Posted by pr337h4m 23 hours ago
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
You can just about make out those goalposts on the surface of the moon with a good telescope at this point.
How is this not just another proposed problem (albeit with a search space much larger than an Erdos problem's)?
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.
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.
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.
Citation needed
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
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.
What was that about "spreading FUD about unaffordability"?
[1] https://ourworldindata.org/grapher/share-living-with-less-th...
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.
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.
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?
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.
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.
But you can only do that now, in hindsight. Before calculators, one could argue being able to do math was a sign of intelligence, but once something new comes along which can do math in a non-intelligent way, you can realise “ah, right, my definition was incomplete/incorrect, I need something better”.
> Foul food tastes different.
You’re right, that was a bad example.
> You come across a shiny piece of yellow metal that you think is gold. (…) He's nothing more than a mad man rambling about a distinction he made up in his head.
No, that is not right. Fool’s gold is a thing.
https://en.wikipedia.org/wiki/Pyrite
It’s not the same as gold and you can test for it, but that doesn’t mean you know how to do it. Yet it’s perfectly possible that by being exposed to the real and fake thing you’ll get a feel for each one as there are subtle visual clues. It doesn’t mean you can articulate exactly what those are, yet you’re able to do it.
It’s like tasting two similar beers or sodas. You may be able to identify them by taste and understand they’re difference but be unable to articulate exactly how you know which is which to the point someone else can use your verbal instructions to know the difference. That doesn’t mean the difference isn’t there or that you can’t tell, it just means you haven’t yet found yourself the proper way to extract and impart what you instinctively understood.
No you could always do that. The meaning you take from it is up to you but you could always separate humans and calculators.
>No, that is not right. Fool’s gold is a thing.
I know what fools gold is. I used it for contrast. Fools gold can be tested for.
>but that doesn’t mean you know how to do it.
It doesn't matter. If you claim it exists but you don't know how to do it and you can't point to anyone who can, it's the same as something you made up.
>It’s like tasting two similar beers or sodas. You may be able to identify them by taste and understand they’re difference but be unable to articulate exactly how you know which is which to the point someone else can use your verbal instructions to know the difference.
You are still making the same mistake. Two similar beers or sodas taste different. No one is asking you to come up with a theory for intelligence. All you have to say here is the equivalent of "It tastes different" and let me taste it for myself. But even that much, you can not do. So why on earth should I treat what you say as worth anything ?
With real general intelligence you'd expect it to solve problems above a certain difficulty with a good clip
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.
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.
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?
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?
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.
(To be clear: I'm not agreeing or disagreeing. I sometimes feel the same too. I'm just curious how others reconcile these.)
There, fixed that for you.
Of course LLMs are still absolutely useless at actual maths computation, but I think this is one area where AI can excel --- the ability to combine many sources of knowledge and synthesise, may sometimes yield very useful results.
Also reminds me of the old saying, "a broken clock is right twice a day."
> Every Mathematician Has Only a Few Tricks
>
> A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdös’s work.
> You admire Erdös’s contributions to mathematics as much as I do,
> and I felt annoyed when the older mathematician flatly and definitively stated
> that all of Erdös’s work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs.
> What the number theorist did not realize is that other mathematicians, even the very best,
> also rely on a few tricks which they use over and over.
> Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory.
> I have made a point of reading some of these papers with care.
> It is sad to note that some of Hilbert’s beautiful results have been completely forgotten.
> But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory,
> it was surprising to verify that Hilbert’s proofs relied on the same few tricks.
> Even Hilbert had only a few tricks!
>
> - Gian-Carlo Rota - "Ten Lessons I Wish I Had Been Taught"
We may have collectively filled libraries full of books, and created yottabytes of digital data, but in the end to create something novel somebody has to read and understand all of this stuff. Obviously this is not possible. Read one book per day from birth to death and you still only get to consume like 80*365=29200 books in the best case, from the millions upon millions of books that have been written.
