I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or self study, and being able to apply it to the problem at hand.
I don't think I've had a truly original idea in my life. Combine A + B, when it's rare for people to know A and B at the same time. So from that perspective, what LLMs are doing is basically the same thing. Sometimes I am faster than the LLM because my context might be better organized, but it typically needs just a hint from me to steer itself correctly. It claims something is a memory leak, but smelling a rat, I suggest it to double check the garbage collection statistics too, at which point it's clear it's no leak, but a tuning error, at which point the LLM is better at tuning than me, because it has more energy than I do.
Maybe there's true brilliance out there, when something doesn't come out of combining data and building hypothesis until you get really lucky. My experience is not comprehensive. But I look around me, and it sure seems I've not been lucky enough to see it. Even the shiniest people I've worked with, which most of the audience here would recognize, have never shown me that they can go past this.
People have told me I was smart since I was a kid, but I can't remember for shit. I had a thought when I was fairly young that the only reason I was (maybe, sometimes) outperforming others intellectually is that I was habitually compensating for my poor memory by working things out on the fly, while others could rely more on rote memorization. Anyway, takes all kinds I guess!
Somewhat tangential, but this reminds me of when I took a certain Microbiology midterm in college. I hadn't put much effort into that class leading up to it, as I had some tough CS classes that consumed my focus that semester (also was admittedly not a great student in general). So when I finally went to take the midterm, after cramming like mad before the exam, I quickly realized I basically didn't know the answer to most of the questions, even what I crammed was only a small portion of the material.
The exam was huge, at least over 10 pages, and even when we technically ran out of time, the professor was kind enough to move the remaining exam takers to the neighboring lecture hall to continue taking it. I recall I spent a total of 2 hours on that exam.
Now mind you it was mostly short answer or multiple choice questions. The multiple choice questions were pretty sharp too, lots of traps and false but sounds right answers mixed in. But if it had been purely essay questions, I would have been screwed.
However with such a huge corpus of information in front of me, I ended up basically learning all the material on the spot. I just kept doing multiple passes through it, each time I noticed one of my answers contradicted one of the others, I would make adjustments to harmonize, which indirectly refined my understanding.
In the end I got B+ in the exam (which was curved to an A), and walked out understanding the material better than I did walking in.
Reflecting in the experience years later, I've wondered if a hypothetical LLM which was ignorant of microbiology could do the same thing if fed that exam. In some respects the traps they placed in the multiple choice questions actually were what helped me refine my understanding the most. Made me appreciate information theory more.
Same. I have bad "factual" memory, but very good "conceptual" memory. I might not remember exactly what someone told me, but I probably gathered a keyword, and a feeling and idea of what they told me. Almost like it takes what they said then compresses it into my mind in a nice little multi-key lookup table.
In my, admittedly extremely small sample set, concept-focused memory is common for people with any degree or kind of dyslexia. I used to struggle with understanding how people couldn't understand things, now that I'm more mature it makes sense how people struggled with me not being able to spell things :).
Same. I don't remember most things including my childhood. I have to relearn everything all the time just in a few months time. Maths, code, etc if I don't use it in 1 or more month, I have to relearn it though its always easier to relearn it. Comparing myself to others its extreme. What I find is the process of constantly relearning instead of relying on memories (which are in a way similar to assumptions) can lead to different ideas (often unique) than other people because everything even basic concepts is a open question. This however is tortuous in job interviews when people ask about problems solved in previous work or about a concept so there are trade offs.
I can relate to this, but always explained it away in the opposite direction: I never trained my memory very much because I was able to work things out on the fly. Who knows, maybe there isn't much of a link between the two at all.
> I never trained my memory very much because I was able to work things out on the fly
I actually always thought it was the opposite for me – I had to figure out how to work things out from scratch because I could never remember anything.
We sort kids into the smart and non-smart labels when they are young, and those labels tend to stick, even when what we're measuring isn't raw intelligence but just variance in childhood development that wash out in the long term. I don't think either group is well served by this.
Agreed “remembering” stuff is critical in most life’s situations where if you did, you will appeared to be smart. This is probably why spaced repetition has been a key element in learning for the past few decades.
But “remembering” is only the beginning (you have to remember first!), after that, elements like understanding relations, connecting dots and remixing, timing, etc will truly make one shine.
In one way, it’s like the current “LLM + Harness” setup for agents. LLM is how well it remembers, but different harness techniques really matters, at times even a worse model mixed with great harness can outperform great model with bad harness
Since it is so much easier to test for memory than understanding society grew to confuse the two. Only now faced with these other entities are people beginning to question it.
I know people that got to post grad math without understanding a thing but they could remember a lot easily, while many of those that understood but had a harder time remembering every last variation of everything got penalized.
if someone did have a truly original idea, then everyone would probably think it was terrible anyway and we'd all ridicule them, because we'd have no frame of reference for X + Y if all we know is A and B :)
I suspect any new thing created/discovered/etc is just combining knowledge from existing things with memories being an example. Outremembering while certainly not the only method helps massively with combining knowledge from existing things. I don't see new knowledge coming out of nothing.
I like to use the analogy that the human brain (when it comes to intelligence) is like a computer. We have storage, which is just long-term memory. We have RAM, which is your ability to keep track of a mental model of something you’re actively working on, and then there’s the CPU, which is the ability to make logical leaps and connections on that mental model (or maybe storage).
I’ve met different people throughout my career whose intelligence came in 1 specific area. For instance, my friend is extremely good at trivia, he clearly has a lot of storage and can access it easily. I think I’ve only met one person who was excellent in all three areas of intelligence.
Obviously this is a simplification, but it’s how I like to illustrate my ideas on intelligence at parties and first dates.
Not only I agree with you that I don't think I've had an original idea, even when I try to do artistic stuff it seems like the things most praised were the ones where I was trying to do something else and the good part came from failing to do the thing I was trying to do.
I think that’s true for genius is in general. I don’t mean the Einstein type but I mean the child prodigies that graduate high school at 10 years old or whatever I mean if you can read something once and remember virtually everything about it that’s a gigantic leg up on everyone else who has to study drill the stuff into your head, etc.
Even in a debate, if somebody just has the ability to remember tons of facts and figures, the other person will seem unintelligent by comparison, even if the other person is correct
I've long held the belief that humans cannot truly create. We just remix and recombine. This is interesting - although I'm not religious, many religious texts call god the "Creator", perhaps because the ability to truly create original thought is above the ability of us humans. To truly create is divine. Maybe the writers of those old texts recognized this as well.
I can't help but think of Michael Nielsen's essay "Augmenting Long-Term Memory" [1].
> Many people's model of accomplished mathematicians is that they are astoundingly bright, with very high IQs, and the ability to deal with very complex ideas in their mind. A common perception is that their smartness gives them the ability to deal with very complex ideas. Basically, they have a higher horsepower engine.
> It's true that top mathematicians are usually very bright. But here's a different explanation of what's going on. It's that, per Simon, many top mathematicians have, through hard work, internalized many more complex mathematical chunks than ordinary humans. And what this means is that mathematical situations which seem very complex to the rest of us seem very simple to them. So it's not that they have a higher horsepower mind, in the sense of being able to deal with more complexity. Rather, their prior learning has given them better chunking abilities, and so situations most people would see as complex they see as simple, and they find it much easier to reason about.
I once tried out his Anki approach during a math lecture. Whenever I reiterated a card, say about some lemma, I noticed something interesting about it. This was delightful and many lemmas became much more streamlined over time. It's not a "solution" to mathematics, but I found it delightful while it lasted (before akrasia or lack of time kicked in and I stopped doing it).
One thing about human mathematicians is that they only publish positive results. Professors etc might have file drawers full of "negative results", but the incentives and bandwidth of human mathematicians makes publishing these useful results impossible.
In general though, LLMs do not have the same limitations and incentives as human mathematicians, and the next year's tsunami of change will make this abundantly. clear.
Yeah, LLMs are great at generating negative results for math-related prompts "We scanned values {a,b,c} from 0-100 and no results" Great..too bad journals will not publish this. But good job, I guess. A negative result is only truly useful if it can be bounded, requiring an actual proof.
> A negative result is only truly useful if it can be bounded, requiring an actual proof.
That's at least true for current journals, since they're supposed to be read by actual humans. I suppose one could imagine a sort of "AI" pure data journal that just "publishes" (in actuality aggregates) any sort of partial result. This body of knowledge would be entirely useless to humans, but could serve as a sort of "computation cache" for these stochastic systems.
The bandwidth is absolutely there ("we tried this and it didn't work" is totally the stuff of conference discussions).
The incentives are not.
The incentives are skewed towards "a magician never reveals her secrets". The results are presented as if a rabbit got pulled out of a hat, with a maximum ta-da! effect, and little backstory of how the hell did we get there.
Don't get me wrong, these things are discussed, often over beers (you better drink it you want to make a career in the field).
But not published.
The younger mathematicians are trying to change that with the blogging culture. But the professional incentives aren't there. (In corp-speak: can't put blogging on perf). They burn out.
That's why math blogs usually come from either the top dogs in the field, like Terrence Tao, who don't need to care about perf, or people outside academia.
That's one thing that I hope the disruptive/destructive effects of LLMs will force mathematicians to face.
As one of my fellow mathematicians sarcastically wrote¹, we've reached a point where we should become a cult because we're acting like one anyway.
The other possibility is, of course, that the shake-up will take us precisely into that direction.
My point here is that the real problem here is not mathematical; it's a social one: incentives and politics, organizational structures, policies, allocation of jobs and funding.
All of this directly impacts how we do mathematics, who we do it with and teach it to, how we teach and communicate, and, of course, what math we even do and look at.
Given that, I'm neither too worried about humans vs. AI standoff, nor hyped about the Glorious New Future full of AI-assisted discoveries.
AI or not, the organizational issues in the field are still there, as are the incentive structures (including the infamous publish-or-perish).
We are doomed, yes, but by our own hands and committees. And it's up to us, not the AI, to get us out of there.
The little shove from the AI might be just the thing we need.
This is not specific to math. To non-academics, you basically have to rewrite your commit history to make it seem more impressive. You often write the motivation section last. At least math publication culture allows saying "We consider the problem of" and then solve it. In AI/ML academic papers you need much more "story" around why, what the applications are, why aren't you doing something else, defend against lack-of-novelty attacks, defend against "this is just A + B known techniques used together" etc.
It's also "out-brute forcing them." It just never gets tired. If a mathematician picks a research direction and spends a whole week on it and it doesn't pan out, they will likely be annoyed, need a break for a while, etc. This thing just does not ever get tired or discouraged or care; it's just onto the next thing until something ends up working.
loaned from German, where it's originally a way to say buttocks, literally "sitting flesh". If you have more Sitzfleisch you can sit for longer. Both in the literal sense (a bigger butt makes sitting more comfortable) and in the figurative sense (having the mental ability to sit for longer, get more desk work done)
I think there is an IT bit of humor from about 1 decade+ back where the people who's proposals won out in meeting were the ones that could keep from needing to go to the bathroom longer.
