You want to know how long it takes to solve an optimization problem, in this case over convex, lipschitz functions. (The restriction to a spherical domain is not really a restriction, you can just change variables for any bounded domain.) Anyway, showing upper bounds on time complexity is "easy" because it's just the runtime of your algorithm. Showing (nontrivial) lower bounds is usually much harder because it requires constraining all algorithms.
This proof apparently shows that the lower bound time complexity is equal to the time complexity of an existing 30-year old algorithm: it requires Omega(d^2) function evaluations to solve over this class of functions.
My gut says likely implies that d is the minimal number of evaluations if you have a gradient oracle because you can approximate a gradient with d function evaluations, but I'm not sure how hard it is to make that rigorous.
I used to feel this way about statistics.
The language and terms are hard to understand and many of the formulas are taught as "just memorize this" instead of building up from first principles.
But then I started using statistics to analyze something I cared a lot about (paintball) and I quickly realized it's like learning anything new:
- there is jargon
- and core concepts
- when you learn the above, it suddenly makes a lot more sense.
Then I wrote some more about pro paintball stats in the below three Reddit posts:
1. https://www.reddit.com/r/paintball/comments/1h17f2m/intro_to...
2. https://www.reddit.com/r/paintball/comments/1jy5xqp/paintbal...
3. https://www.reddit.com/r/paintball/comments/1k6bzi7/paintbal...
Some highlights:
- I started with just pen, paper and a stopwatch (as a college coach)
- I assumed paintball would be more like football where it's hard to track individual effects
- Turns out it's a surprisingly simple and stable "state machine". e.g. the odds of winning with +1 body (e.g. 5v4, 4v3 etc) is, in college, about ~75%
- Paintball is one of those sports where "the weakest player determines the outcome". Why? b/c if 1 player gets out early, you are fighting out of a hole.
It also made me appreciate that as good a book as Moneyball is, reading it after you try to create analytics for your own sport makes it 3x as enjoyable/insightful.
One downside though:
I would watch games and I got so good at internalizing the stats per state of the game that it was like watching the world series of poker where I could see both player odds of getting eliminated and probability of winning over time charts as I watched the games. Made it harder to be the "come on guys! we can win this" coach when we were down on points + bodies.
- Millenials who were kids of the baby boomers being in their late teens early 20s
- Disposable income due to the real estate bubble / positive consumer sentiment
It dropped off a lot after the 2008 GFC though.
BUT
A lot of those kids playing in the mid 2000s are now parents of ~10 year olds so apparently there is a bit of a resurgence going on.
Technical language is a tool that allows insiders to say less and refer to more, and to be specific, but it's just a tool. Most things can be described in accessible ways.
I think you'd be surprised at what you could understand and at just how few domains are truly complex enough that a layman couldn't understand with a little bit of patience and an accessible summary.
The fact that neural networks are highly nonconvex has encouraged a lot of research, but it's more of the kind aimed at resolving tension: these methods are probably good for convex functions, why do they continue to work for nonconvex problems, and are there tweaks we can make to improve them in that setting? It's not a lot of de novo theory; more standing on the shoulders of giants, etc etc.
[1] https://parameterfree.com/2020/12/06/neural-network-maybe-evolved-to-make-adam-the-best-optimizer/
[2] https://arxiv.org/pdf/1905.09997
I think that Nesterov's first order method is the most efficient general first order algorithm on convex problems, so anything else is in some sense worse. (Edit: removed incorrect ADAM comment.)
I don't think this changes the point, which is that most optimization methods used in AI owe a substantial intellectual debt to convex optimization theory.
If you have more specific feedback on what you found distasteful, I'd be happy to hear it.
I wonder how this compares to what we see happening with "juniors" in software development? In math research, do you also get the training for the profession from working on the low hanging fruits for a while, to then move to the medium-hanging, and later go on to work on previously unsolved stuff?
This isn't something which is unique to software development though. We're currently building enterprise AI apps that we can deploy into the AI agents working for anyone of our employees. The key thing we're currently seeing is that the people in a team who are the ones that everyone turn to for advice, are the only people who aren't in "danger". Even people who are great at their jobs are being outperformed by AI in many cases.
I think it'll be a massive challenge for our society in the coming years. Maybe we're even going to get to the point where the AI will also be capable of replacing a lot of the "domain experts". Right now that seems far out, but then, if you had asked me about AI four months ago I would've told you it was all hype.
The only people who are safe are those whose jobs depend in some way on their humanity. e.g. yoga teachers, bouncers, etc
It's not a zero sum game. You can have AI "senior engineers" working under humans building bigger things than we've been able to.
We also don't know where the capabilities of current AIs will plateau. The benchmarks aren't really telling the entire story. From my perspective of using the models there are certain axis where they're not making a lot of progress, like being able to have large accurate context on the scale that humans can. There are other dimensions where there is still a large gap between human capabilities and LLMs. It's true that relative to other areas (lessay chess) LLMs are more generalized but they are still not fully generalized (back to the chess example, LLMs are not good at chess).
Resources are, though. The planet cannot support a race of digital super-people, and us, and an continually growing economy.
It's the height of folly to think that, as things are going, we are going anywhere "good".
Once we've met our basic material needs, we're tending to consume things that are replicable with low marginal costs, and which do not interfere with the production of other goods. So maybe we can actually support a continually growing digital and entertainment economy, at least for a few more generations.
