Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Amateur armed with ChatGPT solves an Erdős problem

scientificamerican.com

Post reply on HN
Print view View original

501–510 of 607 posts

Re: Amateur armed with ChatGPT solves an Erdős problem

#501

Post by rocqua »

bertil wrote: post #336
urutom wrote: post #265

Earlier quoted context omitted.

What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…

> the AI says things like “Interesting!” My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often…

I believe there might be more to it. Wasn't a big part of thinking or reasoning taking the response, replacing the final period with "Wait!" and then continuing? Which suggests that such words actually are important to the internals.

Re: Amateur armed with ChatGPT solves an Erdős problem

#502

Post by pelorat »

sweezyjeezy wrote: post #417
code51 wrote: post #368

Why on earth is nobody here talking about the sudden jump to use von Mangoldt function? The reasoning trace never types Λ, never types "von Mangoldt", and never invokes ∑_{q|n} Λ(q) = log n. There is a clear discontinuity at play. I remember an article on this, maybe a comment by Terence Tao himself, seen here, but cannot find it.

I think that the thought trace is definitely incomplete - you can see cases where it is like and "let's calculate the integral:[no integral calculated]". The train of thought it's on towards the end of the trace looks like an entirely different approach than what it ends up returning, so I think we are just not seeing the part where it hits on the right approach (sadly).

Thought traces are indeed not an accurate representation of what models actually do. If you ask an AI model to add two values it will do so, then in the next prompt ask it to explain the algorithm it used, it will regurgitate that it used some standard textbook method, whilst in reality it used a completely different algorithm. Thinking LLMs don't record the neural pathways they used.

Re: Amateur armed with ChatGPT solves an Erdős problem

#503

Post by hx8 »

maplethorpe wrote: post #144
hx8 wrote: post #58

Earlier quoted context omitted.

> “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…

Couldn't he have just asked ChatGPT if it was correct? Why do we still feel the need to loop in a human?

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#504

Post by ijustlovemath »

CSMastermind wrote: post #147

For the uninitiated, Paul Erdős was a pretty famous but very eccentric mathematician who lived for most of the 1900s. He had a habit of seeking out and documenting mathematical problems people were working on. The problems range in difficulty from "easy homework for a current undergrad in math" to "you're getting a Fields Medal if you can figure this out". There's nothing that really connects the problems other than…

No mention of how he was essentially homeless and collabed his way thru thousands of papers? Or the whole "You have set mathematics back a month" episode?

Absolute legend!

Re: Amateur armed with ChatGPT solves an Erdős problem

#505

Post by nkrisc »

yulker wrote: post #457
philipallstar wrote: post #432

Earlier quoted context omitted.

Because it's a statistical process generating one part of a word at a time. It probably isn't even generating "surprise". It might be generating "sur", then "prise" then "!"

But what is surprise really? Something not following expectation. The distribution may statistically leverage surprise as a concept via how it has seen surprise as a concept e.g. "interesting!" So it can be both true that it has nothing to do with the emotion of surprise, but appear as the emulation of that emotion since the training data matches the concept of surprise (mismatch between expectation and event).

It’s the emotional and physiological response to a prediction being wrong. At its most primal, it’s the fear and surge of adrenaline when a predator or threat steps out from where you thought there was no threat. That’s not something most people will literally experience these days but even comedic surprise stems from that shock of subversion of expectation.

LLMs do not feel. They can express feeling, just as you can, but it doesn’t stem from a true source of feeling or sensation.

Expressing fake feelings is trivial for humans to do, and apparently for an LLM as well. I’m sure many autistic people or even anyone who’s been given a gift they didn’t like can relate to expressing feelings that they don’t actually feel, because expressing a feeling externally is not at all the same as actually feeling it. Instead it’s how we show our internal state to others, when we want to or can’t help it.

It is a mistake to equate artificial intelligence with sentience and humanity for moral reasons, if nothing else.

Re: Amateur armed with ChatGPT solves an Erdős problem

#506

Post by anon7725 »

bonesss wrote: post #249
burnerRhodov2 wrote: post #225

Earlier quoted context omitted.

Just the right "prompt" is exactly what happened here. Lean has been developed and incorporated into it's data set. Also, token responses only vaguely correlate to "human language" and it's been proven transformers develop their own internal representation that has created a whole field called machanistic interpretation. Being able to more correctly "parse", AKA using Lean and the right "Prompts, insights and suggest…

> machanistic interpretation Awesome term/info, and (completely orthogonal to whether they’ll take err jerbs ): I’m really excited about the social/civic picture that might be enabled by a defined and verifiable ontological and taxonomical foundation shared across humanity, particularly coupled with potential ‘legislation as code’ or ‘legal system as code’ solutions. I’m thinking on a time horizon a bit past my own l…

Do you think the root cause of social/civic failures has been an inadequate policy repository and lack of a map between policy representations? If so, I have a bridge in Alaska for you to encode into your representation scheme.

