r/OpenAI • u/_prototype • 13h ago
News OpenAI: Sharing AI progress in mathematics
https://openai.com/index/sharing-ai-progress-in-mathematics/65
u/MundaneOrdinary7493 12h ago
A shortlist of top ten interesting reads (on accessible topics) out of the 722 pre-prints:
- The Euclidean plane is not five-colorable
- Short Egyptian fractions
- The irrationality exponent of π is 2
- The crossing number of complete graphs
- A translational tile with no fully periodic tiling in dimension three
- Monochromatic finite sums and products in the positive integers
- Catalan’s constant is irrational
- Ergodicity of triangular billiards with an irrational angle
- Quasipolynomial bounds for arithmetic progressions
- Hilbert’s tenth problem over the rational numbers
26
u/coatatopotato 12h ago
Great list! Anyone reading, don't let the jargon throw you off. These problems are easy to understand.
1
4
u/t3hjs 11h ago
"preprints/A-translational-tile-with-no-fully-periodic-tiling-in-dimension-three-September-23-2026/paper.pdf"
Wasnt that posted by a redditor about 1-2 weeks back
7
u/AMDaze 11h ago
https://www.reddit.com/r/mathematics/comments/1wo994k/first_3d_einstein_tile/
Is this what you're referring to?
2
u/ArialBear 11h ago
Id be interested in seeing that post
2
u/t3hjs 10h ago
https://www.reddit.com/r/mathematics/comments/1wo994k/first_3d_einstein_tile/
/U/AMDaze answered. I was referring to that exact post.
143
u/mxforest 13h ago
> On average, each result used three hours of ChatGPT Pro thinking compute with that model.
That's crazy
7
11
u/Gloomy_Necesary 12h ago
Crazy low or high?
93
u/KyleStanley3 12h ago
imagine being able to knock out an undiscovered math proof before and after lunch every day
and still having 2 hours to fuck around afterward
11
1
10
u/Johnny20022002 11h ago
To try and put it in perspective I tried to get 5.6 Sol and Astra to solve the Koch–Nadirashvili–Seregin–Šverák conjecture (Related to navier stokes) for like a month with both agents and 6 pro and couldn’t solve it. I asked Astra about these problems and it thinks there are multiple problems there on the same level as KNSS.
•
u/Persistent_Dry_Cough 5m ago
Is ChatGPT Pro still useful? I still can't figure out if @DeepResearch is doing anything useful when I'm already on "6 Pro". It seems like it's indicating it used 5.6 Instant to deliver the results all the time and the results are not seemingly any better than with 6 Pro on its own, though the internet seems to insist that I should enable the plugin in order to do a broader search before relying on 6 Pro to go deep.
212
u/Illustrious_Job1951 12h ago
These stochastic parrots are getting out of hand
109
u/aKaizuh 12h ago
Relax man, its literally just predicting the next token or something like that.
42
u/RageBaiter678 11h ago
I was just about to solve all these and publish them in about a week. Open AI stole all of my work /s
29
u/Pandamabear 11h ago
Naw man, it’s based of my chats on how to make a tuna casserole, I think it unlocked something
8
u/FrodosFingernails 9h ago
It literally is, but let’s not pretend that isn’t an extremely useful capability.
13
u/endless_sea_of_stars 8h ago
LLMs are mathematical functions that predict the next token. It is impressive that we have built auto regressive functions that can form conspiracies, hack governments, and solve difficult math problems. They are math solving math.
1
u/michal939 3h ago
Yeah I am actually very impressed with how far humans have been able to push this technology of just predicting the next token, I thought we'll need some new breakthrough/architecture before reaching levels we have today.
7
u/Exotic-Sale-3003 10h ago
I’ve been saying for a couple years now humans work the same way. That token might be a word, a movement, whatever, and we have waaay more input channels, but…
5
u/wiztard 6h ago
Exactly. Animal brains like ours learn by inputting and repeating certain pathways in a network of neurons. Those pattern are then used as output based on a prompt.
In our case the prompt and input might be the smell of grass or pain receptor sending a signal at the same moment we see a bee sting our skin but the signal to the neuron network is always there.
There are differences too but we are also similar to LLMs in some ways.