Maybe these mathematical contributions will also impact the efficiency and capabilities of our material production systems as well, which is another way to keep the economy growing.
I'm optimistic that we'll do more with our resources rather than trying to optimize for doing the same more efficiently with less resources.
I would be willing to be proven wrong, but I doubt the ability of LLMs to give useful corrections in yoga much more than their ability to write useful code.
Actually it's sad there are people out there dumb enough to believe knowing L1 cache is any different than knowing recipies when it comes to the story which jobs AI will take. I'm convinced by now it will be the jobs of those people believing such crap.
In relation to that, I guess my question becomes: if the same thing will happen in math research, who will write the ten page math proof prompts in the future?
What i see today is the opposite of what you see : product owners not knowing a thing about software engineering but being able to vibe code prototypes handed over to the dev team are rock stars.
They are closely followed by senior software developers having more of an architecture & design background than a low-level computer science background. Most businesses are looking for builders these days.
Where what you say may converge with my observation is that to be able to do to things such as proper database query optimization, even using AI assistance, you need to be able to understand the concepts of working memory set, cache misses etc...
I've found huge problems, like database servers being grossly underprovisioned (like, 60% cache hit, 4gb RAM server for a 700gb dataset with an 50gb circa hot data set). SSD were used and only latency was measured, so no one realized how problematic the situation was (including a consulting shop they hired to help them manage their DBs - backup, maintenance etc...).
However, having a high affinity with hardware is not a driver / computer science of hiring decisions from what i can see in the enterprise software world. But it would make sense for it to become the case within 10 years. I suspect that you work in a niche where performance optimization matters a lot.
Calling notable conjectures that have been open for decades “low-hanging fruit” is an act of desperation. Most professional mathematicians couldn’t have proved those conjectures if their lives depended on it.
So, yes, AI is a big deal and we don’t know what it’s going to affect, but the goal of replacing everyone’s job is extremely ambitious and there’s a long way to go.
This has to be assessed separately for each kind of job.
Moravec must be at some level gratified things are arriving close to his predicted timeline.
There might be a thing beyond intelligence that we can't even conceive of.
The “absurd” dimension does not enter. This is a situation where you have no evidence at all.
In the absence of any information, the average (mean or median) is your best guess. Now where that average is, you have no idea.
> There might be a thing beyond intelligence that we can't even conceive of.
This statement already supposes there is a thing called “intelligence”. People have been pretending to measure this for more than a century. Modern thinking at least says what we call intelligence is not a single concept.
Most technologies level off sharply after bouts of boundless improvements.
In 1968 they thought we'd be flying to the moon by now but instead we're flying across the ocean in planes not that different from the 747 that existed back then.
In order to get a Ph.D., you have to do some sort of original research, so in that sense you're working on "previously unsolved stuff" basically right from the start. But that doesn't entail doing anything all that ground-breaking; most Ph.D. dissertations (very much including mine!) contain work that a more senior researcher in the same subfield could probably have produced without too much difficulty. The software development analogy is a pretty good one: a lot of the point of getting junior researchers to do research is to help train them to one day become senior researchers, and often the work itself is nothing all that special.
Given the trajectory of these LLM proofs, this seems like it's going to have to change pretty soon, and to be honest I'm pretty grateful that I'm not in charge of deciding what that's going to look like, because I don't have any good ideas! I'm actually pretty worried about the future of the field.
Back in the before I had put such discipline into my prompting and supporting context.
Now I’m like, “look here and here and here are some tools, and /skill /skill okay go.”
Or “restate this request in your own words and enrich it as appropriate handling any gaps. Okay go”
A few months back this would be something every developer kind of did on their own. Maybe they shared skills, we certainly encouraged it and tried to do all the change management things, but nobody really had the same versions of the skills. Which was horrible in the deployment pipelines, something like the compliance documentation often had to go back and forth several times before it could be approved. Now it's just there, for everyone.
In a year or two, I expect a lot of these things to have become even more standardized. So that we don't even really have to build our own apps, but can simply use the ones in the catalog with minimal configuration (and that config will likely only be necessary because I'm from a tiny country that nobody will maintain standards for).
On the first, there were ~no shared skills. There were some requirements set up but they were not minded properly and became stale / ate context for little gain. The hardest hit was in E2E tests which would flake and create long running, too-often failing CI. People would disable them, because they were not reliable and velocity was so high, no one was happy w them.
I maintained my own set of skills and CLIs to back them. I'd share them if they came up but it was like the old days of manage your own stuff. Not much credit for building and sharing devex tooling to the team.
But then on the second one we were in better shape--we had vendoring set up to distro skills automatically.
Before the project was well underway, I put time into understanding how all of our tests aught to be written. Finding the forbidden things, etc, getting review from our best test folks and ultimately landed on a `/test` that routed across all possible test types.
Like night and day. Instead of finding out while trying to get a release out the door that some corner of the project had a handful of flakes, tests were written the right way from the start.
Like, it was beautiful. And I don't think devs noted difference while building. Only that there was an absence of BS in CI.
Hard to quantify the lack of pain, but it was big!
Look here and here and here are some tools, and /skill /skill [repo of folder paths etc] and here is what needs to happen: [stuff].
---
Restate this request in your own words and enrich it as appropriate handling any gaps.
It is an ultra-lite way to plan, I suppose.
I like the format because:
- I still get to put all my thinking into the request but then easily override the instruction
- It is interesting to see my casual typo-riddled blast professionalized and improved upon.
