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.
nopinsight 2 hours ago [-]
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You might want to track the progress of these models on the CritPt benchmark, which is built on *unpublished, research-level* physics problems:
> 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".
civvv 11 minutes ago [-]
There are many indications that model progress is slowing down, so that is not entirely accurate.
Quothling 7 minutes ago [-]
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.
illiac786 35 minutes ago [-]
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.
timschmidt 32 minutes ago [-]
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
illiac786 30 minutes ago [-]
yeah, I should have been more specific: I meant the type of learning that mentoring fosters, the long term learning.
timschmidt 26 minutes ago [-]
I hear you. I think we are already seeing some middle ground with agentic systems using RAG, skills.md files, etc. It's a sort of disassociated card catalog memory. An engineer's notebook. Not the integrated, correlated, pre-processed set of relationships in the model. How to go backward from the notebook -> model cheaply without tanking performance is definitely one of those billion dollar questions.
maximamas 1 hours ago [-]
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.
ziotom78 14 minutes ago [-]
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.
jillesvangurp 46 minutes ago [-]
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"
tags2k 2 hours ago [-]
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).
mixtureoftakes 2 hours ago [-]
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.
wg0 1 hours ago [-]
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.
smartmic 4 minutes ago [-]
> 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.
cubefox 1 hours ago [-]
Gemini is certainly not behind Claude in terms of physics.
hodgehog11 60 minutes ago [-]
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.
peyton 2 hours ago [-]
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.
recursivecaveat 2 hours ago [-]
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.
tasuki 21 minutes ago [-]
> 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...
wood_spirit 2 hours ago [-]
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.
DeathArrow 47 minutes ago [-]
I don't think the experience with Gemini will be the same when using GPT.
cyanydeez 2 hours ago [-]
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.
leptons 25 minutes ago [-]
We're on the road to Idiocracy.
pmontra 4 hours ago [-]
It's a very long post with a mix of technical (math) and philosophical sections. Here are the most striking points to reflect upon IMHO.
> It seems to me that training beginning PhD students to do research [...] has just got harder, since one obvious way to help somebody get started is to give them a problem that looks as though it might be a relatively gentle one. If LLMs are at the point where they can solve “gentle problems”, then that is no longer an option. The lower bound for contributing to mathematics will now be to prove something that LLMs can’t prove, rather than simply to prove something that nobody has proved up to now and that at least somebody finds interesting.
Training must start from the basics though. Of course everybody's training in math starts with summing small integers, which calculators have been doing without any mistake since a long time.
The point is perhaps confirmed by another comment further down in the post
> by solving hard problems you get an insight into the problem-solving process itself, at least in your area of expertise, in a way that you simply don’t if all you do is read other people’s solutions. One consequence of this is that people who have themselves solved difficult problems are likely to be significantly better at using solving problems with the help of AI, just as very good coders are better at vibe coding than not such good coders
People pay coders to build stuff that they will use to make money and I can happily use an AI to deliver faster and keep being hired. I'm not sure if there is a similar point with math. Again from the post
> suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
bambax 1 hours ago [-]
> by solving hard problems you get an insight into the problem-solving process itself, at least in your area of expertise, in a way that you simply don’t if all you do is read other people’s solutions. One consequence of this is that people who have themselves solved difficult problems are likely to be significantly better at using solving problems with the help of AI, just as very good coders are better at vibe coding than not such good coders
Yes but it's not just that if you solved a problem yourself, you're better at solving other problems; it's also that you actually understand the problem that you solved, much better than if you simply read a proof made by somebody (or something) else.
I see this happening in the enterprise. People delegate work to some LLM; work isn't always bad, sometimes it's even acceptable. But it's not their work, and as a result, the author doesn't know or understand it better than anyone else! They don't own it, they can't explain it. They literally have no value whatsoever; they're a passthrough; they're invisible.
kerabatsos 3 hours ago [-]
But perhaps we should regard it as a major achievement.
lmpdev 3 hours ago [-]
I mean in the same way getting Wolfram Alpha to solve a really hard/ugly differential equation I suppose
palata 55 minutes ago [-]
I feel like you slightly miss both points.
> Training must start from the basics though.
Sure, but the point is that at some point (e.g. when starting a PhD) one needs to do research, not learn the basics. And LLMs make that harder, because they solve the "easy research" part.
Take a young lion "fighting/playing" with another young lion as a way to learn how to fight, and later hunt. And suddenly they get TikTok and are not interested in playing anymore. Their first encounter with hunting will be a lot harder, won't it?
> People pay coders to build stuff that they will use to make money and I can happily use an AI to deliver faster and keep being hired.
Again, that's true but missing the point: if you never get to be a "good coder", you will always be a "bad vibe coder". Maybe you can make money out of it, but the point was about becoming good.
NotOscarWilde 3 hours ago [-]
As a TCS assistant professor from Eastern Europe, I always am a little jealous of the biggest names in math having such an easy access to the expensive, long thinking models.
Paying for Pro from any of my current academic budgets is completely ouf of the field of reality here -- all budgets tend to have restricted uses and software payments fit into very few categories. Effectively, I'd have to ask for a brand new grant and hope the grant rules allow for large software payments and I won't encounter an anti-AI reviewer; such a thing would take one year at least.
As a nail to the coffin, I was "denied" all Claude Opus recently as part of Microsoft's clampdown on individual (and academic) use of Copilot.
(Chagpt 5.5 Plus does not seem sufficient for any deeper investigations into new research topics, I've tried.)
Apologies for the rant.
vthallam 3 hours ago [-]
@NotOscarWilde drop your email here, I will reach out and happy to get you a pro account for a few months so you can try 5.5 pro.(work at OAI)
teiferer 1 hours ago [-]
While this sounds generous (and in some ways it is), it does not address the general point that GP is making. That is, the systematic disadvantage which large parts of humanity have w.r.t. to access to the tools. You could say they can't drive a Lambhorgini either, but that also doesn't solve the problem.
