a very good time to start considering alternatives. Capitalism has no answer to the question, "what do you do with people when you have an 80% unemployment rate?"

azan_ 3 hours ago||
> by raw number of people, non capitalist societies did this for more people.

That's completely false. Please take your time to verify it, I hope that getting your facts straight will make you reconsider your position (and not get mad at facts).

> The PRC indeed has opened their markets, and now has capital allocation issues - their initial chip development programs failed because of market viability issues, and for whatever reason their government didn't put the communism hat on and just nationalize the entire industry like it's done for other ones.

Don't you think that this argument does not make much sense? If the solution is that easy and has been done numerous times, why would they not do it again? Maybe the real answer is that it's just hard problem, and hard problems take time and serendipity.

> It seems quite literally all economic strife in Cuba is due to American sanctions - and in spite of these they still have a lower infant mortality rate than the Americans and make breakthroug medical discoveries.

But why would they need global trade? Isn't that one of inventions and consequences of capitalism? I don't think global trade is possible without free markets at all, so if global trade is necessary for prosperity, then so is capitalism. Also note that Cuba has approximately 25% higher infant mortality rate (I ask you again to look at the data; note that Cuba has higher infant mortality even though it has been criticized for artificially reducing their stats, e.g. by reclassifying part of infant deaths to fetal deaths) and their medical breakthroughs are nowhere near what US (or China, which now beats US because they... made market for pharma more free) is doing.

> So again, given the evidence, it seems capitalism is, at best, equally viable to whatever the Soviets and PRC did, in terms of allocating resources and lifting people out of poverty.

Again, that's completely false and PRC has seen biggest reductions of poverty AFTER implementing market reforms!

Eufrat 18 hours ago|||
I think we should at least ask the latter, if it turned out it cost $100,000 to generate this solution, I would question the value of it. Erdős problems are usually pure math curiosities AFAIK. They often have no meaningful practical applications.
jasonfarnon 17 hours ago|||
Also, it's one thing if the AI age means we all have to adopt to using AI as a tool, another thing entirely if it means the only people who can do useful research are the ones with huge budgets.
peteforde 17 hours ago||
Your logic undoes your point, because the kid who "solved" this technically didn't even have to invest in a degree.
tomlockwood 17 hours ago||
America should fund tertiary education better, and that would solve even more problems.
peteforde 16 hours ago||
Getting off-topic, but as a successful high-school dropout I am compelled to remind anyone reading this that [the American] college [system] is a scam.

That's not to say that there aren't benefits to tertiary education, for many people in different contexts. It's just not the golden path that it's made out to be.

Many people currently in college are just wasting their money and should enroll in trades programs instead.

Meanwhile, nothing about being in or out of school is mutually exclusive to using LLMs as a force multiplier for learning - or solving math problems, apparently.

anematode 18 hours ago||||
Neither does the Collatz conjecture, Fermat's last theorem, ....

(Of course, those problems are on another plane than this one.)

Eufrat 17 hours ago||
But that’s exactly my point.

These are absolutely worth studying, but being what they are, nobody should be dumping massive amounts of money on them. I would not find it persuasive if researchers used LLMs to solve the Collatz conjecture or finally decode Etruscan. These are extremely valuable, but it is unlikely to be worth it for an LLM just grinding tokens like crazy to do it.

azan_ 11 hours ago|||
If solving even the biggest problems in pure maths is not worth it for you, then I guess we should stop all the pure maths research - researchers are getting paid much more than potential token spend, frequently for decades and they frequently work on much less important and easier problems.
mhb 17 hours ago||||
Is it worth it to buy a super-yacht?
Eufrat 17 hours ago||
No.
anematode 17 hours ago|||
Maybe... but I would love if 1% of the investment in AI were redirected to the mathematics education and professional research that would allow progress on any of these problems...
inerte 17 hours ago||||
I would question at $60k. At $100k is a steal.
dinkumthinkum 16 hours ago|||
No meaningful, practical applications? You realize that sounds incredibly naive in the history of mathematics, right? People thought this way about number theory in general, and many other things that turned out to have quite important practical applications. Your statement is also a bit odd in that researchers are already paid throughout their whole careers to solve such problems. I don't know.
Eufrat 15 hours ago||
> You realize that sounds incredibly naive in the history of mathematics, right?

This is after the fact justification. You are arguing that because a thing (number theory) showed practical applications we should have dumped a lot more effort into it. There is no basis for this argument whatsoever; it also seems to involve inventing a time machine. Number theory had no practical applications until the development of public-key cryptography, but you cannot make funding decisions based on the future since it’s unknowable.