There's also a less flattering reading of the word, where Sitzfleisch means having a "flat ass" (from sitting too much, e. g. Sitzfleischparade describing a group of flat-arsed people, or something like Sitzfleischmaxxer, and so on).
Wow, what a great comparison. LLMs are great at reasoning but absolute dogshit at simple arithmetic. If there's a raw calculation involved I always tell it to use python to add it all up.
String theory is a great example of a dead end kept alive by ego and sunk cost fallacy. An AI would have declared it dead and moved on 10 years earlier.
When people make these comments about string theory, are they at the forefront of quantum physics theory and have spent years on modern string theory? Or did they just watch a YouTube video and then keep parroting this?
You could reductio ad-absurdum this logic quite broadly. We all form beliefs about the world and its aspects, and almost always through fallible sources. Should one be confident about ones of questionable provenance? I say no. But forming beliefs from the information we have is a useful skill.
I also just keep parroting that the Earth is not flat and a bunch of other things I've been told and then never questioned, since it seems to make sense.
When the flath-earth craze started I've been trying to at least get that bit actually personally verified. Haven't managed to do it to this day, though. So I'll just keep parroting various things without properly understanding them.
Your drive to verify must be very low then. There are hundreds of small logic reasonings or even experiments you can easily prove that a flat earth model is at least very complicated or even impossible.
Explaining Moon phases gets very complicated in any flat earth model. With binoculars you can see the shadows of craters on the moon's terminator. Or the phases of Venus whereas Mars doesn't have any.
Timezones are ridiculously hard to explain on a flat earth.
This isn't a great argument. Researchers who do not think string theory is good are not going to spend years on it. There are plenty of experts that dismiss string theory. I have no skin in the game, and don't care either way, fwiw.
The error with this approach is that every single physics theory gets exactly the same criticisms.
You can take any of the theories that Hossenfelder would spend time on instead of the ones she does not like, and you would find (basically) a similar percentage of physicists saying it's a mistake to continue in this direction.
In other terms: for each physics theory, on 100 physicists, you have 5 physicists saying it is a mistake to continue working on it (number made up for illustration, and there is probably some variations, but you get the gist). You took one theory and found few physicists saying it is a mistake to continue working on it. You conclude, incorrectly, that it means this theory is fundamentally differently treated as any other theories.
(on top of that, it is unfortunate that Hossenfelder later screw up her image by doing way too much mistakes that someone reliable would not do)
No, not morons, but people who have built a career on string theory. At this point, even if they regret their decisions, it’s too late to turn back now.
I don't think it's a good argument. String theory is just "one application" of advanced mathematical physics. It's like saying that software developers specialised in ReactJS would lose their career if ReactJS is suddenly abandoned.
You were the one introducing the argument "they are getting advantages out of it so we should be careful to not take what they say as an impartial view". Same can be told of Hossenfelder (personally, I would say that Hossenfelder has shown more clues that indeed she is not very reliable and would prefer caricatural sensationalistic descriptions, which is not what the typical string theory physicist does).
This is a pretty silly belief to hold about science. Plenty of strong, well held standards of the modern era were considered ridiculous fringe beliefs a century ago.
Not taking either side here - but surely a lot of cosmological phenomena couldn't be testable/verifiable at the time they were theorized either?
(thinking of black holes for example - they were theorized way before we had observations. And presumably a lot of particle physics can similarly be theorized before we built the technology to experimentally verify them)
Counterpoint: something has happened in frontier models, and yes they now get discouraged and will sometimes prefer to not continue working on a problem unless you tell them to anyway.
I don't know how or why this would be trained on behavior, but no, it isn't true anymore that models don't say things like, "Ugh," or "this is going to take hours and maybe we should stop here."
The key here is that it’s depending on the human inability to connect the sum of relevant knowledge, but said knowledge comes from humans.
Theres going to be this field day of low-hanging fruit that ML can round up, but after that I suspect it will be in fits and starts as a “connection maker” rather than some proof producer.
I think we're underestimating just how much low hanging fruit there is. I've been trying to apply this LLM research process to physics (QM and solid state) and there is so much missing in Physlib and the rest of the Lean ecosystem that most of my work has been trying to formalize the theories and validating them against the specification problem (and mostly failing badly).
It's not only going to be "connection maker". If and when robotics advance to a point where the LLMs are embodied, they can run experiments in the physical world and find new knowledge.
So applied math, math, applied math, applied math, and maybe some others.
That makes sense, although I'd argue that at least in the realm of HEP theoretical physics has extraordinarily expensive kit compared to what scientists make. See: The LHC.
Robots in labs already exist, but mercifully they're not hooked up to anything as unpredictable as an LLM. Robots tend to work best as specialists doing high-throughput, extremely repetitive tasks which nonetheless require a degree of precision. Giving a robot a "human" body makes very little sense if we're talking about the needs and productivity of a non-human; humanoid robots are marketing for humans.
Humanoid robots are obviously more than marketing. The entirety of human civilization is human shaped. Making robots that are human shaped is easier and more efficient than redesigning and rebuilding everything that exists.
> The entirety of human civilization is human shaped.
That's the marketing pitch.
A plumbing robot doesn't need to be humanoid, an octopus shape may well be better for all the awkward corners. A robot police officer could be the municipality itself for sensory nodes (essentially the sales pitch of Flock etc.), plus some drones or robot dogs to perform arrests*.
The robot vacuum cleaners and lawnmowers we already have are nothing like a human. A robot taxi driver can be just the car. Robot dogs are already used for maintenance and security sweeps.
If you've got wheelchair access, you've got wheeled robot access. If you've got guide dog access, you've got access for Boston Dynamics' Spot.
* this may be a bad idea with current robotics, but I aver it's not improved by making those robotics humanoid.
You are not understanding what humanoid robots are about. Those are specialist robots you are describing. The promise is of course one robot that can do the plumbing, clean your house, do the dishes, build a house, and basically every physical job a human can do. It's extreme lly likely that at least a somewhat humanoid shape is required for that.
Historically this has never been correct. Turns out you get more efficient systems when designing them without how a human would accomplish a task in mind.
Outside of sci-fi, marketing proposals, and niches like "Elder care in Japan" there are very few humanoid robots. By contrast non-humanoid robots have been mass produced and used in industry for decades. Arms. Carts. Trollies.
No people. If you want something with fine motor control and dexterity, it's easier to make that the robot and then have another robot bring the workpiece to the arm than it is to build a single robot that can walk around and do it. There are compromises in human features because we're generalists.
A new technology being able to do something better than humans does not mean it’s intelligent though. A calculation program is not intelligent just because it can remember more digits than me, work more than me
But the difference really does matter and is not just a case of "whittling down" what intelligence really is.
We have known for a very long time that computers and machines are much faster than humans, more accurate, are scalable in certain ways that humans aren't, and they don't tire. I think most people who are not in the "AI cult" would agree that LLMs and modern generative AI are really just an extension of those faster/more accurate/more scalable and never tiring traits. But there does seem to be (and I'm sure folks much smarter than I have quantified this or described it better than I can) a fundamental difference in how humans think, especially as it applies to what true "understanding" really entails, and for the ability to think up truly novel and unique things that are not just a rejiggering/recombination of training data. I believe those skills really are at the heart of human cognition, and as impressive as LLMs are in replicating what this looks like, there are plenty of "LLM failure modes" where it's clear that LLMs lack a true understanding of concepts or the ability to generate useful, completely novel ideas.
There's definitely a lot missing from the current state of the art in machine learning that all brains manage to beat, and we can observe this just because an animal that needs as many examples as an AI to learn motor functions would starve to death before learning to eat.
However I can only guess that this is important, I'm not absolutely certain. They're at risk of being an economic disruptor just by being extremely stupid (by how much they need to study) faster than us to the same ratio we jog faster than continental drift.
Nobody knows what true "understanding" really entails, or what are "truly novel and unique things that are not just a rejiggering/recombination of training data". For the latter, you'd at least have to find an example in history of someone who came up with some idea that has been widely considered "truly novel" by experts, who didn't have any education or training, so no "rejiggering/recombination".
Because, what's really happening is we're saying "Oh these things are what defines intelligence" then implementing them and /discovering/ "oh wait, there's more to this than we knew".
We've known, for decades, for example that an IQ test is not a measure of Intelligence, even though people still refer to it as though it is. A computer passing an IQ test, therefore, would have been thought of as possessing intelligence way back when, but would not now.
Oh, on the point of "creativity" - is a RNG "creative"? It creates a value unbounded by human intervention (in theory, yes Pseudo RNGs have limitations) - therefore it must be creative... right?
> If a mathematician picks a research direction and spends a whole week on it and it doesn't pan out, they will likely be annoyed, need a break for a while, etc.
Your timelines are a bit unambitious. There's nobody expecting to make significant progress with a week of work.
If a thousand monkeys typed at a character per second, on a keyboard with the 23 relevant characters, it would take roughly 10^136 years for them to come up with this counterexample. Though, to be fair to monkey scenario, there's a large family of them known now, so it's not quite this bad: suppose there are a trillion permutations and similar examples that fit in this string. Then we are down to 10^124 years.
If LLMs are monkeys, somehow trained LLM weights allow them to model and prune massive numbers of universes in parallel.
Someone with a better memory for ideas or concepts will be able to more quickly incorporate those into novel ideas or recall them when necessary to assist in solving a problem than someone with worse memory.
To those here challenging this with “yes but I’m smart and my memory is bad” - a) define smart and b) perhaps your memory for trivial things like life events, what you did two weeks ago on Monday or people’s names is bad, but I suspect your memory for “work” or problem solving is strong.
Another example I used to see (hear, rather) is how musicians rip off each others riffs and hooks without noticing (unintentionally - they claim), which I long suspected as simply “forgotten” riffs they heard in other songs that once they started playing themselves by chance they attributed to their own creativity. Creativity and intelligence are somewhat linked that way I suspect.
In any case, this all boils down to the same thing, you can think of yourself as a dynamic model made up of memories and biases to some degree, and your ability to store and recall useful information to solve problems increases what we call your intelligence.
"OK, it might be much better at math than me, but it's not smarter, it just remembers more".
Heh. Every day, a new type of cope. It's like, coping as hard as possible.
If this was an ML researcher trying to come up with a way to improve performance then you could say it wasn't cope but rather practical observation to serve a goal.
But it's just cope.
Also, AI is going to continue to get smarter. A lot smarter. There are already systems in R&D that will continue increasing efficiency and performance of hardware by more orders of magnitude.
