upvote
Remember when people thought multiplying numbers, remembering a large number of facts, and being good at rote calculations was intelligence?

Some people think that multiplying numbers, remembering a large number of facts, and being good at calculations is intelligence.

Most intelligent people do not think that.

Eventually, we will arrive at the same conclusion for what LLMs are doing now.

reply
Remember when people thought solving Erdos problems required intelligence? Is there anything an LLM could ever do that would cound as intelligence? Surely the trend has to break at some point, if so what would be the thing that crosses the line to into real intelligence?
reply
> Remember when people thought solving Erdos problems required intelligence? Is there anything an LLM could ever do that would cound as intelligence?

Hah. It reminds me of this great quote, from the '80s:

> There is a related “Theorem” about progress in AI: once some mental function is programmed, people soon cease to consider it as an essential ingredient of “real thinking”. The ineluctable core of intelligence is always in that next thing which hasn’t yet been programmed. This “Theorem” was first proposed to me by Larry Tesler, so I call it Tesler’s Theorem: “AI is whatever hasn’t been done yet.”

We are seeing this right now in the comments. 50 years later, people are still doing this! Oh, this was solved, but it was trivial, of course this isn't real intelligence.

reply
That is a “gotcha” born of either ignorance (nothing wrong with that, we’re all ignorant of something) or bad faith. Definitions shift as we learn more. Darwin’s definition of life is not the same as Descartes’ or Plato’s or anyone in between or since because we learn and evolve our thinking.

Are you also going to argue definitions of life before we even learned of microscopic or single cell organisms are correct and that the definitions we use today are wrong? That they are shifting goal posts? That “centuries later, people are still doing this”? No, that would be absurd.

reply
I don't see it as a gotcha. Just an (evergreen, it seems) observation that people will absolutely move the goalposts every time there's something new. And people can be ignorant outsiders or experts in that field as well.

For example, ~2 years ago, an expert in ML publicly made this remark on stage: LLMs can't do math. Today they absolutely and obviously, can. Yet somehow it's not impressive anymore. Or, and this is the key part of the quote, this is somehow not related to "intelligence". Something that 2 years ago was not possible (again, according to a leading expert in this field), is possible today. And yet this is somehow something that they always could do, and since they're doing it today, is suddenly no longer important. On to the next one!

No idea why this is related to darwin or definitions of life. The definitions don't change. What people considered important 2 years ago, is suddenly not important anymore. The only thing that changed is that today we can see that capability. Ergo, the quote holds.

reply
> For example, ~2 years ago, an expert in ML

See, that’s a poor argument already. Anyone could counter that with other experts in ML publicly making remarks that AI would have replaced 80% of the work force or cured multiple diseases by now, which obviously hasn’t happened. That’s about as good an argument as when people countered NFT critics by citing how Clifford Stoll said the internet was a fad.

> made this remark on stage: LLMs can't do math. Today they absolutely and obviously, can.

How exactly are “LLMs can’t” and “do math” defined? As you described it, that sentence does not mean “will never be able to”, so there’s no contradiction. Furthermore, it continues to be true that you cannot trust LLMs on their own for basic arithmetic. They may e.g. call an external tool to do it, but pattern matching on text isn’t sufficient.

> The definitions don't change.

Of course they do, what are you talking about? Definitions change all the time with new information. That’s called science.

reply
The definition of "can/cannot do math" didn't change. That's not up for debate. 2 years ago they couldn't solve an erdos problem (people have tried, Tao has tried ~1 year ago). Today they can.

Definitions don't change. The idea that now that they can it's no longer intelligence is changing. And that's literally moving the goalposts. Read the thread here, go to the bottom part. There are zillions of comments saying this.

You are keen to not trying to understand what the quote is saying. This is not good faith discussion, and it's not going anywhere. We're already miles from where we started. The quote is an observation (and an old one at that) about goalposts moving. If you can't or won't see that, there's no reason to continue this thread.

reply
> The definition of "can/cannot do math" didn't change. That's not up for debate.