- Sometimes it surfaces useful questions that can save some time up front.
Anyhow, to get back to the point, there are still prompt-level tricks--but ultimately if repeated, should probably also be built into skills themselves!
In math, a proof is a proof. We don't know if we can get there and so getting there is the hard part.
In software, we always know that we can solve the problem. So HOW to solve the problem is the hard part. Because the type of solution involves maintainability, which involves planning, LLMs suck at it. This leads to "LLM slop code" whereby the LLM creates ad-hoc convoluted logic with redundancies and no reuse of existing standard library batteries.
Unless you're a Grothendieck who gets mad at Deligne for not solving the Weil's conjecture "THE RIGHT WAY", software is fundamentally different than math in this respect.
So I'll say it again, AI will win a fields medal for before managing a McDonald's simply because there are enough big problems within arms reach than their current capacity to plan over time
Some math research does involve grabbing a single, fully specified conjecture off the shelf and hunting for a proof of it, and it's true that if you manage to solve a long-standing open problem, other mathematicians will be interested no matter how you did it.
But this isn't all of what they do, probably not even most of what they do. Like in software engineering, it's not always obvious which question would be the most useful one to ask. A lot of mathematical work also goes into what we call "theory-building", where you could say that primary work goes into coming up with definitions rather than theorems. Mathematicians also care a great deal about how something is proved; a lot of them are some of the most aesthetically picky people I've ever met. Words like "ugly", "beautiful", "creative", and "boring" are used to describe both definitions and proofs all the time.
From the outside, it can look like all they're doing is pumping out proofs at any cost. But I promise you that when I talk to mathematicians who don't have any experience building software, they have a similarly narrow view of that field as well! Both fields, from the inside, look a lot more human than you might expect.
Now, that still doesn’t help an LLM distinguish between good and bad correct proofs. But it still really helps a lot. On top of that, taste in proofs is a lot more uniform than taste in coding. That helps LLMs be better at judging the quality of a proof, because there’s less disagreement in the wider world.
(Although in general, there's no true difference between "I answered the question correctly, but the question was mapped to this thing we call 'reality' wrong", and "I answered the question incorrectly", because you can (try) adding the constraints that you really wanted targeted in case A, to case B, and boom, suddenly a question/answer pair that was "Answered correctly, but question doesn't map to reality" now becomes, "You answered this question wrong". However, individuals generally tend to have some breakpoint to differentiate between the two).
Math is such that most theories are built after solving a problem and actually don't solve a larger class of problems. Etale Cohomology is an example of a rare exception. Grothendieck was mad that Deligne used adhoc complex analysis techniques to prove Weil. But everyone else was thrilled.
Whereas in CS, a good theory (library) solves a large class of problems. The reason being is that CS tackles general problems while math specific ones. Math on average solves problems that don't lead to solutions to other problems.
To me at least, math is more of a game like chess and coding is more of an art. There are aspects which are a game, like performance engineering but I'm pretty sure that LLMs will become superhuman at that soon
But "what mathematicians care about" is much, much broader than what gets you published in a fancy journal. Mathematics as a human activity is millennia old, much older than the concept of journals or even universities, and that activity is, to me, very beautiful, worth preserving, and more of an art than a game. The incentive structure of academia for the past few decades has done a pretty bad job at preserving that art form, but that doesn't mean mathematicians as actual human beings don't care about it --- if they didn't, they probably would have chosen a different career.
For example, create a DFA for a regex, not too bad just use Thompson's algorithm and then NFA->DFA. But now we have to care about efficiency, user API, maintainability of definitions etc.
Coding is more of a human problem than math
AI can manage a McDonald’s already. If manage means directing humans to do something to ensure the store is running. If manage means running robots, then yes maybe that is 5 years away but just directing humans to run a store, that is possible right now.
My understanding is that ChatGPT Pro is effectively a multi agent system, or somehow uses multiple LLMs in parallel and selects a best answer. And Ultra is more similar to Claude-Code UltraCode where the main agent can choose to create a dynamic JS workflow that deterministically orchestrates multiple agents to handle different parts of a task and have adversarial checkers etc.
Is that more or less the difference? Any substantiating sources would be great to see.
But I agree LLMs have a lot of potential for checking proofs--both informally (they can read quickly and find gaps) and formally (by attempting to formalize).
Overall, this is an impressive proof of capability. But I wouldn't take that proof as anything more than what it is.
Of course money in this situation is a bit of a funny measurement, right, because if I was able to take the rest of the week off as soon as I had solved the one-week problem, then I would have no problem at all throwing even $100 worth of tokens at it, so I could enjoy a nice 4-day "mini-vacation".
How cheap "cheap" is, is indeed "in the eye of the beholder".
In Scrum terms my personal velocity grows by a factor of four or more with access to agentic AI workload, but if it means that I will just be asked to "consume" 4*X more Story Points per sprint, I'm not the winner in the end, my employer is. If they asked me to complete X Story Points per sprint regardless of my velocity, and they let me take the days off when I was done, I would be the winner. But that's not how it works.
AI is "Cheap" for the person/organization that gets more product for less money, not for the individual person building the product faster.
it went from not having a price, to having one, and we are trying to retroactively transpose economic viability or economic existence to it from some parallel and prior time.
