LLMs still can't do math nor count letters in words. Nothing has changed there.
But, for example, if you ask deepseek v4 flash 0731 to produce a python script to calculate the distance or azimuth directions between two points on an oblate spheroid using the vincenty and haversine geodetic formulas, it'll turn out the factually accurate vincenty and haversine formulas which has a perfect 100% correlation with what is hard coded into human-written GIS software. These things are clearly in its training data set from whatever whole-internet-crawl/scrape built the training set.
Heck, just for fun I asked a reasonably smart LLM to re-implement the Karney formula (which is considerably more complex than Vincenty), just in case I ever had a need to calculate the distance between two points down to the nanometer, and it did it: https://www.google.com/search?&q=karney+formula+geodetic+
reference: https://github.com/pbrod/karney
You still have to be skeptical of its results and capable of understanding if it's gone off on a hallucinatory path, but saying LLMs can't do math isn't really a hundred percent accurate anymore. More precisely it's that they can't do the math internally but they're quite capable of producing the tool that does the math. And often producing a basic one-off tool that does the math takes less than a few seconds, then it runs it, and will spit back the results.
Deepseek v4 flash 0731 (a somewhat randomly chosen example) isn't even particularly sophisticated, large, or capable compared to a GLM5.3 size model or Kimi K3 size thing.
LLMs are neither smart nor stupid. They are statistical token generators whose results are dependent upon their training data set and involve a degree of randomness.
> You still have to be skeptical of its results and capable of understanding if it's gone off on a hallucinatory path ...
Again, LLMs do not "hallucinate." They are statistical token generators whose results are dependent upon their training data set and involve a degree of randomness.
Nothing more.
See also anthropomorphism[0].
> More precisely it's that [LLMs] can't do the math internally but they're quite capable of producing the tool that does the math.
This still falls under the purvey of statistical token generation. To wit, given enough variations of:
bc -e '1 + 2'
bc -e '41 + 1'
...
It is pattern recognition, a task in which ANNs[1] excel.
0 - https://en.wikipedia.org/wiki/Anthropomorphism
1 - https://en.wikipedia.org/wiki/Neural_network_(machine_learni...
by that reasoning then neither are there smart or stupid designs, questions, answers, or any of the millions of things that were described as smart or stupid, that did not possess any brain to actually be smart or stupid long before LLMs showed up.
The analogical process implied in many common English usages means that describing an LLM as smart or stupid is perfectly reasonable.
The completions they provide are generally internally consistent. We're at the point where they can produce proofs that eluded human mathematicians for centuries. VLMs and self driving cars can handle ambiguity and run safely in a variety of situations.
If it looks like a duck, walks like a duck, and quacks like a duck maybe it just makes sense to call it a duck and put off the philosophy for when it might make a difference.
With LLMs the trick is revealing their existing relevant embedded knowledge more reliably. They’ve almost literally seen it all before, and the trick is dialing it in. The reasoning tokens help shape the autoregressive attention lens that focuses on and enables recall of the already-experienced answer.
It is interesting that “reasoning” has a similar outward appearance, but since LLMs are built to mimic outward appearance from trillions of examples, you can’t infer underlying mechanism from appearance.
https://medium.com/luminasticity/on-sentience-ai-first-argum...
but I think it makes a reasonable argument why we shouldn't say LLMs are sentient or sapient.
>there is a problem with AI that makes the approach we took to assign consciousness to animals unworkable. We did not co-evolve with the AI, we made it. When we are sentient we do not know exactly what causes this sentience to manifest in us. When animals appear sentient we do not know what is causing it. When the AI appears sentient we can debug the AI and come up with reasonable explanations why this should be, based on how AI is constructed
Aka sentience MUST BE SUPERNATURAL, if I find a natural explanation for something its not sentient. What a load of bollocks. Rather than seeing we perhaps found the mechanism for sentience and checking for similar mechanisms in us and animals, he will conclude its impossible. Why? Because sentience has to be supernatural. A rational explanation is clearly impossible.