NotOscarWilde 16 minutes ago [-]
You're absolutely right (pun intended).
An aside: It was a very nice gesture and completely unexpected by me, so even if it doesn't work out, it made my day. I personally believe that kind gestures have a lot of power.
There is a real danger of the gap between rich and poor universities significantly widening in all fields if the rich can afford Pro level models, or even hardware that can run their own comparable models, and this being fiscally inaccessible to the rest.
One can sweep this under the rug by blaming the educational funding but this just shoots down all discussion. Even if GDP of a country goes up by a lot -- such as Poland -- it takes time before any budget benefit trickles to the education budget, and with some governments it might never do.
I believe Microsoft et al do have the most power here to boost affordable access to AI for researchers on a large scale; the fact that they cut too expensive models from their academic package is a grim omen. I do realize they would like universities to pay them also, and ultimately the universities should do that -- but then we are back at the institutional level of the problem.
Scea91 55 minutes ago [-]
Its a problem of the individual institutions and countries. The budget required for AI tools currently is negligible compared to other university expenses. We don't need to call everything a systemic disadvantage when the disadvantaged (at the institution level) have agency here.
NotOscarWilde 47 minutes ago [-]
Can you tell me what is the budget necessary to supply AI tools capable of substantial research assistance to all academic staff at a university?
You seem to have a good estimate in your head; I definitely do not.
From personal experience, ChatGPT 5.5 (the Plus tier) is excellent for programming tasks and also for various teaching related tasks but I have not observed the research benefits that Tim Gowers has when I asked it questions in my area of expertise. So the costs are definitely higher than a few dozen $ a month per PhD/professor.
You might be right that universities should immediately spring into action and demand funding for research level AI resources and hardware. One thing you might be mistaken in is that public universities are unfortunately very inflexible institutions; one reason for this is that they have a large internal leadership structure AND they are funded by the state, so even if the entire university agrees on something, the funding is at the whim of the ministry of education and thus the current political leadership.
krab 29 minutes ago [-]
> Can you tell me what is the budget necessary to supply AI tools capable of substantial research assistance to all academic staff at a university?
I think the GP meant that *if the tools provide substantial benefit* to staff, their costs can be compared to salaries and other large expenses of the university. The $100/month subscription costs less than your office space.
snayan 24 minutes ago [-]
I mean, I don't think OpenAI should be wading into the policies and practices of foreign institutions and governments. Look at all the blowback we see from the collision of Anthropic or OpenAI and the US government.
At present, the tools are available for whomever wants to buy them. Not OpenAI's fault that parent comment's government and/or institutions policies haven't been updated to allow for their purchase and use.
I'd argue that the OpenAI dude/dudettes level of generosity is appropriate given the circumstances.
NotOscarWilde 2 hours ago [-]
This requires a major "dox" of myself, but I am really grateful for the offer, so these are my academic contacts:
Even if you just drop an email and it doesn't work out, I appreciate this gesture so much. Thank you.
vthallam 2 hours ago [-]
Got the contact, will reach out tomorrow, you can delete them.
teiferer 1 hours ago [-]
[flagged]
thierrydamiba 2 hours ago [-]
Shoutout to you-I will match it if they need other resources. (I don’t work at OAI, just think this is cool)
NotOscarWilde 12 minutes ago [-]
I will leave the contact up for a bit longer if people want to get in touch and share their experience with the research gap of the models -- or anything, really -- but I do not think there is any need of further support. Like I said elsewhere, the offer of support made my day and the gesture is enough.
alsetmusic 2 hours ago [-]
You know what, I'm ashamed that I didn't think of this. I'll sponsor three months. Email in my hn profile. I don't understand the math in the article, but I'd love to help you make progress in it.
fragmede 2 hours ago [-]
same.
johndough 2 hours ago [-]
At my university, everyone had to pay their AI subscriptions out of their own pocket, until a communal AI service was introduced recently. It took 2 years to set up and only serves gpt-oss-120b, so everyone is still using other services. But at least some admin can scatter the word "AI" all over the university's website now and has an excuse to reject any requests for AI subscriptions because "we already have AI".
alsetmusic 3 hours ago [-]
It’s a classic example of the best positioned people being in the best position to keep reaping all the rewards.
There’s the example of a poor person and a rich person buying boots. The poor person’s boots wear out and have to be replaced while the rich persons boots last for many years due to higher quality craftsmanship. Over years, the poor person’s boots wear will pay may for boots.
huijzer 2 hours ago [-]
I know the example, but as a counter-argument: often more expensive boots are not more durable. It’s about spending time to learn to spot the quality.
Of course if you are really poor, then you have to take expensive shortcuts, but for most people that shouldn’t be the case. Learning to do more with less money isn’t as bad as many people think. It’s also good for the brain to be a bit more creative.
m_mueller 2 hours ago [-]
here I think it's less about "poverty" (non-US acedemic budgets are still high, though not in the same sphere), but it's about having red tape when it comes to software. My experience doing a PhD in Japan was: Everything you can touch was basically a free for all - including $500 keyboards and $10k Mac Pros, especially if you are a valued researcher. But software, oh man, how can we prove receipt of goods to accounting...
bambax 2 hours ago [-]
OpenRouter lets you pay by the token only (no subscription), has all the frontier models (including Opus 4.7, GPT-5.5) and most of the others, and if you use it sparingly it usually turns out to be quite cheap.
tasuki 8 minutes ago [-]
My problem with pay-by-the-token is that it discourages me using the thing ("oh the prompt will cost me $0.1"), so I pay a subscription which I'm pretty sure costs me about two-three times what I'd pay just for the api costs, but encourages me to use it more ("oh I have a subscription already, better make use of it").
johndough 1 hours ago [-]
API pricing for Claude is about an order of magnitude more expensive than subscriptions (numbers: https://she-llac.com/claude-limits). But it may be worth it with DeepSeek V4 Pro, which is currently on discount.
bambax 1 hours ago [-]
Depends very much on usage! If you connect it to tools like Cursor, etc. then yes a subscription is probably cheaper -- although, you'd have to subscribe to each provider if you want to use them all.