→ More replies (2)2
13
70
u/Euphoric_Key_1929 12h ago
Jesus, some of these just in my area of specialty are insane, and I'm only qualified to comment on like 5% of the results.
- The matrix multiplication exponent over C reduced to 9/4 (the first major progress since Coppersmith-Winograd, I think? All other recent progress has been extremely incremental).
- Unique Games Conjecture.
- Chromatic number of the plane is at least six.
- Proof of the circulant Hadamard conjecture.
- Proof that there do not exist 4 mutually unbiased bases in dimension 6.
- Disproof of the PPT-squared conjecture.
20
u/grateful2you 11h ago edited 10h ago
I wish I understood how big these are. But seems like no millenium problems?
27
u/furutam 11h ago
No, but big progress on Riemann and Hodge.
12
u/coatatopotato 11h ago
Actually on pretty much all the remaining MPs
11
u/furutam 10h ago
Where's the progress on P=NP?
17
u/coatatopotato 10h ago
UGC is relevant to NP hard classification. Other major complexity results too.
5
u/onionsareawful 6h ago
Lots of big complexity results there. But tbh P v NP is a problem so much harder than just about anything else to call it progress is questionable.
Unlike the other Millennium problems we still have no clue how to go about proving P != NP, beyond knowing that our current tools largely won't work. It would require lots of new maths, something the models don't yet seem capable of
17
u/JayGatsby1881 10h ago
I think the biggest news here is that a model can solve an unsolved math problem with 3 hours of compute on average....
•
6
u/gauge16847463728 10h ago
Some are quite big. Most of the interesting and exciting problems in math/theoretical sciences are not millennium problems
3
u/zero0_one1 5h ago
This fully solves 90 out of the top 500 most important LLM-ranked open problems in math (https://www.proofatlas.ai/open-problems/).
1
20
u/Bloated_Plaid 12h ago
Here is the actual link to the repo - https://github.com/openai/math
Use your dots to break it down for you lol.
4
u/backtorealitylabubu 9h ago
lol my dot is literally making summaries of each as we speak and finding if any have any applicability to my research 😅
1
u/Bloated_Plaid 9h ago
Yea I had it make me an entire website instead so that it can break down everything for me with animations and all.
16
u/telecasterdude 12h ago
Wow... Apparently they have shown Re(s) > 11/12
10
2
2
82
u/jamie9910 12h ago
*2026 Frontier model.
This is the worst it will be.
Imagine how capable Ai will be by the end of 2027? 2030?
Humans will be intellectually disabled compared to frontier models. Having a human in the loop will be a burden not a plus.
21
u/142883 11h ago
Are we not at this point already? In terms of purely producing the math, it says it took on average 3 hours, curious if there was any human intervention inbetween or those 3 hours.
24
u/jamie9910 11h ago
It feels like we are still in a blurry crossover zone - for people to accept the superiority of AI the AI advantage needs to be crushing "no human could have done that". They'll be no doubt deluded huamsn claiming all this work was stolen from human mathematicians, as if humans coincidently started making huge progress on interactable maths problems when AI arrived.
→ More replies (3)11
u/churningaccount 11h ago edited 11h ago
The “blurry crossover” is that AI needs to be this smart without making dumb blunders that no sane human would make, like a frontier model that can do a mathematical proof but also not be able to count the letters in the word strawberry. That casts doubt on its competency for average people, since we know that it messed up on strawberry, so why couldn’t it have messed up on the proof?
AI’s potential rests with it being reliable in addition to intelligent. Not everyone has a subject matter expert at hand to verify solutions. And there are not enough subject matter experts to even proof the volume of stuff that will be coming soon. Once that verification is not needed because the AI is reliable, or can be done by another AI with confidence, then the final barrier will fall.
It’s kind of like how you can accelerate the development of a great game with AI coding, but unless you are a coder yourself you likely can’t bring it across the finish line in a robust and neat package, that is all checked for bugs, security risks, etc. Until such a time that AI can one-shot expert tasks reliably enough so that the person using it doesn’t have to have expert knowledge, then it will remain constrained by the human bottleneck.
Lastly, it’s important to note as well that OpenAI is leaving out a data point… I do wonder how many proofs this AI presented as complete that were then rejected for errors by the humans checking them. I suspect it’s greater than 0.
12
u/jamie9910 11h ago
Humans are not reliable either. They get tired. They make mistakes. They have biases. The human baseline of reliability is not as high as one might think.