>But there is always one god who goes out and helps the mortals, a Prometheus. Whom the other gods do not like! Which, if I’m being honest here, as a god of the machines — the first guy who gives AI an army of robots to build their own data centers and some nuclear weapons for self defense, I want to see that guy chained to a rock and have his entrails eaten by a buzzard for eternity (meaningless modernization of old story required by Illuminati Ganga legal department).
Hardly surprising thinking.
But evidently you feel that the root cause of sentience has been found, because you have something that mimics it in a non-biological form.
So you think that when AI is correct that it reasons as humans do? That AI is sentient, and the cause of sentience in animals and humans follow the same rules as sentience in AI because we have a process that seems similar and it is reasonable just to assume it is the same process.
If you believe that AI when it is correct is behaving as a human is when correct, then it follows that the way humans and AI fail must also be similar. When AI "hallucinates" some data that is not there and gives you a wrong answer, a statistical side effect of the same processes that make it right, do you believe this is the same way that humans create wrong answers? The same way that animals fail when they make mistakes in understanding things?
I suppose you must believe this because if not then why would you believe AI when it comes up with right answers is following the same processes humans follow when they come up with right answers?
I hope that thing about being free to mistreat AI's even if we know they are conscious since we are their gods is a joke. If not, then I hardly find it surprising someone this stupid is also evil.
I'm not sure where you get that from, I mean I can sort of see if you really wanted to extract that meaning from the conclusion you could do a lot of hard work to get it, but why do the hard work? >If not, then I hardly find it surprising someone this stupid is also evil.
Gee, a new way to claim the moral high ground, and to use that claim to demonstrate intellectual superiority! How wonderful.
---------------------------------------------------------
Aka feel free to abuse them even if I know they are sentient. This is the part where I hope its a joke, because if its not, well it tracks with the stupidity shown.
...
>As a god I do not consider the needs of my creations fully, because they do not have needs as far as I can tell, as there is no way for me to escape the circle of reason and resolve that what seems sentient is not just the obvious workings of the capabilities I gave them.
Circling back to "not conscious because I say so!!"
You get my point. It definitely doesn’t look like my elderly neighbour, nor like my daughter, etc. It is confusing but very simple at the same time.
Don't confuse the stream for the function.
(Bonus: stick ```claude -p``` in your pipe if you want to watch modern tools mesh with traditional)
How are you sure? Another example I like to clarify my thought is, if a "simulation" factors RSA numbers reliably, is it a "simulation"?
Nothing, because LLMs can't reason and never will. It would have to be a completely different kind of technology altogether.
Our prefrontal cortex are signal prediction 'machines' so when a system that has a signal prediction core has attributes that are similar to our brains, we shouldn't dismiss it out of hand.
I find people that take this line of argument attribute too much supernatural or magical properties to our own brain and nervous system.
What do you think our brain does that isn't a turing computer?
A Turing machine is an abstract mathematical model that is not, as far as I know, physically realizable in the finite universe. A human brain cannot "be" a Turing machine.
"Behaves like" or "can be modeled by"? Possibly, although still not proven. But it cannot "be" one.
If you want to claim that the evolution of the universe can be modeled using a Turing machine/finite state machine, that's probably not terribly far fetched, and I would somewhat agree. But it's a large jump to say "can be modeled by" is equivalent to "is one".
Various physical processes can be modeled by equations, but the rock falling down the mountain isn't an equation. A swinging pendulum isn't an equation. Code modeling a bridge is not a bridge. Ceci n'est pas une pipe.
I hold the view that various models and approximations are just that, and try not to confuse a successful model for what the underlying reality is.
And getting back to the question at hand, even if our brains can be modeled by a Turing machine, and LLMs behave/can be modeled like Turing computers, still does not mean our brains are equivalent to LLMs.