But if you ask questions occasionally, (and don't resend, for example, your whole codebase with each request), then the API feels really cheap, even for the frontier models.
ziotom78 2 hours ago [-]
I fully understand your rant! I pay ~20€/month for the Pro account, as my university has a deal with Microsoft and only seems to recognize Copilot, so it’s very hard to use one own’s funding for paying something else.
qq66 2 hours ago [-]
Paste what you want me to ask 5.5 Pro and I'll paste you the response.
dyauspitr 3 hours ago [-]
[flagged]
bananaflag 3 hours ago [-]
For a TCS assistant professor in Eastern Europe, $200/month would be 20% of their salary.
And the situation is better, ten years ago it would have been 80%.
iammrpayments 3 hours ago [-]
Average European salary is around $4000/month, in eastern Europe is half of that. Median is probably lower than that. Makes me want to quit visiting places like reddit where everybody claims to be making 100k+/year
goobatrooba 3 hours ago [-]
All salary discussions need a cost of living context. Yes in Europe you earn a bit less but the public services are much better than in the US and one emergency (r.g. healthcare) won't ruin you as it's mostly a public system.
I'll take a Euro salary and qualify life over a FIRE-typs salary and daily fear of falling into the abyss any day.
revolvingthrow 2 hours ago [-]
Given the topic and the fact llm providers charge global rates, the absolute take-home money is much more relevant. Even if you live like a king on $1000/mo, 5.5 pro is still $200.
fakedang 2 hours ago [-]
Their loss if they don't move to regional pricing. AI will continue to remain an upper-management luxury then, and won't reach the mass adoption required to justify their outsized valuations.
revolvingthrow 2 hours ago [-]
Regional pricing makes sense for products that don’t have ongoing costs or where most of the input cost can be offset by local labor. You’re not buying server racks nor electricity at 1/3 of the price to serve poorer markets
teiferer 1 hours ago [-]
AI pricing is not mainly about cost, it's about market realities, i.e., charging exactly the sweet spot to maximize profit.
xanrah 3 hours ago [-]
Lots of people in the west can’t afford 200 a month. How rich are you?
dyauspitr 3 hours ago [-]
That’s what most people spend on their phone and Internet connections per month in the US. That’s what the average American family spends on just five days of food.
sevg 3 hours ago [-]
You can afford five days of food, so that must mean you can also afford a Claude Max plan? What kind of logic is this?
skrebbel 3 hours ago [-]
Fwiw your comments here read to me as “I’m super rich and everyone I know is super rich too, and I can’t imagine that anyone isn’t”.
dyauspitr 3 hours ago [-]
People spend much more than that on just commuting to work if you can spend $200 a month to supercharge what you do at work and 1000x your productivity it’s a no-brainer.
skrebbel 2 hours ago [-]
From what money? Just pause the health insurance for a while? Stop paying the rent? No diapers for the kid?
Your entire story only makes sense if you have many hundreds of dollars/euros of entirely disposable income every month left, after all unavoidable expenses have been paid for. I understand that this holds for you and everyone you know but I’d like you to appreciate that for very many people it doesn’t.
fuzzy2 3 hours ago [-]
Yes and? That's money that is already allocated. It cannot be spent on something else.
xmprt 2 hours ago [-]
No you don't get it. If the family just starved for 5 days then they could increase revenue for these AI companies.
xanrah 3 hours ago [-]
37% of Americans would be unable to cover a 400 usd unexpected expense* without using one or more credit cards. 13% would flat out be unable to cover it. [1]
Are you honestly saying most families would be able to justify 200 usd a month for ChatGPT?
There is a significant gap between what academics are paid across European countries, and since most top universities here are public institutions, you are right -- Eastern European government employees tend to be on the poorer side.
There are several other philosophical arguments against what you propose but I do not wish to go down that route.
skullone 3 hours ago [-]
Bruh, $200/m for most people in the US is also a hard "no!". That's a lot of money. Plus Anthropic isn't doing good deals with orgs that spend less than 250k a month. It's ridiculous.
jdw64 3 hours ago [-]
[dead]
mxwsn 3 hours ago [-]
> Here’s a thought experiment: suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
This is a cultural choice. It makes sense that in the mathematics culture we currently have, this is alien. But already, other fields, and many individuals, would disagree and say that the human did have a major achievement here.
As long as human-AI collaborations are producing the best results, there is meaningful contribution by the humans, and people that are deeper experts and skilled LLM whisperers should be able to make outsized contributions. The real shoe drops when pure AI beats humans and human-AI collaboration.
pmontra 2 hours ago [-]
I replied to a comment about AI in sports and I build on that.
We praise car drivers despite most of the performance in their sport comes from the car. The driver makes the difference when two cars are close in performance. Brilliances or mistakes. Horse riders too.
In the case of math, the human can lead the LLM on the right track, point it to a problem or to another one. So it deserves some praise.
Then the team that built the car, cared about the horse, built the AI might deserve even more praise but we tend to care more about the single most visible human.
bambax 1 hours ago [-]
It may not be a major achievement by the mathematician (although it's debatable) but it would still be a major result.
few 4 hours ago [-]
>So if your aim in doing mathematics is to achieve some kind of immortality, so to speak, then you should understand that that won’t necessarily be possible for much longer — not just for you, but for anybody.