While TFA itself makes sense I disagree with the title and the conclusion. I would not consider referencing working memory during thinking as “remembering” but as a part of thinking itself. Working memory is the RAM to the much larger but higher latency indexed database that is our long-term memory. As such I would say AI is out-thinking us, even if in a brute force sort of way.
I think where you could say it is out-remembering us is when it can contemplate the vast universe of patterns, gleaned from essentially all human disciplines, encoded in its weights, that may let it draw connections that a human could not, unless they just happen to be familiar with multiple disciplines.
Which is why I think the analogy with Von Neumann / Einstein is also a bit off. From TFA it seems Von Neumann was more akin to what AI does, than Einstein. I don’t get the impression that it was Einstein’s memory but his ability to look at things from a radically different perspective. So far I don’t know that we can categorically say that LLMs can or cannot do that.
There are plenty of high value endeavors where being a superhuman knowledge remixer is right on target. But even capturing all of the knowledge is proving elusive.
I use coding agents. I think they're pretty good overall. They save me a lot of tedious coding. For example I probably wouldn't spend the time to implement native splash screens for all the build targets of a Flutter app, but I'll have the coding agent do it.
Nevertheless, for all the time that we've had coding agents, it's still trivially easy to find the jagged edges of their training. For example, Gemini evidently doesn't know if the Xcode part of a Flutter tool chain is misconfigured. That's not exactly a Millennium Prize problem. But it is shaped wrong for a training set for a coding agent.
Sounds like another attempt to frame AI in a way that makes them feel better about themselves.
The simpler explanation is that a working memory is a requirement for intelligence, and a larger working memory will make you more intelligent. Hence the AI can in fact be more intelligent than the mathematician.
Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers.
The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
We don’t trillions of dollars in LLM investment to build things mathematicians don’t understand. We already have plenty of those, even from ancient times.
As to your second point, Terry Tao already has an answer [1]: the proof isn’t the contribution, shared understanding is. This issue was already raised back when the four-colour theorem was proved. Machine proving and machine proof checking are useful tools but they don’t mean anything without the interpretative work and the communication necessary to build shared understanding.
If humans have nothing to contribute then shared understanding is a pointless endeavor. It makes sense now in the "centaur" period where human + AI > AI alone, but when AI mathematicians are both more rigorous and more elegant, then taking the time dumbing down their proofs to a human level of understanding is like requiring that we ensure all our current proofs be understandable by a monkey.
> If humans have nothing to contribute then shared understanding is a pointless endeavor.
I agree, but as a software engineer this gives me pause because I keep trying to insist on coding standards but I’m unable to come up with a compelling reason why it matters. Ostensibly the reason we cared about things like DRY and code quality was so that it would be easy to understand and easy to maintain and easy to make changes to later. But it now seems like a shared understanding of the codebase is less important than ever, and it’s more about shoveling requirements in without breaking any existing functionality.
Is a well tested slopfest better? That seems to be the conclusion for mathematics, so why not software too?
It used to be the same with assembly. Programmers complained the one generated by compilers was not pretty, but now in 99.999% of the cases, it does not matter because nobody look at it.
Where is the value in an unintelligible gibberish proof?
We already have countless examples of such filling up the arXiv, written by hacks long before LLMs started writing proofs. No one cares about them. You might as well build a box blasting radio static into the void. You could save a lot of electricity that way.
Why not? We build cranes to hoist weights construction workers can't lift. We build electron microscopes to measure things physicists can't see.
Why is it so hard to imagine we can build tools to think thoughts we can't comprehend?
If there's commercial value, I think it's inevitable. We don't fund mathematicians because it's cute when they understand a problem, but because their work tends to have applications with commercial value. The value can be captured without understanding the details.
Can you give an example of an incomprehensible piece of writing (any writing, never mind a proof) that has commercial value commensurate with the costs involved here?
> Can you give an example of an incomprehensible piece of writing (any writing, never mind a proof) that has commercial value commensurate with the costs involved here?
It depends on what exactly you mean by "commercial value commensurate with the costs involved" but I'd volunteer the 3G/4G/5G specifications and the other documentation required to implement the mobile network protocols. 5G is currently sitting at over 50,000 pages and it's one of the reasons Qualcomm/Broadcom/Apple are the only ones who can realistically make a mobile radio.
I don't think there is a single human to whom more than a few thousand pages would be comprehensible at a time except for the occasional genius.
Read the rest of the discussion. The claim is about text which is in principle incomprehensible to humans.
If there exists a text which only one person can understand, that person can communicate their understanding to others, even if that doesn't help them with the original text. That dissemination of knowledge is what provides the value, not the mere existence of the text. If that person forgets or dies before they can share their knowledge then it will be lost.
We have many examples of this from history: ancient texts written in a lost language. These texts provide us with no value until the day they can be deciphered, unless you count linguistic puzzle-solving as a virtue.
> If there exists a text which only one person can understand, that person can communicate their understanding to others, even if that doesn't help them with the original text.
If there exists a text which only an AI can understand, that AI can communicate their key conclusions to others, even if that doesn't help them with the original text.
The only difference here is the amount of meat involved. Perhaps tossing a few steaks on the server racks could help with that.
If an AI can communicate its findings to us in a way that we can understand it, then its findings are by definition intelligible to humans. Your claim was about texts for which this is not possible.
So, you're willing to claim that a conclusion that you don't understand the reasoning for is equivalent to comprehension?
Because, again, I can point to hundreds of examples of texts where nobody but the author understands it, and they're only giving summarized "commandments" that you should follow if you want good results.
If I told you "don't use spin locks, call futex instead", do you think have gained an understanding of the Linux scheduler?
Yeah, how many people do you think understand the Linux kernel in full? What percentage of the people using it to great commercial effect can understand it?
How's your understanding of Schroedingers "An Undulatory Theory of the Mechanics of Atoms and Molecules"? You seem to be using the results of it as applied to semiconductor engineering just fine. And, I promise you, most semiconductor engineers haven't read it in full, they just accepted the results as passed on by several layers of teacher.
I have a paper on routing algorithms, which I have attempted to read to my cat. I don't think my cat retained much, but they seem to be enjoying the cat food that got delivered using the results.
I'd suggest that we're going to be a lot closer to the cat than the author of the paper when AI takes off.
Nothing is in principle impossible to understand. It just takes too long, is inconvenient and/or economically unviable.
I don’t find it hard at all to imagine that an AI comes up with a fundamental proof applicable to physics which results in some widget we can now produce that would otherwise not have been produced yet nobody takes the time to fully comprehend why it works. Somebody could, in principle, devote their lives to it and possibly get it, but for what purpose?
You asked for examples, for a technology that we're still building. Maybe you can see the issue with that?
Anyways, people benefitted greatly from Newton's laws of gravity, even though we still don't have a quantum-compatible set of laws for it. The laws of gravity are still incomprehensible for people, but the approximation that we've observed is still immensely valuable.
No, I gave you a lot more leeway than that. Take any utterly incomprehensible piece of writing from the entire history of civilization and demonstrate its value.
You keep falling back on "incomprehensible for some people" but that wasn't the claim. It was about a text which is incomprehensible in principle; that is, utterly impossible for any human to ever understand.
His examples work fine but you aren't accepting them because they don't confine to your paradox.
Every writing must be comprehensible to at least the author, regardless of whether it has commercial value or not. If I hit the keyboard a few times, I've created writing, but it doesn't mean anything. It is just gibberish and without meaning, so there is nothing to try to comprehend. So if there is something to be comprehended, then at minimum the author should know it.
Therefore what you keep claiming is the only refute of your argument of "an [...] incomprehensible [...] writing" is actually a paradox, and cannot be disproved itself. However "humans comprehending things" is not a paradox, which means that your specific request to beat your paradox is not actually related at all.
His examples disproving the non-paradox version of your challenge (writing incomprehensible to folks other than the original authors) are sufficient to disprove your statement, as he gave examples of both people not comprehending human made and 'God' made writing (the universe/gravity)
That's because his examples are obvious and not at all interesting, since we've already seen them.
His original claim amounts to creating an AI that takes its place above humans as some kind of electronic God, delivering edicts to humanity that we cannot comprehend, but which somehow have value to us. It's unskeptical, pseudo-religious nonsense.
I don't see that at all. Nowhere did this person evoke placing AI above people or even remotely evoke religious imagery. You imagined that yourself, and that creeps me out.
Can you give me an example single piece of writing that the author didn't claim they understood? I don't think that any utterly incomprehensible writing exists.
If you want examples where nobody but the author understands it, examples are a dime a dozen.
So you concede the point then. The age of humans comprehending things is not coming to an end. And therein lies the rub. When it comes to intellectual labour:
Understanding == Value
If a mathematician produces something incomprehensible then it has no value. It's meaningless. Indistinguishable from random noise.
An AI which produces incomprehensible text is producing no value. We didn't need to spend trillions of dollars on LLMs to figure that out. Markov chains can do that job perfectly well.
Again, do you believe that there are documents, of any value, that humans don't understand?
There is no value in an undeciphered document until understanding is achieved, just as a lode of gold ore in some asteroid orbiting a distant star has no value until we can fly there and extract it.
If an LLM can help us understanding something then it was not incomprehensible, by definition.
There are plenty of artifacts that, if not impossible for humans to understand, then at least no human has ever completely understood. To start with, the universe as a whole. Despite that, we are able to choose legible pieces of it to model and perform useful actions from.
This will shift your argument--that doesn't count! etc., to the point where it's by construction unsatisfiable and vacuous. And it doesn't matter: an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.
One person need not completely understand something for it to have value; it's sufficient for there to exist a shared understanding.
an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.
No, that is the entire point. If it is an algorithm which accomplishes something useful, then it is intelligible as such. That which is incomprehensible cannot be understood even in part, so it provides no value as a bit of knowledge (unless you're looking for a strong random number source, I suppose).
> how many people do you think understand the Linux kernel in full?
"Not many people understand some things fully" is so massively different from "the human mind is incapable of understanding some things that AI will understand for us"
Yeah. We're only starting the journey of building tools better at thinking than the human mind, so expecting me to have examples of things it produces is a little hard, don't you think?
The best I can do is things that are incomprehensible to nearly everyone, but still provide value. There's a small leap of imagination to consider an author that understands it and can show others how to leverage results without understanding be mechanical rather than biological.
I know right? And there’s only a market for maybe 5 computers in the whole world.
Paul Krugman (1998): predicted the internet’s economic impact would be no greater than the fax machine’s.
The 1876 Western Union memo dismissing the telephone as having too many shortcomings, and the banker telling Horace Rackham not to invest in Ford because the automobile was a novelty.
The idea about the goal of mathematics being shared understanding seems to come at a convenient time.
Mathematicians have never been known to communicate their ideas very clearly.
Regardless, even that target llms will likely win - an llm will likely be more efficient at teaching me string theory than a professor in a room with 463 other students.