That is not the argument. The point is that the way you phrased it is ambiguous. “Math” isn’t a single thing, and “cannot” can either mean “cannot yet” or “cannot ever”. I don’t know what the “expert” said since you haven’t provided that information, I’m directly asking you to clarify the meaning of their words (better yet, link to them so we can properly arrive at a consensus).

> Definitions don't change.

Yes they do! All the time!

https://www.merriam-webster.com/wordplay/words-that-used-to-...

> And that's literally moving the goalposts.

Good example. There are no literal goal posts here to be moved. But with the new accepted definition of the words, that’s OK.

> There are zillions of comments saying this.

Saying what, exactly? Please be clear, you keep being ambiguous. The thread barely crossed a couple of hundred comments as of now, there are not “zillions” of comments in agreement of anything.

> You are keen to not trying to understand what the quote is saying. (…) If you can't or won't see that, there's no reason to continue this thread.

Indeed, if you ascribe wrong motivations and put a wall before understanding what someone is arguing, there is indeed no reason to continue the thread. The only wrong part of your assessment is who is doing the thing you’re complaining about.

reply
He’s a booster and I don’t think he argues in good faith.

He seems to be fixated on this notion that humans are static and do not evolve - clearly this is false. What people thought as being a determinant for intelligence also changes as things evolve.

reply
I've spend a good chunk of time formalising mathematics.

Doing formalized mathematics is as intelligent as multiplying numbers together.

The only reason why it's so hard now is that the standard notation is the equivalent of Roman numerals.

When you start using a sane metalanguage, and not just augmrnted English, to do proofs you gain the same increase in capabilities as going from word equations to algebra.

reply
>the standard notation is the equivalent of Roman numerals.

But the Roman numerals are easy. I was able to use them before 1st grade and I can't touch any "standard notation" to this day.

reply
Well, the famous Turing test was evidently insufficient. All that happened is that the test is dead and nobody ever mentions it anymore. I'm not sure that any other test would fare any better once solved.
reply
When will LLM folks realize that automated theorem provers have existed for decades and non-ML theorem provers have solved non-trivial Math problems tougher than this Erdos problem.

Proposing and proving something like Gödel's theorem's definitely requires intelligence.

Solving an already proposed problem is just crunching through a large search space.

reply
Automated theorem provers can't prove this problem. Which non-trivial Math problem you think are thougher than this Erdos problem?
reply
So the only intelligent people in history are those who invent new fields of mathematics, got it.

You can just about make out those goalposts on the surface of the moon with a good telescope at this point.

reply
"Hi ChatGPT, propose and prove something radically new in the genre of Gödel's theorem."

How is this not just another proposed problem (albeit with a search space much larger than an Erdos problem's)?

reply
I think the point the GP is making is that Gödel's theorem wasn't part of any "genre". Gödel, or somebody, had to invent the whole field, and we haven't seen LLMs invent new fields of mathematics yet.

But this isn't a fair bar to hold it to. There are plenty of intelligent people out there, including 99% of professional mathematicians, who never invent new fields of mathematics.

reply
I've had a similar notion that Time() is a necessary test function. Maybe it's because of the limitations of human cognition. (We have biases and blind-spots and human intelligence itself is erratic.)

I find it's helpful to avoid conflating the following three topics:

/1/ Is the tool useful?

/2/ At scale, what is the economic opportunity and social/environmental impact?

/3/ Is the tool intelligent?

Casual observation suggests that most people agree on /1/. An LLM can be a useful tool. (Present case: someone found a novel approach to a proof.) So are pocket calculators, personal computers, and portable telephones. None of these tools confers intelligence, although these tools may be used adeptly and intelligently.

For /2/, any level of observation suggests that LLMs offer a notable opportunity and have a social/environmental impact. (Present case: students benefitted in their studies.) A better understanding comes with Time() ... our species is just not good at preparing for risks at scale. The other challenge is that competing interests may see economic opportunities that don't align for social/environmental Good.