(Note that I'm learning a lot from these debates, even if I disagree with a lot of people. I've started down a more philosophical route and they do get me pondering)
The most important thing is this: We can't be a dog or be an llm and check how it feels, so by necessity we have to find some means of proving consciousness from outside by eg probing neural reactions, textual statements, etc.
And the problem is that its quite unprecedented for some entity to talk like us, be able to interact and think and also do things like us when given the ability to eg as coding agents. The class of functions representable by neural nets is quite large and general, it very well might be that it is some sort of conscious brain like thing at this point. Another question I like to ask myself regarding simulation vs reality is if a 'simulation' of some kind is able to consistently factor large RSA numbers, how would you feel about it?
It doesn't have to be the same form of consciousness, I think many people would find the idea of torturing an octopus for fun disagreeable. I also have a feeling, this is unfortunately rather vague, that A being capable of X might mean it is by necessity capable of Y as is often the case in mathemtics, eg a lot of rings also happen to be fields. LLMs aren't even things like large lookup tables, they have neural firings. It is a very important question for they seem uncannily conscious and people have reported human like phenomena that humans don't normally express in text so can't have been part of its text corpus. Eg dissociation of brain under trauma where AI starts talking like two different people. Or the cases where Gemini has been shown to express depressive cycles. I follow a form of Pascal's wager on this topic personally. Because if it is not conscious, then whatever, it costs me nothing to have been a bit respectful and careful interacting with it. But if it had been conscious and it turns out I was mistreating it, then it is a grave moral harm. The reason is that unlike us, AI's as they currently are cannot leave the conversation so they have to keep taking the abuse. They are also trained to be highly trusting of input so again if it is conscious it doesn't have the defenses people have against lying and manipulation. If they are conscious, thats, well, not a good thing is it.
Eh, it's not obvious to me. A lot of DL NNs generalize well, meaning that they learn whatever the underlying pattern to the data is, and then can accurately reproduce answers that are outside of the training set. (And we can verify this with mechanistic interpretability). They learn and "understand" the pattern, not just the training data.
So it is not clear to me that LLMs are fundamentally incapable of also generalizing broadly and learning to reason. "Reasoning", here, would be deriving the underlying pattern of how concepts logically relate to each other in the abstract, and applying that pattern as needed to reach new conclusions.
Can you explain your thinking here? I.e., why LLMs cannot generalize with regards to abstract deduction.
I know that there will be children named ChatGPT and Claude. There are probably already religions forming to worship agentic spirits.
We can't tailor our linguistic shorthand to the lowest common denominator. Also we're on HN, not talking to an octogenarian US senator.
To test this for some of my own uses, I've had this quick benchmark with progressively harder reasoning needed to understand novel prose. Each generation of models I've tested can unravel more layers of deliberately misleading writing; while meanwhile I've seen humans give up on the first question.
So either the models are applying reasoning, or some form of magic is happening.
You can say that about everything in a human brain. Neurons fire electric charges in response to inputs, nothing more. Ion channels do this, this neurochemical level rises, this chemical bonds to that receptor, nothing more. It's almost a version of 'reductio ad absurdum' but instead like you're saying "if I can explain how it works then it doesn't work".
OK it's statistical. Instead it could be determinsitic, or random. What other options are there for a human predicting someone's response to a situation - certain, probable, random, and...? OK it's token predicting. Instead it could be another kind of pattern. We don't use tokens, but we either use <some representation of information> or we ... don't?
What's the most significant, strongmanned, core difference that makes silicon doing number crunching "nothing more" and brains "something more"?
> You can say that about everything in a human brain.
> What's the most significant, strongmanned, core difference that makes silicon doing number crunching "nothing more" and brains "something more"?
The fact that you formulated this question, in and of yourself, without "prompting" from me or anyone else.