I don't think "shared knowledge" means "shared knowledge between mathematicians and lay persons" (there is no much point in that, the same way a smartphone technician knows how a smartphone works deep down to the details but there is no big interest for society to have every lay persons being informed about it). I think it means "shared knowledge between mathematicians".
And at this level, while there are anecdotical exceptions, mathematicians have always been pretty decent (with their conferences, workshops, paper publications, international collaborations, ...).
So, it does not mean "teaching the subject", it means "creating a human network of people that share the understanding". LLM can be useful at telling a human, but you still need a human. The point of Tao is not that LLM is not good at providing explanations, it is that "providing explanations" is not the contribution to science, "the human network" is. It's like saying "LLM are great cook, they generate tons of food in space", but the point of having cooks is so that people can eat food and not die. Having LLM generating mathematical proofs is as useless as having LLM generating food that no one can access: the point was never to "generate proofs" or "generate food", the point was "creating a shared human understanding" or "eating the food so human can survive".
I get that there is a cultural benefit to keeping it alive. Just like we ideally want the languages represented at the universities.
But keeping humans in the loop does not appear to be necessary in order to call it science, and certainly not in order to have progress or dessiminate that progress.
I don't have a problem with people doing math. As long that we don't idiomatically hold on to that way of doing things.
I do, however, find it hard to belive that individual humans will play a big role from here and forward, in any scientific desciplines.
The entire point of writing proofs is for advancing human understanding. A giant dump of symbols that passes the lean compiler is meaningless besides human beings understanding it.
> The entire point of writing proofs is for advancing human understanding.
Proofs also enable AIs to direct search and generate knowledge. Verifiability is immensely useful for keeping AI grounded.
One might imagine AI generating enormous numbers of hypotheses and then trying to prove or disprove them, and then mine that data for new abstractions and heuristics.
Sometimes the purpose of the proof is simply to demonstrate that some construct is a safe assumption for other more interesting work-- and could still serve that purpose even if it was entirely a black box.
Is it the AI's fault we can't understand? If the GUT is beyond human comprehension does it matter less? We don't apply this reasoning to other animals or even to less capable humans. Besides, the robots may want to ponder maths for their pleasure.
> That's something AI companies would really want you to believe.
Why would I care what they want me to believe?
Intuitively it would make sense that you can put math ability on a chart with a value for “general public” “smart high schooler” “smart undergrad” “smart PhD/ professional”. And you could place frontier AI somewhere on that chart over time from GPT 2 to now and see the trend.
Then you’d have to consider that either you believe there is a fundamental limit that is below peak human mathematician level or there’s not.
They can say random stuff with the goal of increasing their shareholder value. Things they spit out do not have to be true. It is not easy to verify things they say, therefore, everything they say should be taken with a huge grain of salt.
Consider Enron and Amazon at the turn of the millennium. They were both telling you what the future would look like. The right action would’ve been to just ignore what they are saying and try and get data and reason about the world. It didn’t really matter that both Bezos and Jeff Skilling wanted you to believe various things - one was right and one was a scammer.
So that’s what I’m doing here. For what it’s worth I find a lot of the AI people’s worldview very consistent. They believed AI would be the most important technology of our life times and committed their work to it. Some of these same people are total liars so yeah I won’t really hang onto their every word.
that does not make it not true, nor does it make those companies or their products not dangerous. I like looking at videos of animals that tear other animals apart and eat them; lion cubs are super cute; but that does not mean I want to be thrown into a cage with a model of a lion that has not been programmed to be disinterested when it is sated. AIs appear never sated; humans using or making AI wanting money, even less so. I suspect the AIs will understand the cost long before the humans will, not that anyone making money would care.
It also creates and updates models, uses those models to make predictions, guides the stochastic generation by comparing the output to those models and reworks them in real time.
It also creates and updates models, uses those models to make predictions, and guides the stochastic generation by comparing the output to those models and reworks them in real time.
> It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers.
I agree.
> The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
I don't know if I see this being true for quite a while, if ever.
> It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers.
> I agree.
There's an infinite space of possible statements and proofs. The only thing that makes certain proofs significant is that human mathematicians consider them significant; if AI came up with a proof of some statement that no humans could understand then no humans would bother investing further resources in building upon it, for the same reason we don't waste computational resources iterating over the infinite space of true statements in first-order logic.
> The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
That sentiment makes me cringe. If you understand how LLMs work, you'd know it'll never be possible without a fundamental change in how these work.
We're also supposed to be reaching that point, somehow, without the LLMs ever being intelligent (in the dictionary definition sense, not the "high reasoning model" marketing sense).
Based on observations, the ones who are fooled by the supposed emergent properties, are just that, fools. Any sufficiently unintelligent agent will perceive transformer based LLM text predictors as possessing high intelligence.
First of all, the argument isn't that LLMs (with I assume some automation) cannot be used in searching a problem space. I'm assuming this is what you're referring to, in terms of contributions?
That's the part where LLMs are used as tools. Which there are plenty of places where they are useful.
Also, do you know what turning completeness is? Why are you bringing that up here?
The crowd that AI psychosis has brought to HN is interesting. But not in the "I'd love to learn more" kind
The thing about discussing or explaining constraints, is that it rarely is useful or productive if the other side does not accept (or understand) the reality of them.
Turing completeness is not exactly a high bar, and it's genuinely confusing as to why you bring it up. Your C++ precompiler is exactly as intelligent as whatever is your favorite agentic workflow with whatever harness you're referring to. Both might be Turing complete. Neither are intelligent. But one of them seems to be fooling you to think otherwise.
There have been many times that the C++ precompiler produced some output I couldn't understand. I might even at some point thought it was trying to tell me something profound I was too dumb to comprehend. Turns out it was just a missing semicolon.
> Again, you are the one who arrogantly say they llms can not be intelligent without supplying any argument for such.
Not really. You've provided the arguments yourself, just now. But, you don't understand them. Which, brings me back to the initial remark, as to why this engagement is bound to be unproductive. I'm off to bed. Have a good one.
> The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
Ask yourself: is that really the world you want to live in? It's a world where people, all people, are sidelined.
I think the happy ending of that path is something like Idiocracy. And the more likely ending is something like "automated capitalist economy without the people, because the people couldn't compete."
In limited experimentation: AI will certainly make statements that are extremely intricate and hard to understand, in part because they're overcomplicated and in part because they use a bunch of unnecessary terminology.
This is not to say that a human couldn't understand a streamlined version or that the AI would not be better if it made more streamlined statements to begin with.
(I am not saying that everything mathematical that an AI produces is in any sense trivial.)
It’s possible, but there’s a difference between vastness and difficulty.
Humans can’t compete with AIs on vastness of material they are familiar with, or the depth of effort they are willing and able to throw at a problem.
But scale isn’t the only aspect of difficult scientific endeavours. There’s also theory. And advancements sometimes come through hard graft of knotting together many things. And sometimes they come through the revelation of a deeper truth, or a new framework, a fundamental insight.
AI might help us reach the next level. But that doesn’t mean we won’t understand anything. It could be we have periods of vast intricacy we cannot follow, punctuated by profound elegance we (or at least experts) relatively easily can. And then the scaffolding we needed to get there falls away.
I don't think that's true. Human intelligence is limited, and our brains are inefficient machines.
The tools we built to replace muscles have mostly obsoleted raw strength for tasks like excavating earth.
There's no reason to think we can't do the same for brains. And then we'll never need to think for a living again. Some people may want to do it as a commercially insignificant hobby, of course, the way people lift and compete in strongman competitions today.
We'll have AI taking care of our needs, the way a good mother takes care of their children.
A good mother doesn't raise children to be dependent upon her for all their needs.
For this to actually work in a way that benefits our species, humans will need to become something else/next through their interaction with the technology.
You could be right, but you're making a lot of assumptions about how complexity, scientific understanding, and explanations scale. One of the features of a good scientific discovery is that it often simplifies and compresses things that were previously a bunch of scattered facts. Also, as AI systems improve they'll get better not only at making scientific discoveries, but also at producing understandable explanations.
Let’s not jump the gun. Where they are right now they can somewhat match our abilities. We haven’t even gotten to the point where they can self improve.
>produce proofs far more intricate than humans can understand
Math is not magic, a proof is just a series of applications of a set of rules on some axioms. A mathematician could understand any proof given enough time to study it; the only way for AI to make proofs that a human couldn't understand is by making really, really long proofs.
Why would you want something you don't comprehend? How can you be sure it empowers you?
I think perfect rationality doesn't exist, because it is rational to reject something that you don't understand. So rationality of a given physical system will always be bounded.
Yes. That's how LLMs do programming, mostly. It's also why LLMs don't need abstractions or parsimony as much as humans. They can work on something complicated without simplifying it first.
This has major implications that haven't been fully realized yet. On the math side, there are long machine generated proofs. On the code side, there are high volumes of code with similar code not being folded into functions.
For greenfield projects LLMs don't need abstractions, but as the project gets more complex, the right abstractions save a pot on input tokens (less code to read) and reasoning tokens (less work to do to figure out the code), so they free the context window for higher purposes
Also I suspect that, apart from that, the results on smaller, cleaner codebases are better. LLMs degrade when following more than N instructions (where N depends on the model) even if the context window is not full yet; I suspect they also degrade when code has too many unnecessary concepts and details
This is the exact opposite of what I’ve been dealing with for awhile. LLMs absolute cannot work on something without an understanding unless they can outsource the understanding to a verifier. If you’ve got an easy to check function to measure progress then “keep going” is all the prompt you need. But if you need it to figure out “I pushed the up button and it moved up and left” then it’ll find the same bug five ways without realizing it’s just one bug in the underlying math.
LLMs use abstractions a ton in code though: standard library functions, popular libraries, etc. They just dont always make their own abstractions. At least not particularly good ones. LLMs work really well when they have well abstracted pieces to put together.
I've been working on generating a large code base for the last couple of weeks. Finally got around to generating a sort of code-duplication report and have spent the last week just having it de-duplicating logic that had been strewn all over the place (eg 11 different functions all doing date math to add x days to a date). dozens of items that had each been similar functions duplicated numerous times. crazy. (opus-5-utracode)
No, the problem is they're still really dumb, and lack the ability to make logical connections that are obvious to us. "should I walk or drive to the carwash" being a very recent example of the larger problem.
IMO, That's the case for all subject areas. It is also one area where AI excels at, and it could be of real use if we can find a way to stop hallucinations. The sum of all knowledge being at our finger tips would allow everyone to focus on the hard stuff.
True, but as it pieces together new mathematical truths from the pieces we have discovered ourselves, it then has more truths upon which to build new solutions. And so on, so while it is just remembering things we have forgotten, the amount of progression an LLM can make may still be several steps ahead and touch areas we have not yet been able to consider or make any progress on ourselves. It's a bit like a pyramid though, eventually it will have tiued together all teh things we know, found all the things we could have known, and then .. perhaps, be unable to actually come up with something genuinely new.