But trying to maintain this distinction leads to insuperable difficulties. Our conceptual framework for understanding the world are always value-laden. There is no "view from nowhere", no historically unconditioned set of values or concepts. Your framing, in which "values" are external to "intelligence" and must be imposed on it (on pain of intelligence being "value-neutral"), leads inevitably to the dead end of "AI Alignment", "superintelligence", etc. Which is a kind of pseudo-theology.
"We humans better [be] refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant."
In light of the untenability of a strong fact/value or intelligence/ethics distinction, I would suggest this alternative advice: humans should focus on critical appropriation and extension of the received wisdom, whether that comes to us directly from human beings or indirectly through an LLM. Perhaps this is compatible with the spirit of your original suggestion.
They will, however, get there as well either directly or as interfaces to models that do, and your core point stands.
If there was a deep fundamental inability, we wouldn't see things like newer generations of LLMs consistently improving on ARC-AGI series (heavy spatial reasoning loading) and SimpleBench (a lot of commonsense + spatial reasoning components).
In a way, it's a surprise that LLMs, notoriously lacking any sort of embodied experience, can even get this close to human baselines on tasks like this.
My takeaway is that text is a far richer modality than anyone has expected - and that high end LLMs are often sharp and flexible enough to recognize their weak points and substitute their strengths. I.e. all the LLMs implementing A* to optimally solve pathfinding in ARC-AGI-3 tasks, often unprompted.
There might still be unrealized gains there from true depth-unbounded recurrence, or maybe from finding better ways to integrate modalities in training. But clearly, a "fundamental limit" it ain't.
Yeah, that's fair.
> My takeaway is that text is a far richer modality than anyone has expected - and that high end LLMs are often sharp and flexible enough to recognize their weak points and substitute their strengths. I.e. all the LLMs implementing A* to optimally solve pathfinding in ARC-AGI-3 tasks, often unprompted.
I agree and disagree with this. I think we've learned a lot of humans are more text based than we thought, but conversely I'm not persuaded what non-textual task reasoning LLMs are doing is necessarily text based, just that models have grown large enough for other reasoning modes to conceivably be hiding in the parameter space.
As I mentioned elsewhere, like many others I find LLMs work entirely by example, and reaching for A* when pathfinding is the single obvious thing to do. In cases where the magic key word is not mentioned and the problem cannot be identified as "pathfinding" (or some other trigger with a highly specific widely documented solution) they will struggle, yet the moment the trigger is hit they get there very fast. This is why prompting remains such an art form.
Fable is the first one I've encountered that is capable of serious open ended 3D programming in ways that suggest it has some grasp of the spatial aspects of the problem (not merely symbolic manipulation of the vectors etc.), but it still misses optimization opportunities a human will find glaringly obvious based on spatially predictable bounds etc.
Basic LLMs don't reason in text, and never did. They use it as an interface - for input, output and some of the intermediate products. Heavy use of those "pseudo-recurrence" intermediates in "reasoning models" is a relatively late post-training adaptation. But the process that happens between those endpoints is not at all text-based. What happens in the hidden dimension is part "output logit domain", tied to probability distributions over possible output tokens, and part "incomprehensible concept-space madness".
The latter being where things like latent world models live. LLMs develop partial world models, right in pre-training, despite not being explicitly forced to - because it brings them closer to heaven of accurate next token prediction.
And yes, larger models like Fable seem to be better at spatial reasoning. Maybe because their large size increases the sample efficiency and improves generalization, allowing them to absorb the sparse signal of "spatial reasoning" in the training text better. Maybe because this extra size means more layers, allowing for deeper latent space reasoning in lieu of true recurrence. Maybe because the default "next token prediction" reward underrates rare spatial reasoning challenges, and the model only starts to "get good" at them once the other sources of loss reduction are heavily depleted. Maybe because no true recurrence is suboptimal for spatial reasoning architecturally. But it is what it is. Spatial reasoning gains in LLMs are extractable, but extracting them is nontrivial.
You don't have to do much statistical analysis to figure out what is meant by the token string "cat under a tree". However you need to do an enormous amount to encode any permutation of pixels that show a cat under a tree from the set of all possible pixels arrangements that illustrate that (along with the massive fringes of ambiguity).
Basically current gen LLMs apparently do spatial reasoning the way they seemingly do everything else: by reference to previous example. I didn't see them work out which known example to use for a given problem until specifically prompted, in my case by accident.
Only a fraction of the games can be solved by Sol, generally at sub-human efficiency in terms of turns, AND at a cost of >$10,000 per game.
I’ve been doing more math as a hobby in the past few weeks — working on lesser-known conjectures and exploring proofs of hard theorems — than I could have managed over the previous several years. It’s an exciting time.
Stored potential.
But will that potential be converted that contributes to the economy..? That requires other traits.
Might be focus, might be discipline, might be the need to get revenge lmao.
This is what the llm-boosters miss. Progress is willed into existence.
At the end of the day it is still making a best guess at what the user wants based on data it has seen before.
It still requires someone smarter than the output to be able to evaluate if the result is any good, or just hand waving.
This is basically what LLMs do on really hard tasks. Prompt it a million times on a really hard problem and it might output the correct answer once.
Given the tokenizers have a vocabulary in the 10k-100k range, "a million attempts" will generally still only get the first token of the answer correct.
Even really rubbish models, e.g. talkie, the "what if we only use pre-1930s data to train a model?"** model, had to be almost all the way to the right answer to reach the really low HumanEval pass@100 score of ~0.04 (I'm only eyeballing the relevant chart).