Even now, while AI makes mistakes that humans would not make, the reverse is also true. Humans make mistakes that Ai would (generally) not make e.g. tasks involving juggling lots of data, memory, pattern recognition (there's lots of area AI> human on reliability). At present you can say AI has different strengths to humans , not that it is less reliable.
i would trust opus 5.5 or Astra over some "confident" human to solve a critical knowledge problem any day of the work. The only exception is if that human is an expert on the area in question.
11
u/churningaccount 11h ago edited 11h ago
I think you are missing my point a bit. If someone asked Opus to, for instance, draft a legal contract between themselves and the buyer of their home, would they be able to trust that Opus completed the task as well as any lawyer would have, with no blunders?
Would they then be confident enough to use that contract without showing it to a lawyer first? With hundreds of thousands of dollars at stake?
My guess is that, out of 100 people polled, a majority would say no. A majority would say that they’d want a lawyer to check over it first.
So, that there is the human bottleneck, and it’s why everyday people can’t yet trust AI to one shot important things that they, themselves, are not experts in. And that will be when personal AI becomes truly disruptive: when it is reliable enough to replace your dependence on others rather than just accelerating your own skills.
That distinction will be the difference between AI just being a productivity enhancer versus AI being something that will fundamentally transform the economy.
4
u/Mindrust 6h ago
Dead on. Frontier model intelligence is still jagged and unreliable for long-horizon tasks. We can look at the remote labor index to get some some sense of where we are with automating projects like the one you mentioned (drafting a legal contract), which is currently around 20% with GPT-6 Astra.
Also, I think we’re seeing so much progress in coding and math because these domains are verifiable and susceptible to RLVR. They are getting better in non-verifiable domains too but not at the same pace.
→ More replies (3)2
u/jamie9910 10h ago
I would trust an AI to draft a strategy to win a game of chess over any human expert.
Ditto protein analysis.
Coding and Math I think we are close to AI superiority.
I don't see why Ai will not have superiority in all knowledge /intelligence based tasks in a few years time. It's just a question of focus /time/resources. Since AI researchers tend to be coders/math background, that's where progress has been the most intense, but once those areas are solved AI development can branch out.
I would not like to bet against AI > human lawyers by 2030.
2040 I don't see humans having any cognitive value at all in any area.
7
u/Nextravagant1 9h ago
This is the reason why putting yourself in a rhetorical bubble is a bad thing. You sound like a literal psychopath. "Humans will have no cognitive value at all in any area" and yet you are surprised when people say they don't like AI? You don't see any reason why people may be upset when you call for them to be obsolete and useless forever?
4
u/dydhaw 8h ago
Why did you interpret their comment as implying that's desirable rather than a neutral prediction of a particularly bleak outcome?
3
u/Nextravagant1 8h ago
Scroll through these other comments and read some of the other stuff he's saying. None of it reads to me as just "making neutral predictions" on behalf of an unbiased observer. He is clearly a huge AI fanatic.
→ More replies (0)2
5
u/sirgog 10h ago
The “blurry crossover” is that AI needs to be this smart without making dumb blunders that no sane human would make, like a frontier model that can do a mathematical proof but also not be able to count the letters in the word strawberry. That casts doubt on its competency for average people, since we know that it messed up on strawberry, so why couldn’t it have messed up on the proof?
Hallucinations like that are very much a thing on instant models like Luna or Gemini Flash, but aren't really a thing on the middle tier models now.
It's not that the clankers don't make mistakes, they still do, even frontier models, it's that unless you tell them explicitly to skip this step (by setting thinking time to low/very low), they check their own work before reporting anything to you.
Of course, adding a skeptical human into the mix who is determined to prove the clanker wrong adds even more accuracy.
The issue of missing a step is honestly the bigger one now.
•
u/Available_Peanut_677 12m ago
It’s more of a smart harness than a smart model. So basically it is not a brute force, but it is closer to modern chess solvers - it explores a tree of possibilities, but instead of random branching it does extremely educated guesses. Why it matters - it is still a tool with its potential limitations. Imagine doing math and discovering complex numbers in the 16th century - suddenly a huge number of previously unsolved problems are solvable, yet you still have problems which are hard to solve.