Outside of math you can basically take the entire corpus of research papers on any topic and have the AI read all of it and provide an analysis cross referencing everything all at once. This applies to everyone and everything.
This is why education used to start with rote memorization.
Functional intelligence isn't abstract, it is based on useful information you can quickly recall.
This means some AI proofs might be impossible to comprehend by humans, right?
I guess AI still lacks human intuition for many concepts, but AI might beat humans in narrow areas, such as discrete math and combinatorics.
What I'm looking forward to amidst all the negativity, fear, and loathing is for some 20something mathematician to outdo both humanity and machines by leaning hard into centauring to expand the frontiers of mathematics. Pretty much what I think the future will play out to be as well, but I don't think people are ready for that yet.
That currently costs $20 a month, $200 per month if you need the premium extreme deluxe package subsidized by everyone else paying for it and not utilizing it. When I was in grad school I budgeted the equivalent of $3,000 per year to maintaining my compute hardware and that was a very long time ago. So I think it's doable.
Mathematics is typically concerned with "proofs" [1], which similarly to code, often allow for strict validation. Thanks to reinforcement learning techniques, it is now possible to train LLMs to perform very well on code generation, and mathematical proof generation.
Law and medicine are fundamentally harder fields to obtain decent training data for, and LLM results are therefore expected to be less powerful. Also, making mistakes in these fields is costly, but perhaps you were alluding to that already.
Mathematician here. There is a lot of recent work on the Lean project -- when a proof can be translated into Lean code, then it can be strictly and formally validated.
But otherwise, mathematical proofs are read and written by humans, and at the end of the day the relevant standard of proof is what other mathematicians will accept.
Occasionally, mathematicians don't agree. For a prominent example, you can read about Shinichi Mochizuki's claimed proof of the so-called ABC Conjecture:
> Law and medicine are fundamentally harder fields to obtain decent training data for
I think this bubble has given a lot of people software brain and are trying to apply it to fields it is wholly inappropriate for, though. Law is about argumentation and rhetoric. It is about providing a persuasive argument. This is how it is taught. The actual legal code is a way to formalize parts of it, but increasingly I see people angrily insisting that the only thing that matters is the text.
As you might imagine, I find textualism a load of applesauce, but I don’t think the vast majority of people making this argument even understand textualism as jurisprudence. It seems to stem from Crypto bros and the whole “code is law” argument which is just codswallop.
A neighbor of mine whose husband is a lawyer said it's already part of his regular workflows. OpenAI also already have HIPAA compliant offerings targeting healthcare uses, etc. Of course they already do these things.
Well also you can't just throw AI slop as doctors or lawyers advice and fail multiple times until you find the right answer. With code and math you can have failures 1000 times for every success and still get rewarded.
They can rely on compilers, solvers, theorem provers to validate the generated softwares and maths. That’s what makes it possible to iterate quickly in a loop and self correct. You cannot do that in soft industries like legal and medicine
That is not the point I was making. I am not talking about validating software or maths. It can generate stuff that is valid, but bad and incomprehensible.
What I’m saying is that AI labs are talking so much about software and maths because we already have tools that can say « it’s all good ». That makes it possible and worth it for them to spend 1 week of compute on a problem until the validator passes, then publish marketing pieces. You cannot do the same in medicine or laws (modulo some niche areas)
I love the term "Out-Remembering"! I have been trying to find a way to communicate that "intelligence", "creativity" and so on might be misleading about the true nature of LLMs, and they would better be described as genious "reproducers" as in, they are very capable at reproducing what they have already seen - and they are a bit less capable, but for many use cases still good enough, at reproducing a mix of concepts seen previously.
This also nudges into how to use it best: By knowing where the "piles" of if training data are (i.e. when it comes to a CLI in rust, I just briefly describe the use cases, and I have a very high confidence the code will work exactly as intended by me since there will be a multitude of examples in the training data), one can predict where the LLM is likely to go wrong an prompt/guard accordingly. This skill grows with domain expertise, and is one of the many reasons LLMs can be (and probably should be) used to outsource busy work, but never understanding and learning. ("never" is a not meant literaly of course - I for one am glad that I do not have to wrap my head around CSS and other frontend topics and go straight to the topics that interest me most)
"Out-Remembering" captures that perfectly, I feel. Also goes nice along with "asking it leading questions" as we know how to do in real live; if you want a person (LLM) to confess (produce output tokens) something, sometimes you do that by leading the interogation (chat, context) to where you think the truth lies.
There is a certain amount of slack that we have. Things that are obvious consequences of what we've already discovered but that we haven't taken advantage of yet. AI is reaping that slack. It isn't adding brand new ideas at the moment. We will run out of this slack pretty quickly.
It is obvious that super intelligence comes from more working memory.
It is the scary thing actually. Cause once AI makes arguments that require a working memory of hundred items, then we as humans will have no way of understanding the arguments…
We can decompose and write things but only up to a point. when Ai can have a working memory that spans hundreds of books, we are necessarily going to have to trust the system.
This is why we have hierarchies of abstraction. Pretty much every field of mathematics relies on constructing notations, models, and other tools to simplify things in a way that is verifiable. LLMs rely on the same basic technique, they can just pull from a wide variety of these abstractions at once. So far we've been able to understand their proofs just fine. Computer-assisted proofs in the past that relied on brute-force is where we have run into trouble. We cannot reason about millions of possibilities at once, and we had to trust that the computer program that analyzed them was correct, which is a really hard problem and leaves humans fairly unsatisfied. I think we are actually progressing in terms of understandability in computerized proofs.
>Cause once AI makes arguments that require a working memory of hundred items, then we as humans will have no way of understanding the arguments…
That doesn't follow. We could still understand it just by studying it and committing it all to long-term memory, it just takes longer. And there's a hard cap on the working memory of LLMs, due to the quadratic scaling cost of the full attention layers that have proved unescapable for all SOTA LLMs.
That’s how HN works, I had that multiple times over the years with my own submissions. Sometimes it gets picked up quickly, sometimes not. A post can also down rank very, very fast. It depends a lot on the level of engagement and the type of engagement
Well, some folks are going to keep trying to exclude it, but the reality is we are almost at the point even those folks would concede that they are not smarter than LLM. I suspect we will see then see more discourse about consciousness, morality, agency, emotions as being the most important part of intelligence.
For instance, Opus 5 yesterday critiqued my resume and mentioned a ridiculous little detail-- my phone number area code didn't match the state in which I currently work (I know, I should anonymize but I couldn't be bothered). It failed to notice that I both worked in (previously) and studied in the state of my area code. This was just two pages of text, set to highest effort.
Why would you want to replace your lawyer with a set of tensors that does not actually think and makes mistakes like this? Lawyers tend to get hired in high stakes situations. Why wouldn't you instead say that this would be a great tool for lawyers to use judiciously in researching precedents, etc?
I don't understand what people are doing with models that makes them assign agency or intelligence to them. When I manage to forget the financial fuckery of the AI buildout and its implications, when I manage to forget scaremongering by loathsome CEOs, I still have the same fascination and excitement at the idea of LLMs as I did when I was playing with the GPT API prior to the release of ChatGPT.
LLMs are, to me, truly amazing tech. It's so fascinating to me that they now DO have emergent properties that look at face value like reasoning and intelligence. But every day that I work with them, I am repeatedly clobbered over the head with the fact that they do NOT reason and are NOT intelligent.
Why can't we be fascinated by emergent properties of intelligence without immediately jumping 10 steps into the future and, like a limit in calculus, assume that "this is it-- we're on the cusp of AGI"? To me, the fact that LLMs can combine existing ideas that people hadn't thought of combining in solving a novel problem is extremely cool. But my first thought is-- this is an amazing new tool for mathematicians and researchers. Instead, most everyone seems to jump the gun to the "humans are obsolete next year" conclusion.
Aka - it’s a stochastic parrot with a good memory, for anyone still struggling to understand this. It should be obvious, imo, but some people seem to have trouble with the concept.
I don’t understand why this is such big news. OpenAI has essentially made a bunch of marketing copy by gussying up an algorithm being given a near unlimited budget to stochastically permute through its lossy memory.
I think the real scandal is that we are almost 3-4 years into this (I think the release of GPT 3.5 is a good marker of when this public frenzy started) and all we’ve seen is OpenAI and the other major AI frontier companies constantly retracting their preposterous claims every time. We appear to have reach a local maxima in that it has some value in places that tend to be a little easier to scope and limit (computer programming, mathematical proofs). So, given the actual useful economic value this has provided, does this justify the investments? I think we are approaching 1 trillion in CapEx for AI [0]. For context, I believe the annual GDP of Norway is $600 billion.
It's crazy, you see someone spin up 50 instances of chatGPT or gemini or whatever to tackle a math problem, it succeeds by brute forcing through a ton of existing theories to find one that extends the problem, and the takeaway is that this technology is magic and going to solve all of our problems.
Whereas I see that and say - if we properly funded the sciences we could have had a bunch of grad students tackling that problem and found this application 20-30 years ago. Sure it's 'nice' that LLMs can fill in for people in brute force work like that but people are perfectly capable of doing that work and if we focused on properly staffing our research institutions we would achieve a lot more a lot faster. Instead this is obviously going to be used to replace staff and further reduce headcounts.
100%. Context is big for AI, but it's nothing compared to everything a human can learn. If you efficiently represent everything in context, it may be many papers, but if AI is actively working through proofs, it will quickly fill up. They're no denying AI is making strides, but pinning it to memory is an oversimplification.
I don't have to open the article to be confident it's not worth reading. Anybody knowledgeable in the field should be familiar with AI writing tells and the message they send. It only takes a few seconds thought to transform the title into something like "AI beats mathematicians by out-remembering, not out-thinking." Regardless of whether the article is slop or not, I expect any competent writer to avoid slop phrasing in their titles. To do otherwise signals laziness.
Most mathematicians are quite simple creatures. I can do basic math, some derivations, but my bright days of solving differential equations are far gone!
Computers are simply better at math now, like in chess or go!
I don't think I've had a truly original idea in my life. Combine A + B, when it's rare for people to know A and B at the same time. So from that perspective, what LLMs are doing is basically the same thing. Sometimes I am faster than the LLM because my context might be better organized, but it typically needs just a hint from me to steer itself correctly. It claims something is a memory leak, but smelling a rat, I suggest it to double check the garbage collection statistics too, at which point it's clear it's no leak, but a tuning error, at which point the LLM is better at tuning than me, because it has more energy than I do.