* Actual monkeys not being like this is, while amusing, irrelevant
Even if every atom in the universe were a supercomputer generating a trillion trillion random characters every second since the Big Bang, the chance of producing Hamlet would still be essentially zero.
Even when you've got an interesting idea, if you're an enthusiastic amateur who don't yet know enough to phrase the question right but does actually know the basics, they'll put you in the same category as the people who think healing crystals can power hyperspace telepathy with Anubis: "oh no not another one".
LLMs have infinite patience, but unfortunately come (came?) with too much sycophancy, giving even more people far too much confidence.
AI hasn’t even taken the class of jobs associated with customer service lmao
This is what the whole https://people.csail.mit.edu/brooks/papers/elephants.pdf is about.
You mistyped it.
Best I've come up with is we'll need to be adopted by technofeudlaist overlords to be our patrons like in the roman days
Continually progressing AI (combined with our current socioeconomic systems) throws a lot of uncertainty into our mid to long term future, but I don't think this is going to be what happens.
There are billions more of "us" than of "them", people don't respond well en masse to a drastic worsening of their societal status and "they" are lagging very far behind on building their robot armies.
If we poorly navigate this transition the outcome should be worrying them more than it worries us.
Fortunately, yes, those robot armies do seem to be rather behind schedule*.
However, even if Musk dies of old age before anything like the Optimus can be connected to useful artificial intelligence, it can still be driven by the common joke a few years back that "AI" really stood for "Actually Indians".
When all the people currently upset about "immigrants coming here taking our jobs" discover those same people are now staying home and remote-working those same jobs over a VR headset and a Starlink connection... my guess is that by this point, Musk will have no political allies left.
> If we poorly navigate this transition the outcome should be worrying them more than it worries us.
It can screw everyone over. Literal communism was invented in response to Laissez-faire capitalism, and while Laissez-faire died with the Great Depression, the form of capitalism which succeeded it in the USA came into conflict with the USSR and gave us the Cold War, the Cuban Missile Crisis, etc.
* 2022 "next year": https://www.cnbc.com/2022/04/08/elon-musk-says-tesla-is-aimi...
Fwiw I was mostly joking. I agree that the techno overlords have no reason to keep us, unlike in Roman times.
Reminds me of Wigner's Unreasonable effectiveness of mathematics in natural sciences [0].
[0]: https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
I don’t know if LLMs will kill the working-mathematicians but at least seem like that it doesn’t seem absurd to imagine LLMs will be good at math…
One solution is to ban LLM’s, to artificially create a demand for human thought, that just feels like living in an artificially constructed zoo.
Another solution is humans don’t do anything that AI can do better , / doesn’t need the human touch. So I suppose we will all become artists, sportsmen or politicians, the only jobs that will remain except for select few. Maybe this is ok, I don’t know.
Another solution is we find a way to mind-meld with AI so that human + Ai >> AI alone. This is dystopian, who gets to decide who mind melds with AI, how much will it cost etc etc.
For the stupid copes that the prompt required human ingenuity, let me first add that the author used GPT5.6 to write most of the prompt. He just gave some mild direction. That amount of direction does not require deep expertise and the expertise required will keep falling with time, eventually an undergrad can create this loop and then maybe a high school student.
And prompt engineering / loop engineering nonsense is not real. Calling it engineering is a psy-op because it is something simple, imprecise and future models will be much better at it than you.
Memes like the permanent underclass and the massive incentive of replacing workers across the world does not bode well for a better outcome for people across the world.
There will be people benefiting from advances in these fields.
Neither you nor I will be one of them.
I wonder which one that is.
Should I ban table saws because they make people too good at woodworking? Should we ban right-angles?
This line of thought doesn't lead anywhere fruitful.
gig economy is a blessing to keep the LCD busy and doing something productive instead of being nihilistic losers
it’s better to focus on how to keep these “knowledge” workers busy for the AI age
they don’t like to work and complain even on a w2 job (where someone else had to figure out how to capitalize them) so in many ways they’re far more dangerous and hopeless.
Also see comparative advantage re best roles for each actor in an economy
If AI improves human productivity so much that millions of people no longer need to work that should be an incredible thing. But the flawed structure of our society punishes those people rather than freeing them to persue endeavors that interest then.
Anything based on a free market just ends up in.. this.
We can also remove all of the loopholes that result in the biggest companies paying basically no taxes. I also think it may make sense to have a dramatically different tax structure for businesses than effectively income tax.
Outside of really bad luck I've never seen a case where someone was in a situation of working hard + making reasonably okay decisions + struggling, and that's purely due to there being avenues available where you can be rewarded well for your effort if you're of average+ intelligence.
AI is threatening to take that opportunity away.
Literally anything you wanted to make is no plausible to make if not now then in the next couple years.
The thing you’re worried about is capitalism and the connection with working to having the right to keep living. If you can throw off that mental shackle you can start to see how this can be amazing, but you have to drop the idea that everyone has to work at a job for someone else to provide some service in order to do it. It’s hard, I know, but change your mindset some and dream for a better world and we can make it.
Yeah, it's fun for 30 minutes.
It’s just depression that another avenue for human craftsmanship has been taken over by the machines. Humans are not just infinite consumers. If AI solves all of humanity problems, it’s like living in a zoo, not a life worth living imo.