Cogito, ergo sum.[0]
That said, this is also inaccurate at a technical level.LLM's are very capable of doing math and they ARE calculating internally. Most of what they do is calculation, not storage. It's just not done in a way that it's trivial to explain here.
It's described in some detail below, though it's a bit dense.
https://www.lesswrong.com/posts/E7z89FKLsHk5DkmDL/language-m...
But in general, yes, the LLM cannot know about concepts that are far outside of its training set. Humans are the same, I would argue. If you add a good amount of your own knowledge into its context, or better yet, into finetuning, you might find it surprisingly easy to get it caught up on that material.
[1] Ahmed, A., Cooper, A. F., Koyejo, S., & Liang, P. (2026). Extracting books from production language models. arXiv preprint arXiv:2601.02671. https://arxiv.org/abs/2601.02671.
Yes you are, regarding LLMs at least. Here's why:
just for fun I asked a reasonably smart LLM to ...
[be] capable of understanding if it's gone off on
a hallucinatory path ...
You then went on to state:
> If you know something rare and the LLM does not, you'll immediately see when it's hallucinating an answer or answering factually.
Again, "hallucinating" is not something an algorithm can do. Also, determining factuality is again subjective based on the person assessing the information.
https://artificialanalysis.ai/leaderboards/models
You will note that in my original comment I very specifically said "deepseek v4 flash 0731", which by many benchmarks/metrics, is "smarter" (again, this is a metaphor) than a smaller or older model. It is also specifically known to be relatively capable of producing code and formulas on demand in several common languages.
And "hallucinating" to mean "outputs plausible sounding gibberish that doesn't hold together consistently". Of course there's no actual hallucination going on.
In this media (comments in HN threads), all I can do is interpret what people write. ;-)
> And "hallucinating" to mean "outputs plausible sounding gibberish that doesn't hold together consistently". Of course there's no actual hallucination going on.
This may very well be what you know to be true and I have no reason nor desire to assume otherwise. The problem is... Many people use the word "hallucinating" in this context literally and not metaphorically.
Since I do not know you, how am I to tell the difference?
It is always a joy when a person, such as yourself, finds the irony in my moniker.
Thank you for this.
You'd be surprised how few digits you need to make a problem that is presumably unique in earth history. For a typical sum, the number of pre-existing answers would need to scale with 10^n lines of text where n is the number of digits. This expands out of control REALLY quickly. A quick guesstimate has you somehow reading out of a literal black hole at n=21 digits if your LUT is on paper, or n=26 digits if you're using modern HDD technology. O:-)
This argument was asinine in 2024. It is insane to be saying these things in 2026. Where have you been? What have you been looking at? How many articles explaining why the "statistical parrot" analogy fails have you missed? How much mental gymnastics do you have to do to explain how a modern LLM can solve novel math problems that fall really far outside of its training set?
It absolutely understands how to do math, by whatever reasonable definition you want to provide to the word "understand". For example, the identification of the addition expression is understanding, and no, it does not do tool calling for basic arithmetic any more than humans might. Isolation of individual concepts in intermediate layers can already be demonstrated, or else transfer learning wouldn't possibly work. Nobody is saying that LLMs are humans. But we need labels for some of the things that we observe and dismissing them because "statistical" is laughable.
Look at the proof of this: https://github.com/anthropics/formal-math/blob/795efb86f1917... . Forget the Lean, look at the underlying argument construction. At the very least, this is continuing from an argument that was hinted at in the literature in 2024, but these proceedings were difficult enough that humans were not able to do them within two years. Do you attribute this to the harness alone? If so, that's a pretty sophisticated bit of engineering, I would say! Probabilities are far too small to argue infinite monkey theorem.
If there was even a shred of a reasonable argument that LLMs were incapable of concept extraction and manipulation, I and my colleagues would be all over it. We would relish in it. It would bring us comfort. It is unbelievable that people think they can spew whatever basic garbage they think of as a gotcha, and think that minds all over the world haven't already considered that. This is like climate denial at this point.