Maybe there's true brilliance out there, when something doesn't come out of combining data and building hypothesis until you get really lucky. My experience is not comprehensive. But I look around me, and it sure seems I've not been lucky enough to see it. Even the shiniest people I've worked with, which most of the audience here would recognize, have never shown me that they can go past this.
The exam was huge, at least over 10 pages, and even when we technically ran out of time, the professor was kind enough to move the remaining exam takers to the neighboring lecture hall to continue taking it. I recall I spent a total of 2 hours on that exam.
Now mind you it was mostly short answer or multiple choice questions. The multiple choice questions were pretty sharp too, lots of traps and false but sounds right answers mixed in. But if it had been purely essay questions, I would have been screwed.
However with such a huge corpus of information in front of me, I ended up basically learning all the material on the spot. I just kept doing multiple passes through it, each time I noticed one of my answers contradicted one of the others, I would make adjustments to harmonize, which indirectly refined my understanding.
In the end I got B+ in the exam (which was curved to an A), and walked out understanding the material better than I did walking in.
Reflecting in the experience years later, I've wondered if a hypothetical LLM which was ignorant of microbiology could do the same thing if fed that exam. In some respects the traps they placed in the multiple choice questions actually were what helped me refine my understanding the most. Made me appreciate information theory more.
I actually always thought it was the opposite for me – I had to figure out how to work things out from scratch because I could never remember anything.
Most of us turn out like the rescued exotic bird which turns out to be a seagull covered in curry.
But “remembering” is only the beginning (you have to remember first!), after that, elements like understanding relations, connecting dots and remixing, timing, etc will truly make one shine.
In one way, it’s like the current “LLM + Harness” setup for agents. LLM is how well it remembers, but different harness techniques really matters, at times even a worse model mixed with great harness can outperform great model with bad harness
I know people that got to post grad math without understanding a thing but they could remember a lot easily, while many of those that understood but had a harder time remembering every last variation of everything got penalized.
There’s no such thing as a truly original idea. It is all just combining A+B!
But often results are incremental and obvious.
But also if you jumped from A to A''''', nobody would understand why or what it relates to.
I’ve met different people throughout my career whose intelligence came in 1 specific area. For instance, my friend is extremely good at trivia, he clearly has a lot of storage and can access it easily. I think I’ve only met one person who was excellent in all three areas of intelligence.
Obviously this is a simplification, but it’s how I like to illustrate my ideas on intelligence at parties and first dates.
Understanding especially in the context of unknowns is what intelligence is.
If a time traveler went back to 1600 and started spouting off about differential equations everyone would think them quite mad.
Even in a debate, if somebody just has the ability to remember tons of facts and figures, the other person will seem unintelligent by comparison, even if the other person is correct
Most humans cannot incrementally contribute since they don’t have many traits required to do so - extreme discipline, imagination etc.
We literally live off and benefit from the investments of the few, in relative terms.
> Many people's model of accomplished mathematicians is that they are astoundingly bright, with very high IQs, and the ability to deal with very complex ideas in their mind. A common perception is that their smartness gives them the ability to deal with very complex ideas. Basically, they have a higher horsepower engine.
> It's true that top mathematicians are usually very bright. But here's a different explanation of what's going on. It's that, per Simon, many top mathematicians have, through hard work, internalized many more complex mathematical chunks than ordinary humans. And what this means is that mathematical situations which seem very complex to the rest of us seem very simple to them. So it's not that they have a higher horsepower mind, in the sense of being able to deal with more complexity. Rather, their prior learning has given them better chunking abilities, and so situations most people would see as complex they see as simple, and they find it much easier to reason about.
I once tried out his Anki approach during a math lecture. Whenever I reiterated a card, say about some lemma, I noticed something interesting about it. This was delightful and many lemmas became much more streamlined over time. It's not a "solution" to mathematics, but I found it delightful while it lasted (before akrasia or lack of time kicked in and I stopped doing it).
[1] https://augmentingcognition.com/ltm.html
But AI agents have no such limitations and can publish and re-use negative traces easily. There have been some recent projects (https://www.theoremdb.org) aimed at exploiting this fact. https://news.ycombinator.com/item?id=49227505
In general though, LLMs do not have the same limitations and incentives as human mathematicians, and the next year's tsunami of change will make this abundantly. clear.
That's at least true for current journals, since they're supposed to be read by actual humans. I suppose one could imagine a sort of "AI" pure data journal that just "publishes" (in actuality aggregates) any sort of partial result. This body of knowledge would be entirely useless to humans, but could serve as a sort of "computation cache" for these stochastic systems.
why useless? humans can navigate these unsuccessful chains of thoughts to build on top of them or reject completely
The incentives are not.
The incentives are skewed towards "a magician never reveals her secrets". The results are presented as if a rabbit got pulled out of a hat, with a maximum ta-da! effect, and little backstory of how the hell did we get there.
Don't get me wrong, these things are discussed, often over beers (you better drink it you want to make a career in the field).
But not published.
The younger mathematicians are trying to change that with the blogging culture. But the professional incentives aren't there. (In corp-speak: can't put blogging on perf). They burn out.
That's why math blogs usually come from either the top dogs in the field, like Terrence Tao, who don't need to care about perf, or people outside academia.
That's one thing that I hope the disruptive/destructive effects of LLMs will force mathematicians to face.
As one of my fellow mathematicians sarcastically wrote¹, we've reached a point where we should become a cult because we're acting like one anyway.
The other possibility is, of course, that the shake-up will take us precisely into that direction.
My point here is that the real problem here is not mathematical; it's a social one: incentives and politics, organizational structures, policies, allocation of jobs and funding.
All of this directly impacts how we do mathematics, who we do it with and teach it to, how we teach and communicate, and, of course, what math we even do and look at.
Given that, I'm neither too worried about humans vs. AI standoff, nor hyped about the Glorious New Future full of AI-assisted discoveries.
AI or not, the organizational issues in the field are still there, as are the incentive structures (including the infamous publish-or-perish).
We are doomed, yes, but by our own hands and committees. And it's up to us, not the AI, to get us out of there.
The little shove from the AI might be just the thing we need.
____
¹ https://www.mcsweeneys.net/articles/an-open-letter-to-the-ma...
https://en.wikipedia.org/wiki/J._Robert_Oppenheimer#:~:text=...
sitzfleisch: the ability to endure or carry on with an activity
Something Oppenheimer did not have, apparently.
People go whole lives without being able to make it pan out.
When the flath-earth craze started I've been trying to at least get that bit actually personally verified. Haven't managed to do it to this day, though. So I'll just keep parroting various things without properly understanding them.
C'est la vie.
Explaining Moon phases gets very complicated in any flat earth model. With binoculars you can see the shadows of craters on the moon's terminator. Or the phases of Venus whereas Mars doesn't have any.
Timezones are ridiculously hard to explain on a flat earth.
And for the inevitable critics of Sabine...maybe Leonard Susskind is good enough for you: https://youtu.be/2p_Hlm6aCok
You can take any of the theories that Hossenfelder would spend time on instead of the ones she does not like, and you would find (basically) a similar percentage of physicists saying it's a mistake to continue in this direction.
In other terms: for each physics theory, on 100 physicists, you have 5 physicists saying it is a mistake to continue working on it (number made up for illustration, and there is probably some variations, but you get the gist). You took one theory and found few physicists saying it is a mistake to continue working on it. You conclude, incorrectly, that it means this theory is fundamentally differently treated as any other theories.
(on top of that, it is unfortunate that Hossenfelder later screw up her image by doing way too much mistakes that someone reliable would not do)
(thinking of black holes for example - they were theorized way before we had observations. And presumably a lot of particle physics can similarly be theorized before we built the technology to experimentally verify them)
Out-ralphing them, you might say!
https://ghuntley.com/ralph/
AGI ≈ artificial stupidity × infinite persistence
That is also approximately what people have always done to succeed.
I don't know how or why this would be trained on behavior, but no, it isn't true anymore that models don't say things like, "Ugh," or "this is going to take hours and maybe we should stop here."
Theres going to be this field day of low-hanging fruit that ML can round up, but after that I suspect it will be in fits and starts as a “connection maker” rather than some proof producer.
That makes sense, although I'd argue that at least in the realm of HEP theoretical physics has extraordinarily expensive kit compared to what scientists make. See: The LHC.
That's the marketing pitch.
A plumbing robot doesn't need to be humanoid, an octopus shape may well be better for all the awkward corners. A robot police officer could be the municipality itself for sensory nodes (essentially the sales pitch of Flock etc.), plus some drones or robot dogs to perform arrests*.
The robot vacuum cleaners and lawnmowers we already have are nothing like a human. A robot taxi driver can be just the car. Robot dogs are already used for maintenance and security sweeps.
If you've got wheelchair access, you've got wheeled robot access. If you've got guide dog access, you've got access for Boston Dynamics' Spot.
* this may be a bad idea with current robotics, but I aver it's not improved by making those robotics humanoid.
In the last 100-200 years, that has been proven wrong at every single step.
No people. If you want something with fine motor control and dexterity, it's easier to make that the robot and then have another robot bring the workpiece to the arm than it is to build a single robot that can walk around and do it. There are compromises in human features because we're generalists.
It's not out-thinking, it's just out-remembering
It's not out-thinking, it's just out-working
It's not out-thinking, it's just able to consider more things simultaneously
It's not creative, it's just randomly generating things and then selecting viable ones
We have known for a very long time that computers and machines are much faster than humans, more accurate, are scalable in certain ways that humans aren't, and they don't tire. I think most people who are not in the "AI cult" would agree that LLMs and modern generative AI are really just an extension of those faster/more accurate/more scalable and never tiring traits. But there does seem to be (and I'm sure folks much smarter than I have quantified this or described it better than I can) a fundamental difference in how humans think, especially as it applies to what true "understanding" really entails, and for the ability to think up truly novel and unique things that are not just a rejiggering/recombination of training data. I believe those skills really are at the heart of human cognition, and as impressive as LLMs are in replicating what this looks like, there are plenty of "LLM failure modes" where it's clear that LLMs lack a true understanding of concepts or the ability to generate useful, completely novel ideas.
However I can only guess that this is important, I'm not absolutely certain. They're at risk of being an economic disruptor just by being extremely stupid (by how much they need to study) faster than us to the same ratio we jog faster than continental drift.
Could is carrying a lot of weight here.
Because, what's really happening is we're saying "Oh these things are what defines intelligence" then implementing them and /discovering/ "oh wait, there's more to this than we knew".
We've known, for decades, for example that an IQ test is not a measure of Intelligence, even though people still refer to it as though it is. A computer passing an IQ test, therefore, would have been thought of as possessing intelligence way back when, but would not now.
Oh, on the point of "creativity" - is a RNG "creative"? It creates a value unbounded by human intervention (in theory, yes Pseudo RNGs have limitations) - therefore it must be creative... right?
Your timelines are a bit unambitious. There's nobody expecting to make significant progress with a week of work.
