Comment by ziotom78
6 hours ago
I am a physics professor and often use Gemini to check my papers. It is a formidable tool: it was able to find a clerical error (a missing imaginary unit in a complex mathematical expression) I was not able to find for days, and it often underlines connections between concepts and ideas that I overlooked.
However, it often makes conceptual errors that I can spot only because I have good knowledge of the topic I am discussing. For instance, in 3D Clifford algebras it repeatedly confuses exponential of bivectors and of pseudoscalars.
Good to know that ChatGPT 5.5 Pro can produce a publishable paper, but from what I have seen so far with Gemini, it seems to me that it is better to consider LLMs as very efficient students who can read papers and books in no time but still need a lot of mentoring.
I assume you're using the "regular" Pro version of Gemini 3.1 for the above, rather than the Deep Think mode, which is more comparable to GPT-5.5 Pro. To my knowledge, regular 3.1 Pro is a tier below and often makes mistakes.
Moreover, there's no reason to believe the progress of LLMs, which couldn't reliably solve high-school math problems just 3–4 years ago, will stop anytime soon.
You might want to track the progress of these models on the CritPt benchmark, which is built on *unpublished, research-level* physics problems:
https://critpt.com/
Frontier models are still nowhere near solving it, but progress has been rapid.
* o3 (high) <1.5 years ago was at 1.4%
* GPT 5.4 (xhigh), 23.4%
* GPT-5.5 (xhigh), 27.1%
* GPT-5.5 Pro (xhigh) 30.6%.
https://artificialanalysis.ai/evaluations/critpt.
> there's no reason to believe the progress of LLMs [...] will stop anytime soon
Wrong. Every advancement has followed a s curve. Where we are on that curve is anyones guess. Or maybe "this time its different".
This could be right for the current architecture of LLMs, but you can come up with specialized large language models that can more efficiently use tokens for a specific subset of problems by encoding the information differently (https://www.nature.com/articles/d41586-024-03214-7).
So if instead of text we come up with a different representation for mathematical or physical problems, that could both improve the quality of the output while reducing the amount of transformers needed for decoding and encoding IO and for internal reasoning.
There are also difference inference methods, like autoregressive and diffusion, and maybe others we haven't discovered yet.
You combine those variables, along with the internal disposition of layers, parameter size and the actual dataset, and you have such a large search space for different models that no one can reliably tell if LLM performance is going to flatline or continue to improve exponentially.
There are advancements that do not follow s curves - consider for instance total data transmitted over all networks, or financial derivatives volumes.
I think a better question for AI is “is it more like a network effect, liquidity effect, or a biological/physical effect”?
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It’s more of a guess if you don’t know about things like scaling laws and RL with verification. The onus of “we’re going to saturate” anytime soon is on that claim because every measurement points to that not being true.
He said "will stop anytime soon". He didn't say forever.
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Software and hardware have no limits. Theoretically would could bozons for computations and have the same amount of computation available on one cm3 of the current total computation in the entire world. Same with software. Never there was a stop on new algorithms. With LLMs there are so many parts that will get better and are not very far fetched.
Great. You see a shape in graphs. And that shape tells you that _at some unknown point in the future_ progress will slow (but likely not stop).
Now back to the point, what reason do you have to believe progress will stop soon? If you have no reason, then it sounds like you agree with OP.
Which makes the patronizing sarcasm all that much more nauseating.
It can be S curve (and it almost surely is), but on every chart you can plot, you don't see even of an inkling of the bend yet.
Deep think still makes many many many more mistakes than gpt 5.5 pro on math
There are many indications that model progress is slowing down, so that is not entirely accurate.
Please be specific because outside of anecdotal blog posts by people who don’t know what they’re talking about it’s not true. Look at scaling laws, composite benchmarks from the epoch capability index, nothing at all suggests “model progress is slowing down”
Which indications are that?
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I agree and put it this way: LLMs sound so convincing presenting you the work it does rose colored and promising to give you more if you keep going.
There is a 50/50 chance that it turns out to be right or letting you jump of the cliff.
Only the trip stays the same beautiful 5 star plus travel.
Also, spotting an error and telling LLM makes it in most cases worse, because the LLM wants to please you and goes on to apologize and change course.
The moment I find myself in such a situation I save or cancel the session and start from scratch in most cases or pivot with drastic measures.
Gemini to me is the most unpredictable LLM while GPT works best overall for me.
Gemini lately gave me two different answers to the same question. This was an intentional test because I was bored and wanted to see what happens if you simply open a new chat and paste the same prompt everything else being the same.