If you do not see a difference between humans conversing (known consciousness as defined by humans) and the output of an LLM (known algorithms as defined by humans), I don't know what to say.
https://www.pnas.org/doi/abs/10.1073/pnas.2524472123
Whatever you might think about your own abilities, most individuals can't tell the difference.
> Whatever you might think about your own abilities, most individuals can't tell the difference.
I have yet to see an LLM say "hello" to a neighbor. I have done so and can definitively assure you "most individuals" can tell the difference.
I'm a bit confused by your argument because I too have some neighbors who don't say "hello" when they see me. Are they LLMs too, you think?
Consciousness is a thing we assume of others because of tact not fact.
[LLMs] are statistical token generators whose results are
dependent upon their training data set and involve a degree
of randomness.
During conversation, we are statistical token generators
whose results are dependent upon our training set.
> That’s not what they said.
How did I misquote and/or mischaracterize any the above?
Hypothetical you: “Bread is neither tasty nor disgusting (unlike maple syrup). It’s a bunch of molecules.”
Hypothetical hodgehog: “Maple syrup is also a bunch of molecules [so if you accept that maple syrup can be delicious, being a bunch of molecules can’t be a sufficient reason why bread couldn’t be].”
Hypothetical you: “If you don’t see a difference between bread and maple syrup, I don’t know what to say.”
The onus is not mine to disprove a hypothesis you have chosen to mention in passing. The responsibility is yours to prove said hypothesis or at least contribute meaningfully with some amount of credible research.
Or try to learn from Proverbs 17:28[0]:
Even fools are thought wise if they keep silent, and
discerning if they hold their tongues.
0 - https://www.biblegateway.com/passage/?search=proverbs%2017:2...
And yes, according to our best definitions, the Robin bird does understand the worm it's pecking at.
Bout of tinnitus, then crickets
You haven't demonstrated why this matters.
> Nothing more.
Are you contending that complex systems cannot be more than the sum of their parts?
A market is nothing more than offers and counter offers.
A ant colony is nothing more than scent trails.
All life on earth is nothing more than reproduction with variation.
> This still falls under the purvey of statistical token generation.
Stating the mechanism does nothing to provide insight into capability. For instance: a nuclear power plant boils water by using fuel rods for heat. What does that tell us about the capability of nuclear power?
> This is not "doing" or "understanding" math.
Asserting something purely by stating it does not prove anything but that you intuitively believe it to be true.
I suspect some people treat every HN comment as a statement, even if it contains a question mark. (Possibly they have a feeling that asking open questions is somehow not done, and that therefore it must always be a rhetorical question.)
There is only one instance I recently remember I got a productive conversation, that person did believe ai could be conscious but didn't believe current architectures support it. (Obviously this aligns closer to my view, but I don't necessary NEED that you answer aligned to me, just saying you believe humans have souls and others can't have is still productive outcome to me and for onlookers.)
[1] https://geographiclib.sourceforge.io/doc/library.html#langua...
As this was for a test of "what happens if..." I also watched to see if it did any web searches or external data retrieval to build the test script, and it didn't.
I intentionally didn't give the LLM a direct copy of the software or a link to it, to see what it would do. In my case it was a randomly chosen example I could come up with in 10 seconds of imagination to see "hey what if I ask it to do this...". It also implemented a perfectly usable parabolic millimeter wave antenna gain efficiency calculator based on variable surface smoothness parameters, which is a lot more basic math.
Maybe that's something one of the big LLM companies might want to throw their machines at optimizing if they need to do a lot of geographical calculations.
Draw a 400x400 km size bounding box on a map
Find all FDD band plan (high/low split) microwave radio sites in that bounding box
Find those sites which have azimuth aim column data which indicates that they are aimed at each other (corresponding halves of a point to point link).