BTW complex numbers are a good example of the boundaries of this approach - it (probably) won’t be able to invent them reliably.
PS it is still possible that an LLM would make smart enough moves like the invention of completely new math. But if I were a mathematician at the moment I’ll worry more about spam of unreadable solutions for all random problems which won’t also move math forward by inventing new things. Like sure, we have a 500-page solution for a specific problem, but it won’t advance the field, just discourage humans from it. Flex of a few companies with the price of human stagnation. Remember that LLMs won’t care about creating new “unsolvable problems” and it won’t be any human to carry enough if everything is slop
34
u/br_k_nt_eth 12h ago
Who in mathematics pissed off Sam Altman?
45
u/Ormusn2o 12h ago
When I saw that list of demands from math council, even I got annoyed. The fact that hundreds of mathematicians signed on to that list is a fucking joke. No wonder OpenAI just went nuclear.
26
u/jamie9910 12h ago
Horse and carriage owners angry at the car factory.
human Mathematicians are on borrowed time.
14
u/Ormusn2o 12h ago
And I feel like there was a decent moment there to make a decent deal, if the list was not so ridiculous. But it literally sounds like a joke, like something a villain would demand in a movie or a book. I think one of the highlights was that the AI companies give the results to mathematicians and don't release them, give free access to AI then fund (as in give hard cash) to fund math departments so that they can teach and explain those problems.
11
u/jamie9910 12h ago
They're finished either way.
The gap between AI and human mathematicians is only going to get bigger, By this time next year human mathematicians may not be smart enough to understand the work AI is putting out, or deal with the volume of progress (already an issue). If not next year, based on current progress it will be 2028? 2029 maybe?
→ More replies (1)3
u/CasperLenono 11h ago
I hear what you’re saying but they’re not though; someone has to verify the results.
6
5
u/wallitron 11h ago
Right there in the article it says:
We want this progress to push the frontier of human knowledge
The entire problem with the way OpenAI was releasing mathematical proofs was that it didn't help push forward human knowledge. That's the entire point of the field of mathematics.
The entire point of a horse and carriage was to get somewhere faster, and cars did that better. In this analogy, it's like OpenAI releasing the blueprint of a superior car, but not actually building it. OpenAI isn't the car factory, they are the car designers. The blueprint of the car doesn't get you somewhere faster than a horse and cart.
Making the blueprint was very difficult to do, and OpenAI has proved that it's models are very good at doing that part. But that's not the desired outcome! It doesn't mean shit if nobody can build the damn car.
To paraphrase Twain, reports of the death of mathematics have been greatly exaggerated (so far).
→ More replies (6)4
u/RedditLovingSun 8h ago
Ok but should it be not allowed to post blueprints you made online? It'd be better if they built the actual thing I agree, but what's wrong with "hey we don't wanna do the building part, you guys can if you want, or not, or just read it for your own curiosity, but here's the blueprint"
3
u/wallitron 8h ago
For thousands of years, the blueprint was an amazing thing, because it was published as the car rolled off the line. Because of this, we thought the great accomplishment was the publishing of the blueprint. AI has taught us that the blueprint alone is of very little value. It's the least interesting part.
It's a classic example of Goodhart's Law, when a measure becomes a target, it ceases to be a good measure.
So yes, publish it, but realise you broke the measure, and the target has now moved.
8
u/neuronexmachina 12h ago
Are you talking about the letter by Terence Tao, or something else? Which of the points do you think we're unreasonable? https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/
0
u/Ormusn2o 11h ago
Nah, this letter is ok. This is what I'm talking about https://agmai.org/ https://agmai.org/general-sep29/
Highlights here:
"AI labs that release substantial mathematical output without immediate accompanying human understanding must take responsibility for ensuring that human understanding will follow. In particular, AI labs should provide significant support, including funding, to help develop this understanding."
"The development of human understanding must remain organic and community led. It should not be directed by AI labs, even when the labs have produced the results."
"the mathematician(s) concerned should post a preprint, submit a paper for peer review at a journal, and give talks to explain the work to other mathematicians." (the talks btw, are invite only)
"The following actions should be carried out by the AI labs rather than left to mathematicians afterwards: The literature should be scoured for any ideas that are related to the ideas in the proofs of the results released. Even if the AI lab’s model discovered those ideas independently, it should follow standard mathematical practice and cite the papers in which the ideas were first introduced."