This made me a little sad
jdale27 2 hours ago [-]
I don't know that it's that disappointing. I doubt most of the great mathematicians were actually doing it to achieve immortality. I suspect most of them were either after (possibly indirect) practical applications (via the math -> physics -> engineering pipeline) or just "for the love of the game", appreciation of the beauty of math and the intellectual joy of doing it. AI might also take over the practical application side, but the other aspects are still there for the taking.
hodgehog11 1 hours ago [-]
Exactly. Gowers is in the unique position to think about the "glory" of frontier mathematics, but for essentially everybody (especially those working outside of number theory), that dream died long ago. There are far too many mathematicians now.
Many mathematicians work because they love the breakthrough (a certain quote of Villani comes to mind). They love finding new results, uncovering new mysteries. From that point of view, having an AI that can build on your basic ideas and refine them into more powerful arguments is awesome, regardless of who gets the credit. There are those that treat it more like solving puzzles so the result is not of interest. From that point of view, I can see the dissatisfaction. But I have found those with that viewpoint don't tend to make it as far in academia as those with the other viewpoint.
bananaflag 3 hours ago [-]
Now repeat that for every sort of human achievement
Sports are safe. Machines came after runners (motogp, formula 1) and yet we cheer the winners of the 100 m at the Olympics Games. Fully autonomous bikes and cars won't change that. AIs destroy chess players. We still cheer the world champion.
We care about sports with humans.
fragmede 2 hours ago [-]
Robot MotoGP would be amazing to see just how far the limits could be pushed without risking the life of a human though. Or even full size remote control.
MinimalAction 3 hours ago [-]
As a graduate student, this piece made me sad. I always believed that my work speaks for itself and transcends beyond my limited time on this cosmic experience. This notion of immortality was just a small intangible bonus I hoped for when I jumped into grad school. AI is making me feel less worthy.
hodgehog11 1 hours ago [-]
As someone who is much further down the track, I would kindly suggest you drop that line of thought. I've seen far too many brilliant and ambitious people drop into depression because of it.
You are worthy of doing this work because you are able to do it. Do the work because you love it and because you love the mystery. Enjoy every moment that you get to do it. Find joy in the great fortune you have to do this work while others toil away on tasks that bring them no satisfaction. Sometimes it's tedious, but sometimes it's incredibly rewarding in its own right.
Don't work for the possibility of eternal glory though, it just doesn't exist anymore.
ionwake 35 minutes ago [-]
I feel bravery transcends time better than the odd scientific breakthrough which are often attributed to one, but whose roots came from a "lesser" unknown
whatever120 3 hours ago [-]
You are worthy. You will hone your skills in grad school and be able to command these AIs better than somebody who hasn’t struggled with hard problems for a long time.
jlarcombe 3 hours ago [-]
A depressing thought that all that work is just so you can "command AIs better"
folderquestion 12 minutes ago [-]
It could happen than the AI, in a near future, is not something external but just a part of your brain, so you retain the glory.
jlarcombe 6 minutes ago [-]
Hah this is getting worse and worse
bustermellotron 4 hours ago [-]
I saw Tim Gowers give a talk at the AMS-MAA joint meeting in Seattle about ten years ago where he predicted that in 100 years humans would no longer be doing research mathematics. I wonder if he’s adjusted his timeline.
At the time I thought the key missing tool was a natural language search that acted like mathoverflow, where you could explain your problem or ideas as you understood them and get references to relevant literature (possibly outside your experience or vocabulary).
Sorry, I'm reposting a comment I made yesterday that seems fitting:
> This reminds me of Antirez's "Don't fall into the anti-AI hype". In a sentence: These foundation models are really good at optimizing these extremely high level, extremely well defined problem spaces (ie multiply matrices faster). In Antirez's case, it's "make Redis faster".
dabinat 3 hours ago [-]
I feel like this experiment was successful because those prompting the AI were knowledgeable enough to ask the right questions and verify the output was correct. This shows that there is still a place for expertise, even if the LLM does the actual research.
colechristensen 3 hours ago [-]
I feel my input to LLMs is most valuable in the initial idea, big picture design tweaks, and the vast majority of my usefulness is negative feedback. This looks wrong, you've gotten off track, you're cheating with workarounds, you're falling into a rabbithole, etc.
That's the top link (i.e. that the title is linked to), no?
iTokio 4 hours ago [-]
On complex problems with lengthy proofs, the first step that I would have done is to ask 5.5 pro in a new, unrelated, session, to be very critical, to try to find flaws in the arguments.
And certainly not to send it to a fellow colleague to ask its opinion first.
LLMs are certainly becoming capable to code, find vulnerabilities, solve mathematical problems, but we need to avoid putting their works in production, or in front of other humans, without assessing it by any possible mean.
Otherwise tech leads, maintainers, experts get overwhelmed and this is how the « AI slop » fatigue begins.
To be clear I’m talking about this step:
> That preprint would have been hard for me to read, as that would have meant carefully reading Rajagopal’s paper first, but I sent it to Nathanson, who forwarded it to Rajagopal, who said he thought it looked correct.
NitpickLawyer 3 hours ago [-]
> but we need to avoid putting their works in production, or in front of other humans, without assessing it by any possible mean.
I think this is good advice in general, maybe with an emphasis on public vs. private, friendly contact. Having 0 thought AI slop thrown at you out of the blue is rude. "could have been a prompt" indeed. But having a friend/colleague ask for a quick glance at something they know you handle well is another story for me.