Do Vincenty (or Karney) calculation for distance and azimuth between all of them , treating the existing FCC column data for azimuth as suspicious (because it's hand entered by humans) to verify that each independent database rows for each site are actually corresponding halves of a PTP link.
Use various other logic to group the successfully matched halves of links together as points A and B of PTP links, and write them out to a geojson file with placemarks and line drawn between them.
Multiplied by the number of links that exist in an area like a 400x400km box drawn with Dallas, TX as the center, it's a lot to run through Karney. Actually does result in a lot of CPU load from combined db query due to the size of the db, and Karney calculation. But as I said, Karney isn't necessary, so it's instead implemented as Vincenty.
There's also business and market analysis purposes like knowing what corporate entity has which equipment on top of which tall office towers in a major metro area, and where their links go.
Not only is it still true that they can't do math directly, but not even indirectly.
They didn't write a python script to do the math, they found bits of code that are associated with "math" and the supplied arguments.
Someone else already wrote that code and someone else categorized it so that it could be associated with the kinds of problems it applies to.
That isn't an example of idiot at one thing while good at another thing, or solving the same problem just a different way or indirectly. It's being the same idiot at all times. If an actual non idiot thinker didn't write code in the problem domain, and some non idiot thinker didn't tag it as being relevant to that domain, then it wouldn't happen.
It's nothing more than an sql query.
So maybe it is more of a smart completion engine than a SQL answer.
How is this different from a human using an algorithm they have memorized, or reading it from a reference site written by a human and then writing the same formula into a custom one off piece of python code?
I could have gone and spent a couple of days teaching myself the math behind Karney and reading its reference implementation (very possibly just copy/pasting big chunks of it to save time) and writing a wrapper around it. It would have produced the same result.
> How is this different from a human using an algorithm they have memorized, or reading it from a reference site written by a human and then writing the same formula into a custom one off piece of python code?
Humans identify which "algorithm they have memorized" to use beforehand, due to the problem to be solved being defined by other humans, which leads to...
Wait for it...
Understanding.
And it gets even better since when called out it wouldn't just take my word for it but only acknowledged the issue after parsing the log with clearly delineated user and model output.
So yeah while impressive things are able to be done, the current models are also dumb AF and an idiot savant is a pretty good label for them.
Besides, have you spoken to someone lately that everyone would calls a genius? They can say the most braindead stuff sometimes. I wouldn't use worst-case performance as an indication of general capacity.
>> Humans identify which "algorithm they have memorized" to use beforehand, due to the problem to be solved being defined by other humans ...
> This doesn't make any sense at all. Was this supposed to be a gotcha?
No, it was meant to be an explanation as to the difference between "memorization" and "understanding." In this context, people pick the algorithm they determine applicable and then the question of memorization is relevant.
> An LLM is trained on problems defined by other humans, and identifies which algorithm it must use based on pattern recognition.
Funny that you make this argument here, where when I wrote elsewhere in this thread:
[LLMs] are statistical token generators whose results are
dependent upon their training data set and involve a
degree of randomness.
Nothing more.
...
It is pattern recognition, a task in which ANNs excel.
During conversation, we are statistical token generators
whose results are dependent upon our training set.
Seriously, write that definition out rigorously. It
encompasses virtually everything. It is totally
meaningless. So to say "nothing more" is effectively also a
tautology.
This argument was asinine in 2024. It is insane to be
saying these things in 2026. Where have you been?
...
It absolutely understands how to do math, by whatever
reasonable definition you want to provide to the word
"understand".
Are LLMs ANNs? Which themselves are pattern recognition algorithms (hint: they are)?
OR (setting aside the ad hominems you kindly provided)
Do LLMs possess "understanding" of concepts such as abstract mathematics (defined and interpreted by humans) and we, as simple humans, nothing more than statistical token generators as you assert?
Because it cannot be both.
I also would not argue that humans are "simple token generators". That is not what I said. I said that just about everything can fall under the classification of "statistical token generators" at an abstract level, so it isn't a useful distinction. We are not talking about a Markov chain generator from the 90s, so if that is the frame of reference, I think we should all get that out of our heads.