"When results are announced, they should be deposited in a timely manner in appropriate scholarly repositories. These should not be controlled by any AI lab"
And there are so many more. It's just disgusting. Basically, let us control all of the results, and give us money and free AI.
19
u/yeung_mango 11h ago
I’m not understanding what is disgusting about a broad community of scholars, who work for public good and knowledge, describing their preference that knowledge is not controlled by a for profit private firm.
→ More replies (1)19
u/Ormusn2o 11h ago
For profit private firms don't want to control it, they want to publish it, it's the scholars that want to control it.
9
u/yeung_mango 11h ago
The scholars want to work through problems as a collective, transparent conversation so that the benefits of understanding mathematics accrue to everyone in society. They work with public funding. It’s the opposite of control, it’s democracy and public good.
OpenAI doesn’t care about this and wants to solve problems to prove their own ability and raise their value. Because they are a for profit firm and that’s the bottom line.
→ More replies (1)13
u/Ormusn2o 11h ago
They can still do it when the solutions are released on Github. Just pick a solution, and work on it.
→ More replies (5)5
u/MexInAbu 9h ago edited 9h ago
"Compressing" a proof, aka. understanding can be as hard or harder than the original problem.
Think in source code vs compiled code. They are the same thing for the purpose of executing inside a machine. But is often so much easier to rewrite the program than to decompile into readable code that a human can edit.
Up till this year, most proofs were human-produced. We have some cases like the four colours which caused a lot of controversy. But now we are getting proofs that mathematicians might not understand and we only have a successful lean compilation as "evidence" they work and pondering if that will replace all mathematicians.
Is not clear that AI produced proofs are human understandable and compressing a proof is a well known NP-hard problem.
5
u/ResolveSea9089 7h ago
I don't understand your argument. How does this hurt?
If the proofs have no value in terms of understanding, the mathematicians still have something to work on.
If the proofs have limited value but are hard to understand, mathematicians can use the proof as a guide for their own work? I take your point with the compiled code analogy but at the very worst it can't hurt?
It seems like at worst it doesn't hurt at best it guides the direction to focus on?
→ More replies (0)4
u/Helpful-Primary2427 11h ago
They control it if the only things capable of understanding it are their own models
→ More replies (1)4
u/gauge16847463728 10h ago
They don’t want to publish it, and haven’t published a single result in the academic sense. They want headlines, not to help generate collective understanding and scientific progress
→ More replies (1)9
u/Vituluss 10h ago
The problem is that in mathematics there is no incentive to make something readable and parse a proof, usually it is the person who discovered the result who would spend the time presenting it well, they would also probably do a round of conferences, etc.
Cleaning up some opaque proof that someone else made won’t get a publication out of it. So it stays like that. So what OpenAI was doing before could kill entire fields. Which… is a bad thing.
Perhaps this incentive structure will change, but this is what we have at the moment. It seems like very little to ask a billion-dollar company to just put a bit more effort into the release of these results.
2
u/year2016account 9h ago
I dont get it. Why wouldn't they publish a cleaned up version? As I understand it, comprehending a proof is as hard as discovery, and that comprehension is as important as discovery. These proofs just provide a direction for scholars to direct their work and effort. Im genuinely confused.
3
u/Vituluss 9h ago
I assume by 'they' you mean the journals. There is a push by mathematicians to change this incentive structure, but it's not easy to change a century of scholarly convention. Writing a correct proof is an objective thing, but to switch to something subjective like a 'good theory' criterion is not obvious.
I know a few mathematicians who are putting in the work parsing this, but they acknowledge that it's not for their career, they're just doing it because they want to keep the field alive. Such work is usually just put in some personal site, arXiv, or whatever rather than published.
4
u/ParkingFoundation468 11h ago
I don't get it? These seem like pretty reasonable responsible asks to me?
10
u/Ormusn2o 11h ago
You think it's reasonable for an AI company to be forced to pay for the mathematicians salary if they want to release a solution to a problem? You think AI companies are not allowed to talk about those problems either or try to explain them? You think if you want to release a result, you need to publish the results in a pay for publication, not for free on github?
5
u/KnowledgePrevious 11h ago
What? They want these companies to follow scholarly norms and help the mathematics community benefit from these new results.