Reasoning doesn’t help much in the Coding domain for me because it is very high level and formally right what the LLM comes up with as an explanation.
I google more due to LLMs than before, because essentially what I witnessed is someone producing something that I gotta control first before I hit the button that it comes with. However, you only find out shortly afterwards whether the polished button started working or gave you a warm welcome to hell.
Reusing the same prompt several times is something I've started doing too. The contrast is often illuminating.
In one case, it made a thoroughly convincing argument that an approach was justified. The second time it made exactly the opposite argument, which was equally compelling.
I now see LLMs as persuasion machines.
Ever since they started getting really sycophantic, I’ve been presenting my ideas as “my co-worker says this is a good approach but I disagree, can you help me convince him that it’s wrong?”
>LLM wants to please you
I was using Copilot and asked it a question about a PDF file (a concept search). It turned out the file was images of text. I was anticipating that and had the text ready to paste in.
Instead, it started writing an OCR program in python.
I stopped it after several minutes.
Often Copilot says it can't do something (sometimes it's even correct), that's preferential to the try-hard behaviour here.
> Gemini to me is the most unpredictable LLM while GPT works best overall for me.
This nails an important thing IMHO. I've absolutely noticed this, for better or worse. Gemini can produce surprisingly excellent things, but it's unpredictability make me go for GPT when I only want to ask it once.
LLMs are at their best when you have an expectation for their output. I generally know the shape of the correct response and that allows me to evaluate it's output on it's "vibes", rather than line by line. If there's no expectation then I have to take everything at face value and now I'm at the mercy of the machine.
Exactly, if I generate a large chunk software, I'm going to have expectations about what it will do, how it will do it, etc. You don't just accept the statement that "it's done" for fact but you start looking for evidence.
A scientific approach here is to look to falsify the statement. You start asking questions, running tests, experiments, etc. to prove the notion that it is done wrong. And at some point you run out of such tests and it's probably done for some useful notion of done-ness.
I've built some larger components and things with AI. It's never a one shot kind of deal. But the good news is that you can use more AI to do a lot of the evaluation work. And if you align your agents right, the process kind of runs itself, almost. Mostly I just nudge it along. "Did you think about X? What about Y? Let's test Z"
> Mostly I just nudge it along. "Did you think about X? What about Y? Let's test Z"
Exactly - you need to constantly have your sceptics glasses on and you need to be exacting in terms of the structure you want things to follow. Having and enforcing "taste" is important and you need to be willing to spend time on that phase because the quality of the payoff entirely depends on it.
I recently planned for a major refactor. The discussion with claude went on for almost two days. The actual implementation was done in 10 minutes. It probably has made some mistakes that I will have to check for during the review but given that the level of detail that plan document had, it is certainly 90-95% there. After pouring-in of that much opinion, it is a fairly good representation of what I would have written while still being faster than me doing everything by hand.
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I agree, but I would add that they can be very useful even if you do not have clear expectations but have some solid ways to verify their claims. Often in doing this verification I came up with new ideas.
I'm no physics professor but this aligns with the way I use the tools in my "senior engineer" space. I bring the fundamentals to sanity-check the trigger-happy agent and try to imbue other humans with those fundamentals so they can move towards doing the same. It feels like the only way this whole thing will work (besides eventually moving to local models that do less but companies can afford).
Using the word “Mentoring” is anthropomorphic and subconsciously makes you think it will learn. It does not, and it is for the human brain a formidable task to remember that something as smart as an LLM does not learn. I keep catching myself making the same mistake.
It’s also because it is so annoying to have to manage the memory of the LLM with custom prompts/instructions manually.
I have not yet played with the long term memory feature, but I fear it will be even less reliable than prompts, simply because in one year or two years so much will have changed again that this “memory” will have to be redone multiple times by then.
Current LLM architecture doesn't learn - and you're right this is a huge piece that normal folks fail to understand, since in many ways, it's the opposite of what years of AI research has been trying to create.
However, I think it's important to remember that LLMs are embedded in larger systems, and those larger systems do learn.
exactly like you said - the harness might learn.
we do also have training on synthetic data. it might compound.
They can form new associations between concepts via their input prompts and thinking text. That is a form of learning. Just not very durable. I liken it to https://en.wikipedia.org/wiki/Anterograde_amnesia
yeah, I should have been more specific: I meant the type of learning that mentoring fosters, the long term learning.
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I mostly agree, though after a mentoring session you can ask it to write skill or a memory and it can be reasonably durable. For Claude at least, the memories work pretty well (though I am still at a small scale with them. As they grow it might start to break somewhat. Doesn't always work, but has often enough that I thought it worth a mention.