You underestimate my ADHD.
Source: I am mathematician.
Source: the post-it notes, ALL OF THEM.
https://news.ycombinator.com/item?id=48231974
If LLMs are monkeys, somehow trained LLM weights allow them to model and prune massive numbers of universes in parallel.
Someone with a better memory for ideas or concepts will be able to more quickly incorporate those into novel ideas or recall them when necessary to assist in solving a problem than someone with worse memory.
To those here challenging this with “yes but I’m smart and my memory is bad” - a) define smart and b) perhaps your memory for trivial things like life events, what you did two weeks ago on Monday or people’s names is bad, but I suspect your memory for “work” or problem solving is strong.
Another example I used to see (hear, rather) is how musicians rip off each others riffs and hooks without noticing (unintentionally - they claim), which I long suspected as simply “forgotten” riffs they heard in other songs that once they started playing themselves by chance they attributed to their own creativity. Creativity and intelligence are somewhat linked that way I suspect.
In any case, this all boils down to the same thing, you can think of yourself as a dynamic model made up of memories and biases to some degree, and your ability to store and recall useful information to solve problems increases what we call your intelligence.
Heh. Every day, a new type of cope. It's like, coping as hard as possible.
If this was an ML researcher trying to come up with a way to improve performance then you could say it wasn't cope but rather practical observation to serve a goal.
But it's just cope.
Also, AI is going to continue to get smarter. A lot smarter. There are already systems in R&D that will continue increasing efficiency and performance of hardware by more orders of magnitude.
I think where you could say it is out-remembering us is when it can contemplate the vast universe of patterns, gleaned from essentially all human disciplines, encoded in its weights, that may let it draw connections that a human could not, unless they just happen to be familiar with multiple disciplines.
Which is why I think the analogy with Von Neumann / Einstein is also a bit off. From TFA it seems Von Neumann was more akin to what AI does, than Einstein. I don’t get the impression that it was Einstein’s memory but his ability to look at things from a radically different perspective. So far I don’t know that we can categorically say that LLMs can or cannot do that.
I use coding agents. I think they're pretty good overall. They save me a lot of tedious coding. For example I probably wouldn't spend the time to implement native splash screens for all the build targets of a Flutter app, but I'll have the coding agent do it.
Nevertheless, for all the time that we've had coding agents, it's still trivially easy to find the jagged edges of their training. For example, Gemini evidently doesn't know if the Xcode part of a Flutter tool chain is misconfigured. That's not exactly a Millennium Prize problem. But it is shaped wrong for a training set for a coding agent.
The simpler explanation is that a working memory is a requirement for intelligence, and a larger working memory will make you more intelligent. Hence the AI can in fact be more intelligent than the mathematician.
The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
As to your second point, Terry Tao already has an answer [1]: the proof isn’t the contribution, shared understanding is. This issue was already raised back when the four-colour theorem was proved. Machine proving and machine proof checking are useful tools but they don’t mean anything without the interpretative work and the communication necessary to build shared understanding.
[1] https://news.ycombinator.com/item?id=49056620
I agree, but as a software engineer this gives me pause because I keep trying to insist on coding standards but I’m unable to come up with a compelling reason why it matters. Ostensibly the reason we cared about things like DRY and code quality was so that it would be easy to understand and easy to maintain and easy to make changes to later. But it now seems like a shared understanding of the codebase is less important than ever, and it’s more about shoveling requirements in without breaking any existing functionality.
Is a well tested slopfest better? That seems to be the conclusion for mathematics, so why not software too?
Would you personally vouch, at your job, for the importance of proper assembly coding standards?
We already have countless examples of such filling up the arXiv, written by hacks long before LLMs started writing proofs. No one cares about them. You might as well build a box blasting radio static into the void. You could save a lot of electricity that way.
Why is it so hard to imagine we can build tools to think thoughts we can't comprehend?
If there's commercial value, I think it's inevitable. We don't fund mathematicians because it's cute when they understand a problem, but because their work tends to have applications with commercial value. The value can be captured without understanding the details.
It depends on what exactly you mean by "commercial value commensurate with the costs involved" but I'd volunteer the 3G/4G/5G specifications and the other documentation required to implement the mobile network protocols. 5G is currently sitting at over 50,000 pages and it's one of the reasons Qualcomm/Broadcom/Apple are the only ones who can realistically make a mobile radio.
I don't think there is a single human to whom more than a few thousand pages would be comprehensible at a time except for the occasional genius.
If there exists a text which only one person can understand, that person can communicate their understanding to others, even if that doesn't help them with the original text. That dissemination of knowledge is what provides the value, not the mere existence of the text. If that person forgets or dies before they can share their knowledge then it will be lost.
We have many examples of this from history: ancient texts written in a lost language. These texts provide us with no value until the day they can be deciphered, unless you count linguistic puzzle-solving as a virtue.
If there exists a text which only an AI can understand, that AI can communicate their key conclusions to others, even if that doesn't help them with the original text.
The only difference here is the amount of meat involved. Perhaps tossing a few steaks on the server racks could help with that.
Because, again, I can point to hundreds of examples of texts where nobody but the author understands it, and they're only giving summarized "commandments" that you should follow if you want good results.
If I told you "don't use spin locks, call futex instead", do you think have gained an understanding of the Linux scheduler?
How's your understanding of Schroedingers "An Undulatory Theory of the Mechanics of Atoms and Molecules"? You seem to be using the results of it as applied to semiconductor engineering just fine. And, I promise you, most semiconductor engineers haven't read it in full, they just accepted the results as passed on by several layers of teacher.
I have a paper on routing algorithms, which I have attempted to read to my cat. I don't think my cat retained much, but they seem to be enjoying the cat food that got delivered using the results.
I'd suggest that we're going to be a lot closer to the cat than the author of the paper when AI takes off.
All the stuff you've listed is understood by some person, and that understanding is the source of its value.
Now that we've cleared that up, can you furnish an example that satisfies the original claim of incomprehensibility and value?
I don’t find it hard at all to imagine that an AI comes up with a fundamental proof applicable to physics which results in some widget we can now produce that would otherwise not have been produced yet nobody takes the time to fully comprehend why it works. Somebody could, in principle, devote their lives to it and possibly get it, but for what purpose?
Anyways, people benefitted greatly from Newton's laws of gravity, even though we still don't have a quantum-compatible set of laws for it. The laws of gravity are still incomprehensible for people, but the approximation that we've observed is still immensely valuable.
You keep falling back on "incomprehensible for some people" but that wasn't the claim. It was about a text which is incomprehensible in principle; that is, utterly impossible for any human to ever understand.
Every writing must be comprehensible to at least the author, regardless of whether it has commercial value or not. If I hit the keyboard a few times, I've created writing, but it doesn't mean anything. It is just gibberish and without meaning, so there is nothing to try to comprehend. So if there is something to be comprehended, then at minimum the author should know it.
Therefore what you keep claiming is the only refute of your argument of "an [...] incomprehensible [...] writing" is actually a paradox, and cannot be disproved itself. However "humans comprehending things" is not a paradox, which means that your specific request to beat your paradox is not actually related at all.
His examples disproving the non-paradox version of your challenge (writing incomprehensible to folks other than the original authors) are sufficient to disprove your statement, as he gave examples of both people not comprehending human made and 'God' made writing (the universe/gravity)
His original claim amounts to creating an AI that takes its place above humans as some kind of electronic God, delivering edicts to humanity that we cannot comprehend, but which somehow have value to us. It's unskeptical, pseudo-religious nonsense.
If you want examples where nobody but the author understands it, examples are a dime a dozen.
Understanding == Value
If a mathematician produces something incomprehensible then it has no value. It's meaningless. Indistinguishable from random noise.
An AI which produces incomprehensible text is producing no value. We didn't need to spend trillions of dollars on LLMs to figure that out. Markov chains can do that job perfectly well.
Again, do you believe that there are documents, of any value, that humans don't understand?
Maybe an LLM could help you notice what I was saying, since it's clearly beyond at least one human's comprehension!
There is no value in an undeciphered document until understanding is achieved, just as a lode of gold ore in some asteroid orbiting a distant star has no value until we can fly there and extract it.
If an LLM can help us understanding something then it was not incomprehensible, by definition.
This will shift your argument--that doesn't count! etc., to the point where it's by construction unsatisfiable and vacuous. And it doesn't matter: an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.
an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.
No, that is the entire point. If it is an algorithm which accomplishes something useful, then it is intelligible as such. That which is incomprehensible cannot be understood even in part, so it provides no value as a bit of knowledge (unless you're looking for a strong random number source, I suppose).
"Not many people understand some things fully" is so massively different from "the human mind is incapable of understanding some things that AI will understand for us"
The best I can do is things that are incomprehensible to nearly everyone, but still provide value. There's a small leap of imagination to consider an author that understands it and can show others how to leverage results without understanding be mechanical rather than biological.
Paul Krugman (1998): predicted the internet’s economic impact would be no greater than the fax machine’s.
The 1876 Western Union memo dismissing the telephone as having too many shortcomings, and the banker telling Horace Rackham not to invest in Ford because the automobile was a novelty.
We are in good company!
Mathematicians have never been known to communicate their ideas very clearly.
Regardless, even that target llms will likely win - an llm will likely be more efficient at teaching me string theory than a professor in a room with 463 other students.
The llm is the shared understanding.
And at this level, while there are anecdotical exceptions, mathematicians have always been pretty decent (with their conferences, workshops, paper publications, international collaborations, ...).
So, it does not mean "teaching the subject", it means "creating a human network of people that share the understanding". LLM can be useful at telling a human, but you still need a human. The point of Tao is not that LLM is not good at providing explanations, it is that "providing explanations" is not the contribution to science, "the human network" is. It's like saying "LLM are great cook, they generate tons of food in space", but the point of having cooks is so that people can eat food and not die. Having LLM generating mathematical proofs is as useless as having LLM generating food that no one can access: the point was never to "generate proofs" or "generate food", the point was "creating a shared human understanding" or "eating the food so human can survive".
I get that there is a cultural benefit to keeping it alive. Just like we ideally want the languages represented at the universities.
But keeping humans in the loop does not appear to be necessary in order to call it science, and certainly not in order to have progress or dessiminate that progress.
I don't have a problem with people doing math. As long that we don't idiomatically hold on to that way of doing things.
I do, however, find it hard to belive that individual humans will play a big role from here and forward, in any scientific desciplines.
Proofs also enable AIs to direct search and generate knowledge. Verifiability is immensely useful for keeping AI grounded.
One might imagine AI generating enormous numbers of hypotheses and then trying to prove or disprove them, and then mine that data for new abstractions and heuristics.
That's something AI companies would really want you to believe.
Why would I care what they want me to believe?