Topic /3/ is of course the source of energetic, contentious debate. Any claim of intelligence for a tool has always had a limited application. Even a complex tool like a computer, a modern aircraft, or a guided missile is not "intelligent". These tools are meant to be operated by educated/trained personnel. IBM's Deep Blue and Watson made headlines -- but was defeating humans at games proof of Intelligence?

On this particular point, we should worry seriously about conferring trust and confidence on stochastic software in any context where we expect humans to act responsibly and be fully accountable. No tool, no software system, no corporation has ever provided a guarantee that harm won't ensue. Instead, they hire very smart lawyers.

reply
None of it is really from logical thought. The rationalizations don't make any sense, but they haven't for a while. It's an emotional response. Honestly, It's to be expected.
reply
It's because HN is not really full of smart people. It's full of people who think they're smart and take pride in that idea that they're pretty intelligent.

ChatGPT equalizes intelligence. And that is an attack on their identity. It also exposes their ACTUAL intelligence which is to say most of HN is not too smart.

reply
> ChatGPT equalizes intelligence

Citation needed

reply
how can you ask this question with on a post titled "Amateur armed with ChatGPT solves an Erdős problem"???? are you looking for some randomised control trial? omg
reply
We just look at comments from AI boosters and it is self-evident that no intelligence is being equalized.
reply
Idk, going out on a limb and guessing the folks who hang out on erdosproblems.com aren’t run-of-the-mill dumbasses. The prompt, if you look at it, is actually quite clever. Not as clever as the proof. But far from the equalization OP posits.
reply
Directionally it is correct - an amateur wouldn’t be able to do this without ChatGPT. You can’t expect maximal democratisation
reply
> ChatGPT equalizes intelligence

Yes, I love living in communism too. Imagine if you had to pay money for it or something. The wealthiest people would get unrestricted access to intelligence while the poor none. And the people in the middle would eventually find themselves unable to function without a product they can no longer afford. Chilling, huh? Good thing humans are known for sharing in the benefits of technological progress equally. /s

reply
Huh?

Before ChatGPT it costs ~$100,000 to aquire intelligence good enough to solve this Erdos problem, now it costs ~$200.

I'm really confused at what you are even taking an issue with.

reply
what? the post is literally titled "Amateur armed with ChatGPT solves an Erdős problem". stop spreading FUD about unaffordability
reply
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...

reply
They didn't buy ChatGPT Pro themselves. You could've done the same as the students in the article and get a free subscription if you were interested in this instead of trolling.
reply
> You could've done the same

Please show me the steps to get a $200 subscription for free that works 100% of the time regardless of who you are. I'm listening.

reply
ChatGPT flattened the difference between top .0001 percentile mathematician and an amateur. This is the definition of making intelligence more available.

You are exaggerating the situation by essentially claiming since some people can’t afford 200 dollars this means ChatGPT is not democratising intelligence. It’s a bit strange to claim this because according to you it only becomes affordable when maximal number of people can afford it. It’s a bit childish.

Directionally it is democratising. Are more people able to afford higher level intelligence? Yes.

reply
> ChatGPT flattened the difference between top .0001 percentile mathematician and an amateur

It flattened the difference between a top epsilon percentile mathematician and an amateur with money. It didn't flatten the difference between an amateur with a little money and an amateur with a lot of money. It widened it. That's the part I'm scared about.

You are shrugging this off because it currently isn't that expensive. But we're talking about the massively subsidized price here, which is bound to get orders of magnitude higher when the bubble pops. Models are also likely to get much better. If it gets to a point where the only way to obtain exceptionally high intelligence is with an exceptionally high net worth and vice versa, how is that going to democratize anything?

reply
Proving a negative is a pretty high bar. You also have the problem of defining "real intelligence", which I suspect you can't.
reply
Intelligence is Intelligence. It's intelligent because it does intelligent things. If someone feels the need to add a 'real' and 'fake' moniker to it so they can exclude the machine and make themselves feel better (or for whatever reason) then they are the one meant to be doing the defining, and to tell us how it can be tested for. If they can't, then there's no reason to pay attention to any of it. It's the equivalent of nonsensical rambling. At the end of the day, the semantic quibbling won't change anything.
reply
> It's intelligent because it does intelligent things.