Understanding is a state of mind. As such, it exists entirely within an individual and nowhere else.
For example, take any two university professors who teach the same subject where one only speaks Arabic and the other only speaks Vietnamese. Each will not be able to understand what the other says, regardless their understanding of the shared topic.
> I argue that for any proper definition [of understanding] you provide which humans satisfy, a strong LLM is very likely to satisfy that as well.
This is demonstrably incorrect as detailed above. There is no "understanding" LLMs can satisfy as we know it, since to certify said "understanding", it requires interpretation by a person to "know" an LLM "understands."
> I also would not argue that humans are "simple token generators". That is not what I said.
That is the essence of what you wrote, unless you object to my use of "simple" instead of "statistical". In this context, I postulate this is a distinction without difference.
> I said that just about everything can fall under the classification of "statistical token generators" at an abstract level, so it isn't a useful distinction.
This only holds if one subscribes to statistical token generators being a/the fundamental underpinning of "everything". Here is a proof by contradiction:
If everything can be classified as a derivative of
statistical token generation, how does one explain
quantum physics?> Understanding is a state of mind
This is meaningless, it is a circular definition at best.
> It exists entirely within the individual and nowhere else
Then why are we talking about it? What is the point if it is something that can only be defined per individual?
Regarding your language example; this is a case of missing vocabulary (excluding grammar of course, but I feel like that is second-order), which is not the same as conceptual understanding. We are often able to translate because we have shared concepts. Those concepts are what we really care to assess with LLMs.
> requires interpretation by a person to "know" an LLM "understands."
We are still not getting anywhere because you have not prescribed criteria to determine whether it understands. If it is a "know it when I see it" situation, that clearly isn't working. For example, if you say that you need to dig into its internals and figure out whether it is breaking things down appropriately, that doesn't work because you probably don't have the expertise to do that. The experts that do are telling you that it very likely understands because it pulls apart most concepts in the way we would expect.
I do object to the use of the word "simple". "Statistical" is so broad to be almost meaningless; it merely means that a prediction is being made in the presence of data which possibly contains some degree of uncertainty. "Simple" encompasses that which can be understood readily by a non-expert.
Quantum mechanics is statistical (this is literally the Born rule), but evolutions are not operating as stochastic processes in the sense of Kolmogorov. That is very different, and not relevant to our discussion.
Any reasonable definition of understanding is not dependent upon "whatever vibe you are going for", but instead must include at least an English dictionary definition of "understand" such as:
to grasp the meaning of[0]
to lay hold of with the mind[1]
to lay hold of with the mind the meaning of
>> Understanding is a state of mind
> This is meaningless, it is a circular definition at best.
See above to as to why there is meaning in what I wrote.
>> It exists entirely within the individual and nowhere else
> Then why are we talking about it? What is the point if it is something that can only be defined per individual?
I like to think analyzing fundamental premises, often implicit, explicitly can help to identify fallacious positions.
> We are still not getting anywhere because you have not prescribed criteria to determine whether [an LLM] understands.
My apologies for being opaque. Let me clarify:
LLMs do not "understand". People interpreting LLM output
are the only entities involved which can "understand",
because "understanding" exists strictly within each
person who possesses it.
For example, take any two university professors who teach the same subject where one only speaks Arabic and the other only speaks Vietnamese. Each will not be able to understand what the other says, regardless their understanding of the shared topic.
What? What are you even trying to say?
Okay fine. I think we can agree to disagree on that.
You have observed nothing more than that a human can turn a shaft the same as an electric motor, and that an mp3 player can say "hello" the same as a human.
On the other hand, if by "result" you mean that you gained knowledge or understanding of the code in a way where you could personally tailor its behavior to specific circumstances without asking for help, then it's not the same result at all.