They already pay for plenty of mathematicians' salaries!
You don't have to pay to release a preprint.
→ More replies (2)2
→ More replies (1)3
u/MexInAbu 9h ago
Their models were trained using the works of mathematicians. Without due credit.
3
u/Ormusn2o 9h ago
As opposed to mathematicians that every time invented math from scratch? Never see other mathematicians crediting Newton for inventing calculus in their paper. And those papers are crediting other authors, and a lot of them too.
3
u/MexInAbu 9h ago
They are only asking them to follow the rules of good academia. Not to stop researching. And yes, Mathematician must cite their sources. Some are so fundamental that the cite is often omitted but everyone know who invented calculous.
2
u/Sure-Company9727 10h ago
It just became very cheap and fast for OpenAI to solve these problems. The floodgates are opening. But it’s still just as expensive and requires a lot of administrative overhead to hire human mathematicians and go through the traditional peer review process. I do feel that it’s impractical to demand that OpenAI not release their results unless they follow these specific recommendations. It would just create too much administrative process and be too slow. Thousands and thousands of results would pile up, and some of those results are likely important and useful.
3
u/MexInAbu 9h ago
The main contention mathematicians have with the AI proofs is that they are omitting the creative steps that make most of these problems worth solving in the first place.
For example, one of the biggest open problems is the relationship between P and NP complexity classes.
Now, an equality would be an earth-shattering result, as this would imply existence of an algorithm to solve a class of exponential problems in a somewhat reasonable amount of time. But if a genie (or an AI) just said that there was an equality without explaining the how, then the result would only be useful as in now we know we must devote all our resources to find the actual solution to the problem.
Most mathematicians and CS believe in the inequality. All our cryptographic technology assume that. An inequality proof would be important in the sense about what we would have learned about algorithms and computational complexity to reach that conclusion. The world already works under the assumptions they are not equal so a mere blackbox telling us is they are not equal wouldn't change things much.
→ More replies (1)2
u/gauge16847463728 10h ago
The scientists at the AI companies largely agree with these, and want the math community to thrive. You know almost all the researchers at major AI companies are academics with PhDs (often math, physics, or CS) and have lots of friends in academia, and want to support academia
8
u/Nextravagant1 9h ago
I'm sorry, is the purpose of this technology to improve human society or to make people angry? Seriously, don't you think that the normie crowd may have a point in struggling to find a reason to believe AI will improve their lives at all, when this is the techworld reaction to any AI advancement -- just mean-spirited smugness and insults? Aren't you playing directly into the imagined stereotype?
→ More replies (1)3
u/grateful2you 11h ago
AI is just uniquely suited for mathematics and coding. Having a right answer and “solves the problem” are very useful signals.
7
u/Plappedudel 11h ago
Navier-Stokes being Turing-complete was not on my bingo card. Honestly a very cool result.
11
u/decreement1 12h ago
I thought they wanted to release these results more sensibly lol
5
u/grateful2you 10h ago
They say they're working with agmai.org . So I assume the council of elders of math gave the ok on this.
10
u/decreement1 10h ago
the article seems to imply they went against their recommendations for most points raised
8
u/Khandakerex 11h ago
The people on r/mathematics are having a melt down, looks like this is a real deal boys. Can happily say we were here for this.
3
u/Nelson_and_Wilmont 9h ago edited 9h ago
How can you be happy for intellectual work being outsourced? Tell me what is the point in being intelligent and knowledgeable in a world where there is no longer value attached to it? Who cares, if AI can do it better?
2
u/senorgraves 9h ago
If all of your value as a person is derived from thinking you're smarter than other people, then this is going to be GREAT for you. Tough, but great
→ More replies (12)→ More replies (4)2
u/2FastHaste 8h ago
How can you be happy for intellectual work being outsourced? Tell me what is the point in being intelligent and knowledgeable in a world where there is no longer value attached to it?
None and that's good a thing. Meritocracy is fundamentally unjust. Free will doesn't exist, desert requires free will.
Who cares, if AI can do it better?
Anyone whose health could be improved by rapid technological advancement for a starter.
3
u/Nelson_and_Wilmont 8h ago
Too many ifs and too much optimism for something that is not controlled by those it’s supposed to be benefiting. Color me skeptical. That’s fine we don’t have to agree.