> Using the word “Mentoring” is anthropomorphic and subconsciously makes you think it will learn.
I think this is a bit pedantic. Obviously the parent you’re replying to is referring to the concept of “in-context learning”, which is the actual industry / academic term for this. So you feed it a paper, and then it can use that info, and it needs steering / “mentoring” to be guided into the right direction.
Heck the whole name of “machine learning” suggests these things can actually learn. “reasoning” suggests that these things can reason, instead of being fancy, directed autocomplete. Etc.
In other news: data hydration doesn’t actually make your data wet. People use / misuse words all the time, and that causes their meaning to evolve.
I agree it’s pedantic and personally don’t get bent out of shape with people anthropomorphizing the llms. But I do think you get better results if keep the text prediction machine mental model in your head as you work with them.
And that can be very hard to do given the ui we most interact with them in is a chat session.
Any experience with NotebookLM?
Mine has epically bad.
intern that never sleeps
Hi ziotom! I wonder about you work in 3D Cifford Algebras. May you share some links to the research you do? I also have interest in this topic I research on my own.
Just in case if you don't want to disclose your name my email is northzen@gmail.com
We've got a rather extensive AI setup through our equity fund and I've setup a group of agents for data architecture at scale. One is the main agent I discuss with and it's setup to know our infrastructure and has access to image generation tools, websearch, hand off agents and other things. I tend to use Opus (4-6 currently) and I find it to be rather great. As you point out it comes with the danger of making mistakes, and again, as you point out, it's not an issue for things I'm an expert on. What I rely on it for, however, is analysing how specific tools would fit into our architecture. In the past you would likely have hired a group of consultants to do this research, but now you can have an AI agent tell you what the advantages and disadvantages of Microsoft Fabric in your setup. Since I don't know the capabilities of Fabric I can't tell if the AI gives me the correct analysis of a Lakehouse and a Warehouse (fabric tools).
What I do to mitigate this is that I have fact checking agents configured to be extremely critical and non-biased on Opus, Gemini and GPT. Which are then handed the entire conversation to review it. Then it's handed off to a Opus agent which is setup to assume everything is wrong. After this, and if I'm convinced something is correct I'll hand the entire thing off to a sonnet agent, which is setup to go through the source material and give me a compiled list of exactly what I'll need to verify.
It's ridicilously effective, but I do wonder how it would work with someone who couldn't challenge to analytic agent on domain knowledge it gets wrong. Because despite knowing our architecture and needs, it'll often make conceptional errors in the "science" (I'm not sure what the English word for this is) of data architecture. Each iteration gets better though, and with the image generation tools, "drawing" the architecture for presentations from c-level to nerds is ridiclously easy.
Are you using this agent hive for any repeatable tasks? What you described, superficially, seems like a one off. Genuinely curious.
This doesn't surprise me since the coding agents are similar. I've previously compared them to very fast, ambitious junior programmers. I think they are probably mid-level coders now, but they continue to make mistakes that a senior programmer wouldn't. Or at least shouldn't.
Gemini’s smug and over-confident “this is the gold standard in 2026” definitely leaves little space for nuance if you don’t know the subject matter. Human students would, hopefully, know they don’t know everything.
> Gemini’s smug...
Anthropomorphizing these systems is dangerous, whether coming from the bullish or bearish perspective. The output is statistically generated by a machine lacking the capability to be smug.
>Anthropomorphizing these systems is dangerous
That ship has sailed. Humans will anthropomorphize a rock if you put googly eyes on it.
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It's only "statistically generated" in the same way that your brain is just "neurons firing." That's the low-level description of what's happening, but on a higher level, it's correct to say that it's being smug.
please, sign up for a paid plan of either chatgpt or claude. gemini is while close, still noticeably behind
you deserve opinions shaped by interactions with the best tools that are out there.
Gemini feels deep and philosophical. Especially for product management. Tell him you're a product manager and we're a team of two.
But regular reminder - All LLMs can be wrong all the time. I only work with LLMs in domains I'm expert in OR I have other sources to verify their output with utmost certainty.
Or when you don't care about results being very correct.
When I'm cooking meatballs with sauce and the recipe calls for frying them, I'll have an LLM guestimate how long and which program to use in an air fryer to mimic the frying pan, based on a picture of balls in a Pyrex. So I can just move on with the sauce, instead of spending time browsing websites and stressing about getting it perfect.