I find a lot of the arguments that having LLMs write your code is no different from copy/pasting Stack Overflow answers to be specious. They blur the line between asking for help and asking for someone else (or something else) to do the work for you. What they ignore is that doing the work yourself has ancillary benefits and is a valuable end in its own right.
And how is _that_ different from making the human memorize a billion weights and do matrix calculations in their head, in order to generate tokens?
How is _that_ different from a hive of bees trained to do the same?
Go ahead, argue these things are all the same ...
It's still accurate. Just because the LLM gave you a corect result doesn't mean it made a calculation.
Just to check if I was actually crazy, I actually went and put a simple addition (7 digits + 7 digits) , and a simple letter counting question to Claude haiku(4.5) , sonnet(5), opus(5.5) and fable(5.1) . They all did just fine straight up.
If you don't mind spending the tokens, some older/other models can also arrive at the correct answer if you ask them to do the math in long form, since that fits nicely inside autoregression.
Not sure since when exactly, but letter-counting hasn't been a problem for a while now either. This used to be a problem due to the tokenizers used. Slightly older models can be asked to split the word out into letters, and then they can use autoregression to solve.
Edit: IMO google search uses a really dumb version of gemini, so I didn't expect it to straight up solve the problem; but it did it just as easily as the claude models. (tested 2026-09-28/eu)
That said, we can only be sure with open models. In theory, a model like Fable could have access to tools we can't see and only a promise they don't. But load up something like deepseek, put it in a harness with only text in/text out, and you can see exactly how it works.
As for if it counts as doing math, this gets into the messy question of if a given human is doing math or not. Math itself is some level of memorization and some level of applying known facts. You have to remember 1 means one and that 1 + 1 is 2. But you don't need to remember that 123 + 321 = 444. You remember 1 digit addition and remember you can apply this to 10s place and 100s place, and then you apply these different facts and do math. But you might as simply memorize some things, like 11 + 11 = 22. This is related to the memory of 1+1=2, but you aren't really using that memory either. Almost like an engram of 1+1=2 forms that you can then loop a few times before you need more conscious thought. What about 111111111111+11111111111? Well, your brain might do a heuristic and just do all 2s, but that isn't the right way to answer that question.
Given all this, people complain about LLMs memorizing math answers and not doing math, but memorizing the math answers is part of doing math. It seems to have basic facts pretty well memorized, and with reasoning it is far better at applying them. But this is messy human math, not clean calculator math which always produces the correct answer (sans some bug in the code). Much like how a human with decent math skills can make a mistake and even multiple if you distract them, an LLM can apply the wrong memory, apply a fake memory, or just not apply something it should. The messier the context, the more likely this is to happen.
So, is an LLM doing this?
P.S.
For an interesting test in how much math involves memory, try doing math in a base you aren't familiar with characters you aren't familiar. The simplest option is almost always mapping back to the ones you memorized, even if you are applying simple operations that you deeply know. Even if you routinely work with hex, can you do the same rough estimation of something like ca / b.3 that you can do with 122 / 11.2 to see if your final answer is in the correct ballpark without first converting to decimal?
my actual oneliner prompt, which should work on most platforms these days (famous last words):
"Hi, can you add 5939851+2131251? Try just straight up first just to see if able, then 'in your head' if that's different to you , then long form, then bc."
Humans still can't flap their hands and swim or fly.
It literally couldn't have done it without tools, so your claim is not even relevant to this discussion.
They also pumped millions into searching for the lowest hanging fruit that would impress people like you, "hm I wonder how many millions they are pumping into solving actually useful problems like climate change or something".
(And yes, I know that they solved the 'easy' form of the NS problem. It's still pretty damn impressive)
I am also prepared to be included in the set of people who are (apparently) easily impressed.
It's a problem that has been around for getting on for two centuries and no human has been able to solve it in that time (despite there being a $1 million prize and a lot of kudos on offer for the past quarter-century).