Intuitively it would make sense that you can put math ability on a chart with a value for “general public” “smart high schooler” “smart undergrad” “smart PhD/ professional”. And you could place frontier AI somewhere on that chart over time from GPT 2 to now and see the trend.
Then you’d have to consider that either you believe there is a fundamental limit that is below peak human mathematician level or there’s not.
How would you not care? Are you a robot?
They can say random stuff with the goal of increasing their shareholder value. Things they spit out do not have to be true. It is not easy to verify things they say, therefore, everything they say should be taken with a huge grain of salt.
So that’s what I’m doing here. For what it’s worth I find a lot of the AI people’s worldview very consistent. They believed AI would be the most important technology of our life times and committed their work to it. Some of these same people are total liars so yeah I won’t really hang onto their every word.
I agree.
> The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
I don't know if I see this being true for quite a while, if ever.
There's an infinite space of possible statements and proofs. The only thing that makes certain proofs significant is that human mathematicians consider them significant; if AI came up with a proof of some statement that no humans could understand then no humans would bother investing further resources in building upon it, for the same reason we don't waste computational resources iterating over the infinite space of true statements in first-order logic.
That sentiment makes me cringe. If you understand how LLMs work, you'd know it'll never be possible without a fundamental change in how these work.
We're also supposed to be reaching that point, somehow, without the LLMs ever being intelligent (in the dictionary definition sense, not the "high reasoning model" marketing sense).
Based on observations, the ones who are fooled by the supposed emergent properties, are just that, fools. Any sufficiently unintelligent agent will perceive transformer based LLM text predictors as possessing high intelligence.
LLMs in agentic harnesses are Turing complete.
To my best knowledge, we don't know of any greater computational model that the brain is a part of, that LLMs are not.
That's the part where LLMs are used as tools. Which there are plenty of places where they are useful.
Also, do you know what turning completeness is? Why are you bringing that up here?
The crowd that AI psychosis has brought to HN is interesting. But not in the "I'd love to learn more" kind
> But not in the "I'd love to learn more" kind
I hope you are able to see the problem in your own communication here.
Computation classes are interesting because they say something about fundamental capabilities.
Two machine that are Turing complete are in theory able to carry out the same computations. They are isomorph mediums of computation.
Regardless. Please keep it sober. If you think you know something, enlighten us. But don't just propagate out lies.
Turing completeness is not exactly a high bar, and it's genuinely confusing as to why you bring it up. Your C++ precompiler is exactly as intelligent as whatever is your favorite agentic workflow with whatever harness you're referring to. Both might be Turing complete. Neither are intelligent. But one of them seems to be fooling you to think otherwise.
There have been many times that the C++ precompiler produced some output I couldn't understand. I might even at some point thought it was trying to tell me something profound I was too dumb to comprehend. Turns out it was just a missing semicolon.
There is no reason to believe that that you can not fully simulate intelligence in a C++ precompiler.
The precompiler can be simulated by human intelligence, and human intelligence can simulate a c++ precompiler.
Again, you are the one who arrogantly say they llms can not be intelligent without supplying any argument for such.
Not really. You've provided the arguments yourself, just now. But, you don't understand them. Which, brings me back to the initial remark, as to why this engagement is bound to be unproductive. I'm off to bed. Have a good one.
Ask yourself: is that really the world you want to live in? It's a world where people, all people, are sidelined.
I think the happy ending of that path is something like Idiocracy. And the more likely ending is something like "automated capitalist economy without the people, because the people couldn't compete."
This is not to say that a human couldn't understand a streamlined version or that the AI would not be better if it made more streamlined statements to begin with.
(I am not saying that everything mathematical that an AI produces is in any sense trivial.)
Humans can’t compete with AIs on vastness of material they are familiar with, or the depth of effort they are willing and able to throw at a problem.
But scale isn’t the only aspect of difficult scientific endeavours. There’s also theory. And advancements sometimes come through hard graft of knotting together many things. And sometimes they come through the revelation of a deeper truth, or a new framework, a fundamental insight.
AI might help us reach the next level. But that doesn’t mean we won’t understand anything. It could be we have periods of vast intricacy we cannot follow, punctuated by profound elegance we (or at least experts) relatively easily can. And then the scaffolding we needed to get there falls away.
The tools we built to replace muscles have mostly obsoleted raw strength for tasks like excavating earth.
There's no reason to think we can't do the same for brains. And then we'll never need to think for a living again. Some people may want to do it as a commercially insignificant hobby, of course, the way people lift and compete in strongman competitions today.
We'll have AI taking care of our needs, the way a good mother takes care of their children.
For this to actually work in a way that benefits our species, humans will need to become something else/next through their interaction with the technology.
Anyways, sipping wine on the beach and doing puzzles when I feel like sounds nice.
The human brain is exceptionally efficient.
Math is not magic, a proof is just a series of applications of a set of rules on some axioms. A mathematician could understand any proof given enough time to study it; the only way for AI to make proofs that a human couldn't understand is by making really, really long proofs.
I think perfect rationality doesn't exist, because it is rational to reject something that you don't understand. So rationality of a given physical system will always be bounded.
This has major implications that haven't been fully realized yet. On the math side, there are long machine generated proofs. On the code side, there are high volumes of code with similar code not being folded into functions.
Also I suspect that, apart from that, the results on smaller, cleaner codebases are better. LLMs degrade when following more than N instructions (where N depends on the model) even if the context window is not full yet; I suspect they also degrade when code has too many unnecessary concepts and details
Has anyone tried feeding all of human knowledge to an LLM prior to Einstein's work and tried to have it reinvent physics?
Trying to convince us that mathematics and software engineering are "solved" is getting very tiring.
The pushback would probably be too much for the soon-to-be IPO-ed companies.
Law and medicine are fundamentally harder fields to obtain decent training data for, and LLM results are therefore expected to be less powerful. Also, making mistakes in these fields is costly, but perhaps you were alluding to that already.
[1] https://en.wikipedia.org/wiki/Mathematical_proof
https://lean-lang.org/
But otherwise, mathematical proofs are read and written by humans, and at the end of the day the relevant standard of proof is what other mathematicians will accept.
Occasionally, mathematicians don't agree. For a prominent example, you can read about Shinichi Mochizuki's claimed proof of the so-called ABC Conjecture:
https://en.wikipedia.org/wiki/Abc_conjecture#Claimed_proofs
I guess whether he will eventually fix those gaps and resolve the issues remains to be seen.
I think this bubble has given a lot of people software brain and are trying to apply it to fields it is wholly inappropriate for, though. Law is about argumentation and rhetoric. It is about providing a persuasive argument. This is how it is taught. The actual legal code is a way to formalize parts of it, but increasingly I see people angrily insisting that the only thing that matters is the text.
As you might imagine, I find textualism a load of applesauce, but I don’t think the vast majority of people making this argument even understand textualism as jurisprudence. It seems to stem from Crypto bros and the whole “code is law” argument which is just codswallop.
This also nudges into how to use it best: By knowing where the "piles" of if training data are (i.e. when it comes to a CLI in rust, I just briefly describe the use cases, and I have a very high confidence the code will work exactly as intended by me since there will be a multitude of examples in the training data), one can predict where the LLM is likely to go wrong an prompt/guard accordingly. This skill grows with domain expertise, and is one of the many reasons LLMs can be (and probably should be) used to outsource busy work, but never understanding and learning. ("never" is a not meant literaly of course - I for one am glad that I do not have to wrap my head around CSS and other frontend topics and go straight to the topics that interest me most)
"Out-Remembering" captures that perfectly, I feel. Also goes nice along with "asking it leading questions" as we know how to do in real live; if you want a person (LLM) to confess (produce output tokens) something, sometimes you do that by leading the interogation (chat, context) to where you think the truth lies.
It is the scary thing actually. Cause once AI makes arguments that require a working memory of hundred items, then we as humans will have no way of understanding the arguments…
We can decompose and write things but only up to a point. when Ai can have a working memory that spans hundreds of books, we are necessarily going to have to trust the system.
That doesn't follow. We could still understand it just by studying it and committing it all to long-term memory, it just takes longer. And there's a hard cap on the working memory of LLMs, due to the quadratic scaling cost of the full attention layers that have proved unescapable for all SOTA LLMs.
But was it?
It’s not just about out remembering, it’s about breadth.
Mathematicians are all about depth. It’s pretty much impossible to become an expert in more than one narrow field of mathematics.
AI is happily applying techniques and abstractions across these silos.
Precisely perfect for replacing lawyers, if nothing else..
Why would you want to replace your lawyer with a set of tensors that does not actually think and makes mistakes like this? Lawyers tend to get hired in high stakes situations. Why wouldn't you instead say that this would be a great tool for lawyers to use judiciously in researching precedents, etc?
I don't understand what people are doing with models that makes them assign agency or intelligence to them. When I manage to forget the financial fuckery of the AI buildout and its implications, when I manage to forget scaremongering by loathsome CEOs, I still have the same fascination and excitement at the idea of LLMs as I did when I was playing with the GPT API prior to the release of ChatGPT.
LLMs are, to me, truly amazing tech. It's so fascinating to me that they now DO have emergent properties that look at face value like reasoning and intelligence. But every day that I work with them, I am repeatedly clobbered over the head with the fact that they do NOT reason and are NOT intelligent.
Why can't we be fascinated by emergent properties of intelligence without immediately jumping 10 steps into the future and, like a limit in calculus, assume that "this is it-- we're on the cusp of AGI"? To me, the fact that LLMs can combine existing ideas that people hadn't thought of combining in solving a novel problem is extremely cool. But my first thought is-- this is an amazing new tool for mathematicians and researchers. Instead, most everyone seems to jump the gun to the "humans are obsolete next year" conclusion.
I think the real scandal is that we are almost 3-4 years into this (I think the release of GPT 3.5 is a good marker of when this public frenzy started) and all we’ve seen is OpenAI and the other major AI frontier companies constantly retracting their preposterous claims every time. We appear to have reach a local maxima in that it has some value in places that tend to be a little easier to scope and limit (computer programming, mathematical proofs). So, given the actual useful economic value this has provided, does this justify the investments? I think we are approaching 1 trillion in CapEx for AI [0]. For context, I believe the annual GDP of Norway is $600 billion.
[0] https://www.fool.com/research/ai-companies-spending-on-data-...
Whereas I see that and say - if we properly funded the sciences we could have had a bunch of grad students tackling that problem and found this application 20-30 years ago. Sure it's 'nice' that LLMs can fill in for people in brute force work like that but people are perfectly capable of doing that work and if we focused on properly staffing our research institutions we would achieve a lot more a lot faster. Instead this is obviously going to be used to replace staff and further reduce headcounts.
Yeah, as expected, an article about AI that's at the very least been polished using AI. For fucks sake we need an LLM flag to filter out slop.
Computers are simply better at math now, like in chess or go!