So these "few tricks" are the accumulation of a lifetime of mathematical training, the culmination of the slice of knowledge that the respective mathematician immersed themselves into. To discover new math and become famous you need both the talent and skill to apply your knowledge in novel ways, but also be lucky that you picked a field of math that has novel things with interesting applications to discover plus you picked up the right tools and right mental model that allows you to discover these things.
This does not go for math only, but also for pretty much all other non-trivial fields. There is a reason why history repeats.
And it's actually a compelling argument why AI is still a big deal even though it's at its core a parrot. It's a parrot yes, but compared to a human, it actually was able to ingest the entirety of human knowledge.
Even this, though, is not useful, to us.
It remains true that, a life without struggle, and acheivement, is not really worth living...
So, it is nice that there is something that could possibly ingest the whole of human knowledge, but that is still not useful, to us.
People are still making a hullabaloo about "using AI" in companies, and there was some nonsense about there will be only two types of companies, AI ones and defunct ones, but in truth, there will simply be no companies...
Anyways I'm sure I will get down voted by the sightless lemmings on here...
The combinatorial nature of trying things randomly means that it would take millennia or longer for light-speed monkeys typing at a keyboard, or GPUs, to solve such a problem without direction.
By now, people should stop dismissing RL-trained reasoning LLMs as stupid, aimless text predictors or combiners. They wouldn’t say the same thing about high-achieving, but non-creative, college students who can only solve hard conventional problems.
Yes, current LLMs likely still lack some major aspects of intelligence. They probably wouldn’t be able to come up with general relativity on their own with only training data up to 1905.
Neither did the vast majority of physicists back then.
Indeed, and so do current humans! And just like LLMs, humans are bad at keeping this fact in view.
On a more serious note, we're going to have a hard time until we can psychologically decouple the concepts of intelligence and consciousness. Like, an existentially hard time.
I've been using LLMs for much the same purpose: solving problems within my field of expertise where the limiting factor is not intelligence per se, but the ability to connect the right dots from among a vast corpus of knowledge that I would never realistically be able to imbibe and remember over the course of a lifetime.
Once the dots are connected, I can verify the solutions and/or extend them in creative ways with comparatively little effort.
It really is incredible what otherwise intractable problems have become solvable as a result.
I don’t know what this claim is supposed to mean.
If it isn’t supposed to have a precise technical meaning, why is it using the word “interpolate”?
and homo sapiens, glancing at the clock when it happens to be right, may conjure an entire zodiac to explain it.
A broken clock can be broken in ways which result in it never being correct.
2) If you have something to say, just say it. Don't put words in my mouth and then argue with a thing I didn't say.
A way to test might be running an open model locally, directly (without a harness) where you could be sure it's not going through a translation layer. I think these days it might have this tool call behavior built in, but I think back in the day it was treated more like a magic trick. Without it, it behaved similar to "how many r's are in strawberry" for simple math.
They are not great at playing chess as well - computational as well as analytic.
Further evidence for the faultiness of your claim, if you don't want to take me up on that: I had problems off to GPT5 to check my own answers. None of the dumb mistakes I make or missed opportunities for simplification are in the book, and, again: it's flawless at pointing out those problems, despite being primed with a prompt suggesting I'm pretty sure I have the right answers.
I found and fixed bugs I wrote into the formulas and spreadsheets, and the LLMs were not my sole reference, but once the LLM mentioned the names of concepts and functions, I used Wikipedia for the general gist of things, and I appreciated the LLMs' relevant explanations that connected these disciplines together.
I did this on March 14, 2026
That's one way to waste a ton of tuition money to just have a clanker do your learning for you.
Unless you're teaching it, in which case I hope your salary is cut by whatever percentage your clanker reduces your workload.
80 hours! 80 hours of just trying shit!
That is not nothing, no matter how much you hate AI.
If/when these things solve our hardest problems, that's going to lead to some very uncomfortable conversations and realizations.