Most people would consider someone who can calculate 56863*2446 instantly in their head to be intelligent. Does that mean pocket calculators are intelligent? The result is the same.

> then they are the one meant to be doing the defining, and to tell us how it can be tested for. If they can't, then there's no reason to pay attention to any of it.

That is the equivalent of responding to criticism with “can you do better?”. One does not need to be a chef (or even know how to cook) to know when food tastes foul. Similarly, one does not need to have a tight definition of “life” to say a dog is alive but a rock isn’t. Definitions evolve all the time when new information arises, and some (like “art”) we haven’t been able to pin down despite centuries of thinking about it.

reply
>Most people would consider someone who can calculate 56863*2446 instantly in their head to be intelligent. Does that mean pocket calculators are intelligent? The result is the same.

If you wanted to insist a calculator wasn't intelligent and satisfy my conditions then you can. At the very least you can test for the sort of intelligence that is present in humans but absent from calculators and cleanly separate the two. These are very easy conditions if there is some actual real difference.

>That is the equivalent of responding to criticism with “can you do better?”. One does not need to be a chef (or even know how to cook) to know when food tastes foul.

No it's not, and this is a silly argument. Foul food tastes different. Sometimes it even looks different. You can test for it and satisfy my conditions.

You come across a shiny piece of yellow metal that you think is gold. It looks like gold, feels like gold and tests like gold. Suddenly a strange fellow comes about insisting that it's not actually gold. No, apparently there is a 'fake' gold. You are intrigued so you ask him, "Alright, what exactly is fake gold, and how can I test or tell them apart ?". But this fellow is completely unable to answer either question. What would you say about him ? He's nothing more than a mad man rambling about a distinction he made up in his head.

What I'm asking you to do is incredibly easy and basic with a real distinction. I'm not going to tell you to stop believing in your fake gold, but I am going to tell you I and no one else can be expected to take you seriously.

reply
LLMs are definitely intelligent - just not general like humans, and very very jagged (succeedingand failing in head-scratching ways).
reply
Well it still gets easy problems wrong

With real general intelligence you'd expect it to solve problems above a certain difficulty with a good clip

reply
That "it" is a huge variety and range of things...
reply
For one, everything its 'intelligence' knows about solving the problem is contained within the finite context window memory buffer size for the particular model and session. Unless the memory contents of the context window are being saved to storage and reloaded later, unlike a human, it won't "remember" that it solved the problem and save its work somewhere to be easily referenced later.
reply
For one, everything humans' "intelligence" knows about solving the problem is contained within the finite brain size for the particular person and life. Unless the memory contents of the brain are being saved to storage and reloaded later, it won't "remember" that it solved the problem and save its work somewhere to be easily referenced in a later life.
reply
There's humans that have memory issues, or full blown Anterograde amnesia.
reply
There are humans who can’t read. That doesn’t mean Grammarly is “intelligent”. These things are tools - nothing more, nothing less.
reply
What your describing sounds more like the model is lacking awareness than lacking intelligence? Why does it need to know it solved the problem to be intelligent?
reply
We say African Elephants are intelligent for a number of reasons, one of which is because they remember where sources of water are in very dry conditions, and can successfully navigate back to them across relatively large distances. An intelligent being that can't remember its own past is at a significant disadvantage compared to others that can, which is exactly one of the reasons why alzheimers patients often require full time caregivers.
reply
There's probably a limit to how intelligent something can be with no long term memory, but solving Erdos problems in 80 minutes is clearly not above it, and I think the true limit is probably much higher than that.
reply
You are confusing lack of intelligence with the presence of impairment.
reply
As another commenter pointed out these models are being trained how to save and read context into files so denying them to use such an ability that they have just makes your claim tautological.
reply
All modern harnesses write memory files for context later.
reply
<edit> My mistake. Responded to a bot but can't delete now. Sorry. <edit>
reply
No, but I'm interested to know what it is?
reply
I think one day the VCs will have given the monkeys on typewriters enough money that these kinds of comments can be generated without human intervention.
reply
[dead]
reply
You're really telling on yourself if you think LLM is intelligence
reply
This is real intelligence is the bear position, so I think it’s real intelligence.
reply
And how about the creative rationalizations about how statistical text generation is actual intelligence? As if there is any intent or motive behind the words that are generated or the ability to learn literally any new thing after it has been trained on human output?
reply
2022 called, wants this argument back. When you're "statistically generating text" to find zero-day vulnerabilities in hard targets, building Linux kernel modules, assembly-optimizing elliptic curve signature algorithms, and solving arbitrary undergraduate math problems instantaneously --- not to mention apparently solving Erdos problems --- the "statistical text" stuff has stopped being a useful description of what's happening, something closer to "it's made of atoms and obeys the laws of thermodynamics" than it is to "a real boundary condition of what it can accomplish".