If I've worked on a subject for a few years, and know the particulars in and out, I'd have no trouble skimming something that a friend or a colleague sent me. I am sparing those 5-10 minutes for the friend, not for what they sent. And for an expert in a particular domain, often 5 minutes is all it takes for a "lgtm" or "lol no".
ionwake 32 minutes ago [-]
one thing I was wondering, is, if LLMs are word completions seemingly coming up with new solutions could this just be because stuff that was kept secret and now - is no longer is due to ingestion? I dont know enough about it tho
adammdaw 3 hours ago [-]
This is certainly interesting, though I would say that based on my understanding of how the current models work combinatorial problems would be an area where they could be particularly successful. They are pretty good at combinatorial creativity - its the exploratory and transformational aspects that are still pretty tricky, and I expect would come to bear in other areas of mathematics.
hodgehog11 1 hours ago [-]
Indeed, analysis is a bit more loose in its arguments, and so I've found LLMs tend to make more mistakes there.
__rito__ 3 hours ago [-]
> So maybe there should be a different repository where AI-produced results can live.
M3 module was formalized fully purely from experimental data and from a nudge by earlier versions of codex in 15-30 minutes in a simple write/compile/fix-first-error loop. I was a bit surprised how fast it picked up the pattern but given there was a paper from '70s it became clear why later.
locknitpicker 43 minutes ago [-]
From the article:
> Conversely, for problems where one’s initial reaction is to be impressed that an LLM has come up with a clever argument, it often turns out on closer inspection that there are precedents for those arguments, so it is still just about possible to comfort oneself that LLMs are merely putting together existing knowledge rather than having truly original ideas. How much of a comfort that is I will not discuss here, other than to note that quite a lot of perfectly good human mathematics consists in putting together existing knowledge and proof techniques.
This is exactly what leads me to believe that the real impact of LLMs in human history is yet to come. My work as a researcher was mostly spent on two classes of workloads: reading papers that were recently published to gather ideas and keep up with the state of the art, and work on a selection of ideas gathered from said papers to build my research upon. It turns out that LLMs excel at the most critical component of both workloads: parsing existing content and use it when prompting the model to generate additional content based on specific goals and constraints. I mean, papers are already a way to store and distribute context.
CharlesLau 4 hours ago [-]
Is the assessment system of undergraduate mathematics education no longer effective?
margalabargala 4 hours ago [-]
Undergraduate? No. We've had calculators able to solve undergraduate problems for decades. AI doesn't change the need to understand how calculus works any more than calculators did. The foundations remain valuable.
Graduate? Yes.
whatever120 3 hours ago [-]
How should graduate school be changed then? Specifically for mathematics
dyauspitr 3 hours ago [-]
90% of the final grade are in room examinations with proctors, maybe two sets of exams of midterms and finals that the vast majority of the final grade comes from. This is already how most of East and South Asia does it anyways and it’s probably the best.
For publications and theses, as long as the final results hold and can be replicated and validated, I don’t see why we shouldn’t allow the wholesale use of LLMs
dyauspitr 3 hours ago [-]
I don’t think it’s just mathematics. We don’t hear enough about this, but if I think back to my undergraduate years, which were less than 10 years ago, every homework assignment and every take-home exam I had would be trivial for LLMs to solve at this point I wonder what is actually happening on the ground.
globular-toast 2 hours ago [-]
I wish people would stop generating stuff they don't understand only to forward it to someone who does. Something about that really rubs me the wrong way.
hodgehog11 1 hours ago [-]
May I remind you that this is Timothy Gowers. He says he doesn't understand, but he most certainly has far greater capacity than most to detect complete junk from a maybe plausible argument. His colleague is even better able to judge this, hence why he sent it to him.
Also if he did send me complete junk, I would still parse it for multiple days to see what is there.
adaml_623 1 hours ago [-]
"It is the sort of idea I would be very proud to come up with after a week or two of pondering, and it took ChatGPT less than an hour"
This comment about time is very interesting to me. I know it's "just" doing mathematical proofs but the possibilities of speeding up planning, proposals and decision making in the physical world should excite people.
SubiculumCode 2 hours ago [-]
I honestly can't say this isn't AGI anymore.
AGI shouldn't be a bar so taboo that it has to be at the extreme capability in every domain. What human is?
This is as AGI as it needs to be to get my vote. And it's scary.
MrScruff 39 minutes ago [-]
It's ASI with jagged intelligence, which is probably what it will remain for a while.
It still sounds to me like remarkable automation rather than something that's expanding the frontier of human knowledge, for now at least.
agiipullor 44 minutes ago [-]
to quote Demis Hassabis, "these models can solve frontieer problems in math, but also fail in really dumb ways at trivial questions - the car wash question".
jagged AGI
jdw64 3 hours ago [-]
[dead]
bananaflag 3 hours ago [-]
> it sounds like there were already precedents or existing pieces of knowledge, but humans had not thought to connect them
A lot of math research is like that. And, like the blog post suggests, problems one gives PhD students are 95% like that.
jdw64 3 hours ago [-]
Maybe I am still fortunate to have become a programmer.
Most of what I do is just assemble things that other people have already built.
tanepiper 3 hours ago [-]
Basically medical science too. My wife was able to diagnose her own anemia that the doctors kept missing, and has since been able to have iron infusions.
The human doctors kept ignoring the signals, kept putting it down to 'diet' and 'exercise' (even though she does plenty of both)
agiipullor 41 minutes ago [-]
no blood tests were done?
themafia 3 hours ago [-]
> there were already precedents or existing pieces of knowledge, but humans had not thought to connect them
Maybe if you find AI to be doing stuff you find impressive, the stuff you were doing wasn't that impressive? Worth ruminating on your priors at least.
hodgehog11 1 hours ago [-]
This is beyond ridiculous to say considering whose blog this is.
For those that don't know, this is Timothy Gowers. He is one of the most accomplished mathematicians in the world. Like Terence Tao, he is considered one of the world leaders in mathematics and tends to have good judgement in where the field is going.