It's good if we can have robots building things instead of having humans slumped over a workbench in a sweatshop piecing things together. It's good if we can have LLMs spitting out code rather than CS grads working 15 hour days at fintech startups or whatever. The conditions were never (ever) good before.
And, it won't be like a zoo - you'll be able to go wherever you want, do more or less whatever you want. Think about living in The Culture, or the Star Trek universe or whatever. There are options beyond "I'm a pet to the machines." Think big, dream big, then help make it a reality!
Like, out in space you're still going to need a human to make decisions because you can't wait 30min for the tight-beam signal to get back to earth. Also, we're pretty good at soaking up rads and still being "useful" - at least so far I don't see that being a major advantage to the robots. Maybe our place is to be the deep space mechanics that keep the robots alive? I don't know, regardless, you should dream big. What kind of world do you want to live in? Ok, how do we make that world happen?
My big (somewhat unspoken and somewhat immature dream) is that advances in regenerative health tech fix my optic nerves and I can get into the cockpit again one day, then maybe later I can fly some space vehicle like I wanted to since I was a 12 year old. Immature I know, but I miss flying still.
Is that world possible without AI? Probably/maybe? But it's a lot more plausible in a world where we have folded every protein, we have robot surgeons doing robotic procedures, AI generated research, etc.
I actually want to exit. I want to live in a society where humans flourish not AI.
Actually one just needs to walk the streets of Japan and compare that to US. Tokyo has hundreds of small shops with humans doing specific niche stuff, perfecting their arts. That’s all so beautiful.
America has massive warehouses and supermarkets, with completely uninterested and bored out of their mind humans working and I suppose now we will replace them with robots. Great I guess. Maybe all Americans should just sit at home and consume Netflix and Doritos ig.
I want technology to increase human flourishing, not turn us into WallE humans. I am only interested in technological progress when it is done by humans who trained their whole lives for it, as it is a display of human excellence and that can be a beautiful thing. I’m not interested in it if some AI builds it.
Like, I'm building a cabin in the woods (original, I know), but you can build things and do things. You can be that kind of human if you want. But, if Americans could sit at home and consume netflix and doritos I suppose some would, but many would decide to start doing other things too.
I don't think the worlds we want to live in are that far apart to be honest. If I could make a living doing it, I'd try to build wooden sailboats for a living. That would be awesome. I would love it! In a world where I don't have to work to win capitalism tokens, I would probably spend a few years just building wooden sailboats to sail around the bay by my cabin.
Dude, I'm nearly 40. I've seen the shit. When I was flying for a living, literal close friends died because of the results of avarice.
Dream big dude! This constant "doom and gloom" narrative is toxic to your ability to flourish. I have been there, I understand the urge to doom and gloom, but we make the world we want to live in. We do. We choose it.
What world do you want to live in? What is your "optimal" version of the future? How do we get there? What steps would we have to take to make it a reality?
If your vision of the future is "oh, like 10 years ago before $problem_du_jour" then you're already off to a bad start because we ain't going back. There's no regulation that will actually change anything materially (seriously, you think the people getting rich off all this stuff in Congress will voluntarily shoot themselves in the foot?), there's no way to go but forward, so how do we proceed?
I want to live in The Culture, or something like it if it's possible. So, let's start building it and ask permission later.
Maybe average human lifespan gets kicked up to 200 years or whatever and we make do with robots to fill in the gaps in labor with robots?
I don’t know? But this kind of seems to track with how we’re trending now?
Working all day, then not wanting to do much else after because you're tired, is also fun for all of 30 minutes.
People are all “shucks how am I going to be able to justify my career at $job” and are missing the bigger opportunity. Such a lack of imagination I see…
The reality is nobody is going to build robots to clean the ocean because there is no money to be made. There will be robots to clean rich people's pools, sure. And it will put pool boys out of a job, great.
What if money wasn't a thing? What if that wasn't the only incentive in the economy? What if there were other ways to balance supply and demand curves (which is basically the principle use for money) so we could reduce shortages, etc.
Dream big man, I'm serious! And who cares if there is no money to be made? Like, what are you (individually you) doing to create the world you want to live in? What world do you even want to live in?
there will always be disruption and frictions, 頑張って ください
People in the real world all having god mode cheats is good, actually
Or imagine a world where we could basically cure every disease? Or a world where people could assume any form factor that they wanted? I don't know, the list goes on and on in a post-scarcity world... and we're seeing how we basically live in a sort of digital post-scarcity now and it is really cool.
If I need a software tool these days I don't buy it, I tend to see if I can make it. Now imagine that for physical things? What a time to be alive.
Can I make food with LLMs? Can I build a house and make clothes? This is stupid. No real wealth is being created for the general population here.
Dream bigger buddy! We can make the world better, we’re not powerless here.
I’m convinced many of you barely go outside and have the capacity for original thoughts.
Sloppity slop slop.
- Hasn't been peer reviewed yet, so take with a grain of salt. This applies to all claimed proofs, not just AI-generated ones. Even humans hallucinate proofs too!
- The prompt is on page 27 here[1]. It is ten pages of advanced mathematics priming the model in the right direction, apparently informed by a year of prior research. That doesn't invalidate the result if it is genuine, but it is worth noting that this wasn't a matter of "ChatGPT, solve this unsolved problem. Make no mistakes." and required substantial domain expertise and human research beforehand.