I don't doubt that there are many very real and meaningful limitations of these systems that deserve to be called out. But "text generation" isn't doing that work.

reply
But the systems that do that impressive work are no longer just LLMs. Look at the Claude Code leak - it’s a sprawling, redundant maze relying on tools and tests to approximate useful output. The actual LLM is a small portion of the total system. It’s a useful tool, but it’s obviously not truly intelligent - it was hacked together using the near-trillions of dollars AI labs have received for this explicit purpose.
reply
What does this matter? You can build a working coding agent for yourself extremely quickly; it's remarkably straightforward to do (more people should). But look underneath all the "sprawling tools": the LLM itself is a sprawling maze of matrices. It's all sprawling, it's all crazy, and it's insane what they're capable of doing.

Again if you want to say they're limited in some way, I'm all ears, I'm sure they are. But none of that has anything to do with "statistical text generation". Apparently, a huge chunk of all knowledge work is "statistical text generation". I choose to draw from that the conclusion that the "text generation" part of this is not interesting.

reply
Well, hang on a second - it sounds like you may actually disagree with the user who created this thread. That user claims that these systems exhibit “real intelligence”, and success on this Erdos problem is proof.

You seem to be making the claim that LLMs are statistical text generators, but statistical text generation is good enough to succeed in certain cases. Those are different arguments. What do you actually believe? Are we even in disagreement?

reply
I don't have any opinion about "real intelligence" or not. I'm not a P(doom)er, I don't think we're on the bring of ascending as a species. But I'm also allergic to arguments like "they're just statistical text generators", because that truly does not capture what these things do or what their capabilities are.
reply
Just to clarify because I’m not sure I understand:

So you agree that LLMs are in fact statistical text generators but you don’t like people use that fact in arguments about the capabilities of the things?

reply
It's like a genotype/phenotype distinction, the genotype may be statistical text generator but the phenotype is something much more.
reply
deleted
reply
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 approximately as useful as saying "well it's made of atoms so ...". There are probably some very niche circumstances under which statements of each of those forms is useful but by and large they are not and you can safely ignore anyone who utters them.

reply
He does say that LLMs are just a part of the models used these days.
reply
Solving open math problems is strong evidence of intelligence so there's not really any need for rationalization? I don't understand why intelligence would require intent or motive? Isn't intent just the behaviour of making a specific thing happen rather than other things?
reply
I'm curious, do you think that this also applies to stable diffusion? Are these models "creative" too?
reply
I haven't used stable diffusion enough to have a strong opinion on it. But my thinking is LLMs have only recently started contributing novel solutions to problems, so maybe there is some threshold above which there's less sloppy remixing of training data and more ability to form novel insights, and image generators haven't crossed this line yet.
reply
Yeah? Those models are creative.
reply
The LLM did not solve the problem.
reply
Who did then?
reply