Even without that knowledge, no, this article is certainly not AI generated. It has none of the tells.
reasonableklout 2 hours ago [-]
What makes you think either the tweet or blog post are AI generated?
zuogl 2 hours ago [-]
The HTML generation is surprisingly good because the training corpus for markup is cleaner than most programming languages.
bambax 1 hours ago [-]
> quite a lot of perfectly good human mathematics consists in putting together existing knowledge and proof techniques
Creativity is connecting ideas from different domains and see if something from one field applies to another. I do think AI is overhyped generally; but a major benefit from AI could be that after ingesting all the existing human knowledge (something no single human can ever hope to achieve) it would "mix and connect" it and come up with novel insights.
Most published research sits ignored and unread; AI can uncover and use everything.
imiric 46 minutes ago [-]
> Creativity is connecting ideas from different domains and see if something from one field applies to another.
That's true. The question is whether the produced pattern has any value. LLMs are incapable of determining this, and will still often hallucinate, and make random baseless claims that can convince anyone except human domain experts. And that's still a difficult challenge: a domain expert is still needed to verify the output, which in some fields is very labor intensive, especially if the subject is at the edge of human knowledge.
The second related issue is the lack of reproducibility. The same LLM given the same prompt and context can produce different results. This probability increases with more input and output tokens, and with more obscure subjects.
The tools are certainly improving, but these two issues are still a major hurdle that don't get nearly as much attention as "agents", "skills", and whatever adjacent trend influencers are pushing today.
And can we please stop calling pattern matching and generation "intelligence"? This farce has gone on long enough.
agiipullor 36 minutes ago [-]
> And can we please stop calling pattern matching and generation "intelligence"
thats literally what an IQ test tests - abstract pattern matching. but I guess you dont like IQ tests either
einrealist 2 hours ago [-]
"After 16 minutes and 41 seconds, it came back" ... "further 47 minutes and 39 seconds" ... "After 13 minutes and 33 seconds" ... "After 9 minutes and 12 seconds" ... "After 31 minutes and 40 seconds" ... plus other computations
Anyone spotting the issue here? What did that really cost?
I am not against compute being used for scientific or other important problems. We did that before LLMs. However, the major LLM gatekeepers want to make all industries and companies dependent on their models. And, at some point, they need to charge them the actual, unsubsidized costs for the compute. In the meantime, companies restructure in the hopes that the compute costs remain cheap.
sidkshatriya 1 hours ago [-]
> "After 16 minutes and 41 seconds, it came back" ... "further 47 minutes and 39 seconds" ... "After 13 minutes and 33 seconds" ... "After 9 minutes and 12 seconds" ... "After 31 minutes and 40 seconds" ... plus other computations
Anyone spotting the issue here? What did that really cost?
Whatever the Joules... (convert to $ using your preferred benchmark price) it is a fraction to what it might take a human Ph. D. weeks to feed and sustain themselves when working on the same problem. The economics on LLMs is just unbeatable (sadly) when compared to us humans.
einrealist 47 minutes ago [-]
Compute in science was already subsidized by public funding or by donations. Most supercomputers are financed this way. And that's a good thing. If you have a good science problem that can be computed, apply for compute time. There is nothing wrong to apply that to LLMs as well, like I wrote in my initial post. The human is still required to identity problems that are worth to be computed, to create prompts that the LLM can act on, and to verify results. But, OpenAI providing compute for basically free is still tied to a different incentive: to fuel the hype and to capture the market, while distorting/obfuscating the real costs. That's also the reason for why we cannot claim that 'economics on LLMs is just unbeatable'. It depends on the problem, the reason for a prompt.
colordrops 2 hours ago [-]
Still not as bad for the environment as animal agriculture, and animal agriculture is absolutely not necessary and only causes harm and suffering for taste pleasure. At least with LLMs we get many positive advancements from them. I don't see these sorts of comments every time someone posts a burger review.
einrealist 2 hours ago [-]
Did I praise our animal agriculture anywhere?
Rendered at 09:05:18 GMT+0000 (Coordinated Universal Time) with Vercel.
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.
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.
Wrong. Every advancement has followed a s curve. Where we are on that curve is anyones guess. Or maybe "this time its different".
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.
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.
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"
you deserve opinions shaped by interactions with the best tools that are out there.
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.
This. Should become a general rule for any non-trivial use of LLM in a professionel setting.
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.
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...
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.
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.
> It seems to me that training beginning PhD students to do research [...] has just got harder, since one obvious way to help somebody get started is to give them a problem that looks as though it might be a relatively gentle one. If LLMs are at the point where they can solve “gentle problems”, then that is no longer an option. The lower bound for contributing to mathematics will now be to prove something that LLMs can’t prove, rather than simply to prove something that nobody has proved up to now and that at least somebody finds interesting.
Training must start from the basics though. Of course everybody's training in math starts with summing small integers, which calculators have been doing without any mistake since a long time.
The point is perhaps confirmed by another comment further down in the post
> by solving hard problems you get an insight into the problem-solving process itself, at least in your area of expertise, in a way that you simply don’t if all you do is read other people’s solutions. One consequence of this is that people who have themselves solved difficult problems are likely to be significantly better at using solving problems with the help of AI, just as very good coders are better at vibe coding than not such good coders
People pay coders to build stuff that they will use to make money and I can happily use an AI to deliver faster and keep being hired. I'm not sure if there is a similar point with math. Again from the post
> suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
Yes but it's not just that if you solved a problem yourself, you're better at solving other problems; it's also that you actually understand the problem that you solved, much better than if you simply read a proof made by somebody (or something) else.
I see this happening in the enterprise. People delegate work to some LLM; work isn't always bad, sometimes it's even acceptable. But it's not their work, and as a result, the author doesn't know or understand it better than anyone else! They don't own it, they can't explain it. They literally have no value whatsoever; they're a passthrough; they're invisible.
> Training must start from the basics though.
Sure, but the point is that at some point (e.g. when starting a PhD) one needs to do research, not learn the basics. And LLMs make that harder, because they solve the "easy research" part.