Sure. That is not even remotely the point I was getting at. Already we see the thread filling up with comments about how human skills are irrelevant, using a mathematics PhD applying his expert skills in a way that the people who are saying that could never have done to justify their inane conclusion.
It wasn't the case for this, but when OpenAI disproved the Unit Distance Conjecture, it was really done autonomously by an automated AI pipeline with a completely AI-generated prompt. No human expertise required at all in the process (well, except for the final human verification).
It's not that AI brings equality, but rather that the output varies depending on how much background knowledge you have. You could call it a stratification of input
I'm starting to feel like there's no place left for programmers like me who focus on quickly churning out MVPs.
The obvious baby’s first process is “plan -> execute” but as we learn about the strengths and weaknesses of LLMs you have to start unpacking that process into planning, prototyping, testing, validation, reviews, and tons of research. If you treat it like an extension of your brain that can automate some thought processes, it becomes a lot more powerful.
That skill comes with experience. Most people don't have it immediately after PhD.
Well it seems more and more that 3 months of 500k GPUs churning through data 24/7 to build high dimensional landscapes also counts as experience.
And programming, as the programmer who created Eliza once said, is the act of becoming a legislator of your own universe. So even if there are black boxes, if you want to build a program that fits your own worldview, studying is essential.
> you can't have one LLM to read your mind to prompt another LLM
One might even say that this remarkable facility can be used to “read” the ideas from one entity’s mind, such that after sufficient dialog the second entity obtains a (possibly lossy, but there are mitigations for this) copy of the ideas of the first. You might further be surprised to learn that this sort of idea-transfer business using language has already been happening in our society and species for quite some time indeed.
edit: it reminds me of all that I have to wade through after I've asked an LLM a straightforward question and the answer should have been "yes, you're right."
There are two ways to solve a problem. Either solve the problem, or deem it irrelevant.
The implication here is that, you, the human operator, clearly are just confused. The LLM knows best. You're just a stupid human. The LLM knows objective truth, you do not. You have concerns, questions, the LLM didn't understand your question "properly"? Do not worry, the LLM objectively knows the optimal course of action. It thought through the implications of what you said, took into account all possible data, and came to the objectively correct design for your software, your society, your life.
In some sense, this problem would have been a societal problem within the next several decades anyways, but it's been hyper-accelerated by AI.
Debuggers, testing techniques, testing layers
Essentially things that could be used to ground your ai back to reality and work good for humans too
Of course there is. The same way this was only possible as a result from the professor who prompted it with his specialized 10 page prompt and most importantly his deep knowledge of the problem space, the muscle memory and intuition you've built over the years is what will allow you to get more out of any AI than some guy who says "make a door dash clone" as the entire prompt
I've been realizing that there are more books tied to my background knowledge than I expected, but I'm not sure what will happen as AI advances further.
These days, I'm living for the fun of building my own personal wiki on my homepage
this is changing my mind, at least about experts using advanced tools like any profession where it's like the magic of watching a lifetime of hard-earned skill at work
> After seeing OpenAI’s CDC result, I wrote a much more elaborate prompt following the same general methodology. My prompt is about ten pages long and attached at the end of the preprint (see collection of links below). There is a lot baked into this prompt, on approaches to try and also on how exactly the model should proceed, but it's built exactly in the style of OpenAI's CDC prompt. One note is that I gave it a relatively small error requirement, to prove the quadratic lower bound under order d⁻⁴ accuracy.
> After 148 minutes, GPT-5.6 Sol Pro returned a proposed proof resolving the quadratic dimension dependence at accuracy of order d⁻³. After checking things myself, I formally verified the proof in Lean, and it passed the formal verification check.
>So I wouldn't really say that this result is using or creating some fundamentally new techniques in convex geometry or optimization theory. What this means from my perspective is that if a result is attainable with existing techniques, modern AI methods will be able to solve those problems. I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.
While they’ll never have the same subjective experience as humans, what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?
They are prediction machines, and so are we in a way. We can give them nearly limitless resources to scale their predictive capabilities. We have billions of years of training baked in. They distill directly from our knowledge and can walk down paths that no human has before.
It’s silly to say they’ll never do anything novel.
At their current capabilities, it sounds like they are already capable of being a specific type is research assistant. What will that look like in 10-20 years?
AI can be totally biased...
The fact that it can spout bullshit all day long to a human who can be tired and would actually act on the said bullshit, is not very comforting...
For example, an LLM could confidently declare something a tired human would take as a fact, but would backfire in a real world.
One thing is that an LLM can never assume, or find out, an inconsistency in its training data. Novel ideas often require correction of existing assumptions. As far as I understand, it is impossible, by design, for LLMs to contradict what is in its training data.
For example, an LLM trained on the data from an internet comprised of people who believe in the earth centric hypothesis can never say "Hey, that cannot be correct", or come up with the heliocentric alternative
But maybe it is not applicable to pure Math...
You state this as a fact - are you aware the question is unresolved?
EDIT: I'd love to know why you're downvoting me for stating a known fact.
I can confidently state that GPT-5.6 Sol is not experiencing the same reality as me. They _might_ be "experiencing" and I personally think they are, but their reality and experience is not the same as ours.
Maths was already infinite, it's still infinite, but who wants to spend all their lives changing rooms inside Hilbert's Hotel?
Most of us aren't Terence Tao
How's It Hanging, Brother?
Sure, it's not a breakthrough that opens new roads in mathematics- is this where the goalpost has moved now?