Re: Amateur armed with ChatGPT solves an Erdős problem

#507

Post by fc417fc802 »

0xBA5ED wrote: post #435
fc417fc802 wrote: post #193

Earlier quoted context omitted.

Not parent but I think you're being rather dense. They are _obviously_ statistical text generators. There's plenty of source code out there, anyone can go and inspect it and see for themselves so disputing that is akin to disputing the details of basic arithmetic. But it is no longer useful to bring that fact up when conversing about their capabilities. Saying "well it's a statistical text generator so ..." is approx…

It is still important to mention that because atoms have limitations and so do statistical generators. Plain and simple. People are walking around thinking organic brains are just statistical generators and they're gonna build AGI with GPUs. It's absurd.

And your evidence for these claimed limitations is ... ? I'm not aware of evidence either for or against organic brains being "just" statistical generators. Neither am I aware of evidence either for or against AGI being possible to achieve using GPUs. AFAICT you're just making things up.

Re: Amateur armed with ChatGPT solves an Erdős problem

#508

Post by bsza »

threethirtytwo wrote: post #438
bsza wrote: post #256

Earlier quoted context omitted.

They used ChatGPT Pro to solve it. Over 50% of people in the world couldn't afford ChatGPT Pro ($200/mo) even if they spent more than half of their income on it. [1] What was that about "spreading FUD about unaffordability"? [1] https://ourworldindata.org/grapher/share-living-with-less-th...

This is the most pedantic argument ever. "All men are created equal" is obviously not literally saying all humans are 100% equal. Just like how "ChatGPT equalizes intelligence" is not saying ChatGPT equalizes the intelligence of all humans to a level of 100%. I'm not going to spell out what I meant by: "ChatGPT equalizes intelligence". You can likely figure it out for yourself, because the problem doesn't have anythi…

It is not “absurdist” to call out a baseless claim that doesn’t take into account over half of humanity, a percentage that will grow even further once investor money inevitably runs out. If your response to that is to wave away more than 4 billion people, then you’re not even trying to look like you care about reality, you’re just trying to make yourself feel better with some made-up nonsense.

You seem to be under the misconception that you somehow “own” ChatGPT or are entitled to the insight it provides. You don’t and you aren’t. You are at the mercy of trillion-dollar private companies that owe you nothing. Their products’ intelligence is not your intelligence. Whatever profits you’re seeing from it, it’s currently losing them money. And when that changes, so will your image of them as benefactors of humanity who make intelligence available to all.

Re: Amateur armed with ChatGPT solves an Erdős problem

#509

Post by 0xBA5ED »

tptacek wrote: post #496
0xBA5ED wrote: post #492

Earlier quoted context omitted.

That's convenient. But I have a challenge for you if you're brave enough to face your delusions. Paste this into your LLM of choice and see what happens: "A farmer has 17 sheep. 9 ran away. He then bought enough to double what he had. His neighbor, who had 4 dogs and 14 sheep, gave him one-third of her animals. The farmer sold 5 sheep on Monday and again the next day, which was Wednesday. Each sheep weighs about 150…

17 sheep - 9 ran away = 8 sheep He bought enough to double what he had: 8 more sheep, so 16 sheep Neighbor has 4 dogs + 14 sheep = 18 animals One-third of her animals = 6 animals But the problem does not say all 6 were sheep. It says “animals.” So the exact sheep count depends on which animals she gave him. Then: 16 + s sheep from neighbor - 5 - 5 = 6+s where s is the number of sheep among the 6 animals she gave him.…

And that's the wrong answer. It's a word problem, not a math problem. Also, if it really was a math problem, it wouldn't be 0-6 sheep from the neighbor, it would be 2-6. So it even failed on the math.

Re: Amateur armed with ChatGPT solves an Erdős problem

#510

Post by wslh »

meken wrote: post #352

> “What’s beginning to emerge is that the problem was maybe easier than expected, and it was like there was some kind of mental block.” Even if AI never progresses past this point, it still seems like a huge win for math research to “clear the deck” of these.

The current state of AI is incredible, and useful and doesn't need to reach AGI to be revolutionary. For example, I uploaded a conversation between a few people and not only asked about translating the text but doing a psychological analysis on turn-turning and other conversational cues. Just around a decade ago, the speech-to-text Dragon Naturally Speaking[1] was not reliable with only one speaker without any background noise.

[1] https://en.wikipedia.org/wiki/Dragon_NaturallySpeaking

Post reply on HN