Take a young lion "fighting/playing" with another young lion as a way to learn how to fight, and later hunt. And suddenly they get TikTok and are not interested in playing anymore. Their first encounter with hunting will be a lot harder, won't it?
> People pay coders to build stuff that they will use to make money and I can happily use an AI to deliver faster and keep being hired.
Again, that's true but missing the point: if you never get to be a "good coder", you will always be a "bad vibe coder". Maybe you can make money out of it, but the point was about becoming good.
Paying for Pro from any of my current academic budgets is completely ouf of the field of reality here -- all budgets tend to have restricted uses and software payments fit into very few categories. Effectively, I'd have to ask for a brand new grant and hope the grant rules allow for large software payments and I won't encounter an anti-AI reviewer; such a thing would take one year at least.
As a nail to the coffin, I was "denied" all Claude Opus recently as part of Microsoft's clampdown on individual (and academic) use of Copilot.
(Chagpt 5.5 Plus does not seem sufficient for any deeper investigations into new research topics, I've tried.)
Apologies for the rant.
An aside: It was a very nice gesture and completely unexpected by me, so even if it doesn't work out, it made my day. I personally believe that kind gestures have a lot of power.
There is a real danger of the gap between rich and poor universities significantly widening in all fields if the rich can afford Pro level models, or even hardware that can run their own comparable models, and this being fiscally inaccessible to the rest.
One can sweep this under the rug by blaming the educational funding but this just shoots down all discussion. Even if GDP of a country goes up by a lot -- such as Poland -- it takes time before any budget benefit trickles to the education budget, and with some governments it might never do.
I believe Microsoft et al do have the most power here to boost affordable access to AI for researchers on a large scale; the fact that they cut too expensive models from their academic package is a grim omen. I do realize they would like universities to pay them also, and ultimately the universities should do that -- but then we are back at the institutional level of the problem.
You seem to have a good estimate in your head; I definitely do not.
From personal experience, ChatGPT 5.5 (the Plus tier) is excellent for programming tasks and also for various teaching related tasks but I have not observed the research benefits that Tim Gowers has when I asked it questions in my area of expertise. So the costs are definitely higher than a few dozen $ a month per PhD/professor.
You might be right that universities should immediately spring into action and demand funding for research level AI resources and hardware. One thing you might be mistaken in is that public universities are unfortunately very inflexible institutions; one reason for this is that they have a large internal leadership structure AND they are funded by the state, so even if the entire university agrees on something, the funding is at the whim of the ministry of education and thus the current political leadership.
I think the GP meant that *if the tools provide substantial benefit* to staff, their costs can be compared to salaries and other large expenses of the university. The $100/month subscription costs less than your office space.
At present, the tools are available for whomever wants to buy them. Not OpenAI's fault that parent comment's government and/or institutions policies haven't been updated to allow for their purchase and use.
I'd argue that the OpenAI dude/dudettes level of generosity is appropriate given the circumstances.
https://pastebin.com/hNYrCjhL
I probably will erase the contents in a few days.
Even if you just drop an email and it doesn't work out, I appreciate this gesture so much. Thank you.
There’s the example of a poor person and a rich person buying boots. The poor person’s boots wear out and have to be replaced while the rich persons boots last for many years due to higher quality craftsmanship. Over years, the poor person’s boots wear will pay may for boots.
Of course if you are really poor, then you have to take expensive shortcuts, but for most people that shouldn’t be the case. Learning to do more with less money isn’t as bad as many people think. It’s also good for the brain to be a bit more creative.
But if you ask questions occasionally, (and don't resend, for example, your whole codebase with each request), then the API feels really cheap, even for the frontier models.
And the situation is better, ten years ago it would have been 80%.
I'll take a Euro salary and qualify life over a FIRE-typs salary and daily fear of falling into the abyss any day.
Your entire story only makes sense if you have many hundreds of dollars/euros of entirely disposable income every month left, after all unavoidable expenses have been paid for. I understand that this holds for you and everyone you know but I’d like you to appreciate that for very many people it doesn’t.
Are you honestly saying most families would be able to justify 200 usd a month for ChatGPT?
https://www.federalreserve.gov/publications/2025-economic-we...
There are several other philosophical arguments against what you propose but I do not wish to go down that route.
This is a cultural choice. It makes sense that in the mathematics culture we currently have, this is alien. But already, other fields, and many individuals, would disagree and say that the human did have a major achievement here. As long as human-AI collaborations are producing the best results, there is meaningful contribution by the humans, and people that are deeper experts and skilled LLM whisperers should be able to make outsized contributions. The real shoe drops when pure AI beats humans and human-AI collaboration.
We praise car drivers despite most of the performance in their sport comes from the car. The driver makes the difference when two cars are close in performance. Brilliances or mistakes. Horse riders too.
In the case of math, the human can lead the LLM on the right track, point it to a problem or to another one. So it deserves some praise.
Then the team that built the car, cared about the horse, built the AI might deserve even more praise but we tend to care more about the single most visible human.
This made me a little sad
Many mathematicians work because they love the breakthrough (a certain quote of Villani comes to mind). They love finding new results, uncovering new mysteries. From that point of view, having an AI that can build on your basic ideas and refine them into more powerful arguments is awesome, regardless of who gets the credit. There are those that treat it more like solving puzzles so the result is not of interest. From that point of view, I can see the dissatisfaction. But I have found those with that viewpoint don't tend to make it as far in academia as those with the other viewpoint.
https://www.youtube.com/watch?v=VVEzgYxDdrc
We care about sports with humans.
You are worthy of doing this work because you are able to do it. Do the work because you love it and because you love the mystery. Enjoy every moment that you get to do it. Find joy in the great fortune you have to do this work while others toil away on tasks that bring them no satisfaction. Sometimes it's tedious, but sometimes it's incredibly rewarding in its own right.