Oh wait, sorry, I do know why you're getting downvoted. Fear.
Humans have a deep need to be special magic flowers - and they can't stand it when science eventually shows them they're not.
But if the current trends continue, Elon will own all of the robots and the rest of us will be at his mercy.
How we change that - I don't know. But I do know we don't change it by putting our heads in the sand. AI is here and it is real. We MUST take it seriously. Shunning is not a viable option.
Whether that's UBI, or Fully Automated Luxury Gay Space Communism, or UBS, or some AI managed economy, or some other such thing, we need to decide that "hey, we don't want to tied survival to output under our current system."
That's really the Rubicon we have to cross, and there are a LOT of people who can't really come up with a better way in their own heads yet.
Look, we all saw how things can be during the pandemic. That was a dark time, but it also gives us a model, we can just... do things. We just have to decide to do them.
WTF does the pandemic have to do with this? "dark time", oh yeah, people stuck at home watching Netflix, what an incommensurable suffering!
Buddy, I can admire the naive childish optimism to a degree, but come on. "We just have to all decide". Do you live in a Disney movie?
I'm not sure, but if I may guess, I suspect he's talking about the fact that the entire US shut down for a year and people survived because the US Government printed money and gave it away free to businesses so they wouldn't collapse. (PPP loans.)
If we can do something like that for the pandemic, we can do something similar when push really comes to shove.
Like, am I crazy here? The rules that we live by are largely made up and the points don't matter - we can decide to live in a better world if we want to. It's hard, and there are obstacles, for sure, but this appeal to doom for the sake of doom just... why? We have made unfathomable progress over the last century and if we keep trying we can make progress like that over the next century too!
But we also decided during that time to literally pay people to stay home for awhile. That was a really revolutionary thing and it was awesome. We could decide to do that again.
You can ad hominem until the cows come home, but yeah, we literally just kind of have to collectively decide that there are better ways to do things.
There's a fantastic book called "The Last Emperor of Mexico" I read a few years ago that really talks about how the idea of a Republic or Democracy in general was a pretty novel concept in the mid 1800s. People were a lot more skeptical about it than we're lead to believe now. But eventually, the ideas of aristocracy and some "well bred" group of various types of monarchs became silly on it's face. Now the default is that we should have some sort of democratic representation. That would seem utopian AF in 1820.
Well, we're going to have to bridge that sort of gap for getting rid of the need to justify our existence through work too. The transition is going to be weird, but we'll have to come up with something else and run with it.
Dream big buddy, I know it's hard, lord knows I do, but dream big, and work little by little towards those things you want to see in the world.
I'm very curious how people reconcile their fear/hatred of AI with actual objective reality. This is actually what interests me most about the whole AI thing. How we tell ourselves what we tell ourselves.
There was a good comment on the Pelican bicycle svg yesterday about how these models aren't getting much better beyond what the companies focus training them on. I think that's what's happening in this case too, they probably put this in the training set.
- Claude isn't doing that
as evidence to support the assumption that
- it's a marketing trick
Which is obviously non sequitur, as if it were a marketing trick, Anthropic could do it too. Anthropic isn't known for not spending on marketing.
Honestly, nowadays I question human's reasoning ability more than I question AI's.
You are correct that LLMs are trained on existing proofs but hiring researchers to solve unsolved problems is just unrealistic, both in terms of how none of the mathematicians simply came out and took credit for their own discovery or exposed this, and how training sets are not easily memorized (rather, the meta techniques are learned).
OpenAI just has better training methods and techniques for pure math over Anthropic, it’s one of their biggest strengths
Because Claude can't do it. Anyone who tells you that Fable is better than GPT 5.6 at pure math is lying to you.
I do think it's very likely that OpenAI pays for solutions like these to put in the training set, and then we get material like this Reddit thread. They market themselves as selling "intelligence", and solving these math problems is something people view as highly intelligent. I'm not a mathematician, so I cannot fully judge it, but based on my experience using LLMs for novel problems in other domains, they seem to really struggle with things that aren't common. That leads me to believe they train for specific outcomes like this. Also, there are a lot of jobs out there for data annotation, including software problems (Meta has basically reorganized its entire engineering department to create training data for coding problems).
This comment on the Pelican svg better articulates what I'm getting at: https://news.ycombinator.com/item?id=48950883
I hope people are screenshotting this stuff. This really needs to be documented. It's remarkable how wild it's getting.
Making the parrots ever more complex and training on ever more data produced by intelligent, creative beings may make them more useful or convincing but does at no point give rise to intelligence or creativity.
Not much to do about it, I guess, but continue to call it out.
Is "stochastic parrot" too disrespectful for you? Do you think it is a slur?
edit: and this is a genuine question, also. How do you do stochastic parrot = "just summarize everything" = "no form of creativity" = "fear/hatred" so quickly?
Are summaries not creative? Are Maxwell's equations not summaries? Do people hate and fear parrots?
Alternatively, if you think that even Maxwell was a stochastic parrot, then presumably almost every human who has ever lived was also a stochastic parrot except a few rare examples like Einstein. Not sure what definition you are using but it seems too broad to be useful.
It's doing math proofs. At this point, it's fully clear that objective reality is that the LLM is not parroting anything here.
The most interesting thing in research is finding new questions, that we understand and that we know why they are important. And that's something that humans need to do (by definition)
And cancer is not a single disease that can be cured with one therapy.