Once we get something working, sure, you can justify more aggressive investment. This is not to say that we should not invest in pie-in-the-sky ideas. We absolutely should and need to. Moonshot research or even somewhat esoteric research is vital, but the current investment in AI is so far out of the ballpark of rational. There’s an energy of a fait accompli here, except it’s still very plausible this is all unsustainable and the market implodes instead.

azan_ 11 hours ago||
> Number theory had no practical applications until the development of public-key cryptography, but you cannot make funding decisions based on the future since it’s unknowable.

You are completely missing the point. The point is that we should invest in pure maths because it has always been an investment with very good ROI. The funding should be focused on what experts believe will advance pure maths more (not whether we believe that in 100 years this specific area will find some application) and that's pretty much what we are doing right now. I think it's just your anti-AI sentiment that's clouding your judgement and since AI succeeded in proving pure maths results, you are inclined to downplay it by saying that well, pure maths is worthless anyway.

peteforde 17 hours ago||
Can you imagine how many bags of chips we could buy if we stopped funding cancer research?

It's so expensive!

tomlockwood 17 hours ago||
Can you imagine how much ChatGPT cancer research we could fund if we stopped funding cancer research?
quijoteuniv 13 hours ago||
AI is my favourite weird collaborator
jchook 14 hours ago||
Is the conjecture not trivially sound at an intuition level? It's surprising that this proof was difficult.
mhb 17 hours ago||
> He’s 23 years old and has no advanced mathematics training.

How is he even posing the question and having even a vague idea of what the proof means or how to understand it?

hx8 17 hours ago||
> “I didn’t know what the problem was—I was just doing Erdős problems as I do sometimes, giving them to the AI and seeing what it can come up with,” he says. “And it came up with what looked like a right solution.” He sent it to his occasional collaborator Kevin Barreto, a second-year undergraduate in mathematics at the University of Cambridge.

Seems like standard 23 year old behavior. You're spending $100-$200/mo on the pro subscription, and want to get your money's worth. So you burn some tokens on this legendarily hard math problem sometimes. You've seen enough wrong answers to know that this one looks interesting and pass it on to a friend that actually knows math, who is at a place where experts can recognize it as correct.

Seems like a classic example of in-expert human labeling ML output.

lIl-IIIl 15 hours ago|||
According to the article he was using the free ChatGpt tier at first, I til someone gifted him a Pro subscription to encourage "vibe-mathing'.
maplethorpe 15 hours ago|||
Couldn't he have just asked ChatGPT if it was correct? Why do we still feel the need to loop in a human?
hx8 1 hour ago|||
There's two major reasons to loop in humans.

1. How can we be sure ChatGPT knows it's correct or not? It gives out incorrect answers to complex questions all the time. The very fact that it gave out a correct answer is worth talking about.

2. The type of human that can verify a mathematical proof is also the type of human that knows the appropriate communication channels to let every other math-human know about the proof. The math-humans will know the impact that proof has on math, and how to apply it.

Jtarii 8 hours ago|||
Because society is run by humans, not chatpgt.
ChrisGreenHeur 17 hours ago||
my guess would be due to having an interest in the field
ghstinda 17 hours ago||
Scientific American going out of business next lol, weak headline. Chat GPT let's have a better headline for the God among Men that realized the capability of the new tool, many underestimate or puff up needlessly. Fun times we live in. One love all.
nadermx 15 hours ago|
This just shows that with the right training, in this case a thesis on erdos problems, they where able to prompt and check the output. So still needed the know how to even being to figure it out. "Lichtman proved Erdős right as part of his doctoral thesis in 2022."
fwipsy 15 hours ago|
Lichtman is an expert who commented for the story. Liam Price is the one who prompted ChatGPT. "He’s 23 years old and has no advanced mathematics training."
nadermx 15 hours ago||
“I didn’t know what the problem was—I was just doing Erdős problems as I do sometimes, giving them to the AI and seeing what it can come up with,” he says. “And it came up with what looked like a right solution.”

"He sent it to his occasional collaborator Kevin Barreto, a second-year undergraduate in mathematics at the University of Cambridge."

So basically two undergrads/graduates in math, "advanced" is subjective at that point.

fwipsy 15 hours ago||
I don't see where it says Price was an undergraduate/graduate in math.
nadermx 15 hours ago||
I don't see where it doesn't say he is, I feel its implied. Another source, proves me right? https://www.newscientist.com/article/2511954-amateur-mathema...

https://archive.is/oQvO4

fwipsy 15 hours ago||
It's implied by "no advanced mathematics training?"

The article you linked (thanks for the unpaywalled link, by the way) describes him only as an amateur mathematician, but describes Barreto as a math student. If they were both math students, I feel it would say so?

Or perhaps you're arguing it's implicit in him having solved the problem? If so, you're just assuming your conclusion. "AI didn't prove it by itself; Price was a mathematician. Well, he must have been a mathematician to be able to prove it!"

nadermx 14 hours ago||
I'm saying that it wasn't a random person who had no training in math, still miraculous achievement; just trying to show they still had to study maths to even understand how to present the problem and verify it.