Don't work for the possibility of eternal glory though, it just doesn't exist anymore.
At the time I thought the key missing tool was a natural language search that acted like mathoverflow, where you could explain your problem or ideas as you understood them and get references to relevant literature (possibly outside your experience or vocabulary).
> This reminds me of Antirez's "Don't fall into the anti-AI hype". In a sentence: These foundation models are really good at optimizing these extremely high level, extremely well defined problem spaces (ie multiply matrices faster). In Antirez's case, it's "make Redis faster".
And certainly not to send it to a fellow colleague to ask its opinion first.
LLMs are certainly becoming capable to code, find vulnerabilities, solve mathematical problems, but we need to avoid putting their works in production, or in front of other humans, without assessing it by any possible mean.
Otherwise tech leads, maintainers, experts get overwhelmed and this is how the « AI slop » fatigue begins.
To be clear I’m talking about this step:
> That preprint would have been hard for me to read, as that would have meant carefully reading Rajagopal’s paper first, but I sent it to Nathanson, who forwarded it to Rajagopal, who said he thought it looked correct.
I think this is good advice in general, maybe with an emphasis on public vs. private, friendly contact. Having 0 thought AI slop thrown at you out of the blue is rude. "could have been a prompt" indeed. But having a friend/colleague ask for a quick glance at something they know you handle well is another story for me.
If I've worked on a subject for a few years, and know the particulars in and out, I'd have no trouble skimming something that a friend or a colleague sent me. I am sparing those 5-10 minutes for the friend, not for what they sent. And for an expert in a particular domain, often 5 minutes is all it takes for a "lgtm" or "lol no".
Does the author know about CAISc 2026 [0]?
[0]: https://caisc2026.github.io
https://github.com/vjeranc/fixed-rtrt
M3 module was formalized fully purely from experimental data and from a nudge by earlier versions of codex in 15-30 minutes in a simple write/compile/fix-first-error loop. I was a bit surprised how fast it picked up the pattern but given there was a paper from '70s it became clear why later.
> Conversely, for problems where one’s initial reaction is to be impressed that an LLM has come up with a clever argument, it often turns out on closer inspection that there are precedents for those arguments, so it is still just about possible to comfort oneself that LLMs are merely putting together existing knowledge rather than having truly original ideas. How much of a comfort that is I will not discuss here, other than to note that quite a lot of perfectly good human mathematics consists in putting together existing knowledge and proof techniques.
This is exactly what leads me to believe that the real impact of LLMs in human history is yet to come. My work as a researcher was mostly spent on two classes of workloads: reading papers that were recently published to gather ideas and keep up with the state of the art, and work on a selection of ideas gathered from said papers to build my research upon. It turns out that LLMs excel at the most critical component of both workloads: parsing existing content and use it when prompting the model to generate additional content based on specific goals and constraints. I mean, papers are already a way to store and distribute context.
Graduate? Yes.
For publications and theses, as long as the final results hold and can be replicated and validated, I don’t see why we shouldn’t allow the wholesale use of LLMs
Also if he did send me complete junk, I would still parse it for multiple days to see what is there.
This comment about time is very interesting to me. I know it's "just" doing mathematical proofs but the possibilities of speeding up planning, proposals and decision making in the physical world should excite people.
This is as AGI as it needs to be to get my vote. And it's scary.
It still sounds to me like remarkable automation rather than something that's expanding the frontier of human knowledge, for now at least.
jagged AGI
A lot of math research is like that. And, like the blog post suggests, problems one gives PhD students are 95% like that.
Most of what I do is just assemble things that other people have already built.
The human doctors kept ignoring the signals, kept putting it down to 'diet' and 'exercise' (even though she does plenty of both)
We used to call that "low hanging fruit."
Maybe if you find AI to be doing stuff you find impressive, the stuff you were doing wasn't that impressive? Worth ruminating on your priors at least.
For those that don't know, this is Timothy Gowers. He is one of the most accomplished mathematicians in the world. Like Terence Tao, he is considered one of the world leaders in mathematics and tends to have good judgement in where the field is going.
Even without that knowledge, no, this article is certainly not AI generated. It has none of the tells.
Creativity is connecting ideas from different domains and see if something from one field applies to another. I do think AI is overhyped generally; but a major benefit from AI could be that after ingesting all the existing human knowledge (something no single human can ever hope to achieve) it would "mix and connect" it and come up with novel insights.
Most published research sits ignored and unread; AI can uncover and use everything.
That's true. The question is whether the produced pattern has any value. LLMs are incapable of determining this, and will still often hallucinate, and make random baseless claims that can convince anyone except human domain experts. And that's still a difficult challenge: a domain expert is still needed to verify the output, which in some fields is very labor intensive, especially if the subject is at the edge of human knowledge.
The second related issue is the lack of reproducibility. The same LLM given the same prompt and context can produce different results. This probability increases with more input and output tokens, and with more obscure subjects.
The tools are certainly improving, but these two issues are still a major hurdle that don't get nearly as much attention as "agents", "skills", and whatever adjacent trend influencers are pushing today.
And can we please stop calling pattern matching and generation "intelligence"? This farce has gone on long enough.
thats literally what an IQ test tests - abstract pattern matching. but I guess you dont like IQ tests either
Anyone spotting the issue here? What did that really cost?
I am not against compute being used for scientific or other important problems. We did that before LLMs. However, the major LLM gatekeepers want to make all industries and companies dependent on their models. And, at some point, they need to charge them the actual, unsubsidized costs for the compute. In the meantime, companies restructure in the hopes that the compute costs remain cheap.
Whatever the Joules... (convert to $ using your preferred benchmark price) it is a fraction to what it might take a human Ph. D. weeks to feed and sustain themselves when working on the same problem. The economics on LLMs is just unbeatable (sadly) when compared to us humans.