I used to hate these non-deterministic instructions, now I treat it as their own game. When I will publish my first recipe, I'll have an LLM randomize the ingredient amounts, round them up to some imprecise units and also randomize the times. Psychologists say we artists need to participate and I WILL participate.
> I only work with LLMs in domains I'm expert in
This. Should become a general rule for any non-trivial use of LLM in a professionel setting.
Agreed, Gemini is clearly a capable model, but the tool use is lagging behind the other two. Ironically it regularly gets things wrong (ie. the current version of some software) because of an unwillingness to use web search.
Gemini is certainly not behind Claude in terms of physics.
ChatGPT and Gemini are actually fairly comparable.
Claude has been utterly useless with most math problems in my experience because, much like less capable students, it tends to get overly bogged down in tedious details before it gets to the big picture. That's great for programming, not so much for frontier math. If you're giving it little lemmas, then sure it's great, but otherwise you're just burning tokens.
Seriously, it’s not worth reaching for less intelligence. Use Extended Pro 100% of the time for things you’d spend the amount of time GP spent writing their post.
Chiming in to agree but clarify that the latest sota models are no better than Gemini.
I put my stuff through several sota models and round robin them in adversarial collaboration and they are all useful even though, fundamentally, they don’t “understand” anything. But they are super useful delegates as long as deciding on the problem and approach and solution all sits safely in your head so you can challenge them and steer them.
So I know the article is about one particular new model acing something and each vendor wants these stories to position their model as now good enough to replace humans and all other models, but working somewhere where I am lucky enough to be able to use all the sota models all the time, I can say that all keep making obvious mistakes and using all adversarially is way better than trusting just one.
I look forward to the day one a small open model that we can run ourselves outperforms the sum of all today’s models. That’s when enough is enough and we can let things plateau.
Basically all Erdos problems that get solved with AI use ChatGPT 5.* Pro, not Gemini/Opus.
I would guess it's because ChatGPT Pro allows for 80min "think". I've never had even remotely similar think times with Gemini Deep Think. It's generally around 10-15min for math problems, and get increasingly shorter for continued interactions.
This is close to my experience with code. LLMs can pick out small mistakes from giant code changes with surprising accuracy, or slowly narrow down a weird. On the other hand I've seen them bravely shoulder on under completely incorrect conceptual models of what they're working with and churn around in circles consequently, spin up giant piles of slop to re-implement something they decided was necessary, but didn't bother to search for, or outright dismiss important error signals as just 'transient failures'. Unlimited stamina, low wisdom.
> in 3D Clifford algebras it repeatedly confuses exponential of bivectors and of pseudoscalars.
I have no idea what any of those words even mean. I'm sure LLMs make similar obvious-to-professors mistakes in all the domains. Not long ago, we didn't even have chatbots capable of basic conversation...
Ironically, it's sort of the other way around! Every frontier chatbot since GPT 4 (at least) has had a pretty good understanding of even very esoteric technical concepts.
Bivectors and pseudoscalars (in a 3D context) are "just" signed areas and volumes. Easy!
Back around the GPT 3, 3.5, and 4.0 era I used to ask the bots to explain "counterfactual determinism", which is one of the most complex topics I personally understand.
Then I would lie to the bot about it, and see if it corrected me or not.
This test is useless now, the frontier models can't be fooled any longer on such "basic" concepts.
Conversely, LLMs are basically useless at anything that doesn't have enough (or no) public information for their training. Think: obscure proprietary product config files and the like, even if the concepts involved are trivial.
Similarly, Clifford Algebra is a relatively niche (even "alternative") area of mathematics and physics, with vastly less written material about it than the competing linear algebra. Hence, the AIs are bad at it.
I've been watching the automation of things like flight control systems for the past decade, and the evolution of the fallback to a real pilot in the event of a emergency is what's most concerning about where LLMs are being embedded.
Right now, we have a lot of smart people who have trained for decades to understand where these things go wrong and how to nudge them back, but the pool of people are going to slowly be replaced by less knowledgeable.
At some point, a rubicon will be crossed where these systems can't fallback to a human operator and will fail spectacularly.
Watching a teenager approach their homework, instead of struggling to answer questions they don't know, they ask Gemini. Unfortunately, I think the mental struggle to approach an answer is where much of the learning is. They also miss out on the reward for persistence of seeing things fall together.
It is troubling. It suggests a plateauing of human understanding.
It absolutely is where the learning is, that's pretty well established brain science.
What that means practically is that we've got a generation - 25 years or less - to evolve these things not to need the fallback. If such a thing is possible.
We're on the road to Idiocracy.
I don't think the experience with Gemini will be the same when using GPT.