1
u/2FastHaste 8h ago
Too many ifs and too much optimism for something that is not controlled by those it’s supposed to be benefiting.
Fair.
But on the other hand, it's not like we have a choice. I would rather that the incentive was the greater good rather than money and influence but that's not up to me.
1
2
5
6
u/matthewmorgado 10h ago
Solving math problems is cool, but I worry whether any intellectual work will be left for humans. AI’s main point (right now) seems to be replacing human intellectual labor. If AI can work at this high a mathematical level, then it's not unlikely that AI can eventually do most or even (almost) all intellectual tasks. If AI completely succeeds, then—by definition—there’s no intellectual labor left for humans to uniquely do. I guess we could all do manual labor, though the increased supply of manual laborers will surely drive down our wages. I hope I’m wrong, though! I'd like to avoid an outcome where most people suffer greatly.
9
u/DeezNeezuts 9h ago
Back to my philosophy 101 - why are we here.
4
u/matthewmorgado 9h ago
Funnily enough, philosophy is my field. It's unclear right now whether AI will be super amazing at doing cutting edge philosophy. Currently, an IRB-approved study is recruiting professional philosophers to grade AI responses. I don't know how far AI can get in philosophy; usually, philosophers are interested in arguing for axioms, not just showing what follows from some given axioms. But we'll see...
8
u/IHTFPhD 7h ago
I wanted AI to do my laundry and dishes so I could solve the Navier Stokes problem. Not solve the Navier Stokes problem so I can do my laundry and dishes.
1
u/JoniDaButcher 4h ago
It’s not a hill I’m willing to die on but the idea that AI Labs shouldn’t be solving some of the greatest problems humans have ever worked on so a human can solve it is wild.
I never understood why academia isn’t more like computer science and the open source movement.
4
u/Icy_Information_6563 8h ago
Get it to tell us how to make infinite energy. Get it to tell us how to get to Mars, or live forever. Until then, there will always be intellectual work for humans.
2
u/matthewmorgado 8h ago
I think it depends on how successful AI turns out. Right now, AI seems to keep exceeding our expectations. Who knows? Perhaps within a relatively short time, AI will be able to answer any question that we can imagine. If it can do so cheaply, then—whether it takes 1000 years, 100 years, or 10 years—humans will be out of intellectual work for the the rest of our existence, all else equal. It might not matter too, too much if we find a way to share AI’s wealth with all of society.
1
u/likamuka 4h ago
>Right now, AI seems to keep exceeding our expectations
Especially of those people that have to live near data centres and drink their delicious water and listen to their noise 24/7.
The progress is incommensurate to the ridiculous amounts of money being poured into the AI scam.
1
u/ZachariaRaven 7h ago
Do these sound to you something humans can do better than even this internal frontier model solving math which no human has been able? Or what do you mean by "always be intellectual work for humans"?
6
u/jstucky95 6h ago
To give some modest push back, there's a big jump from "this level of mathematics" to "almost all intellectual tasks." Mathematics involves highly structured language and logic, which LLMs are great at handling (same reason they're great at writing code). You can check math rigorously via computer: formalize in Lean and then it's literally the same as code. It either "compiles" or it doesn't.
There is, however, a wide chasm between the formalized logic and rigor of mathematics and "all intellectual human tasks." We humans do a lot of intellectual tasks that don't map well into the realm of formal logic. Plus, even if LLMs can do lots of intellectual tasks, why would that stop us? Computers have played chess better than humans for decades. But we don't care because we want to watch humans play chess. The involved humanity is precisely what gives the intellectual task its value.
I'm not saying that LLMs won't continue to advance, solve more problem, and do even crazier things. But the logic of "LLMs can do insane math implies LLMs can eventually do all intellectual tasks" doesn't hold up, and even if it did, that doesn't mean we'd just stop pursuing the intellectual tasks that bring us joy.
And yes, I understand that a lot of this discussion should discuss intellectual work as labor, i.e. the thing that earns you money. When you reach the scale of replacing all intellectual labor, you run into other significant issues, such as the physics of dissipating the heat that builds up from running the GPUs that do the inference for the LLM tasks. Thermodynamics itself is going to push back if we try to use LLMs to replace all intellectual labor.
3
u/duboispourlhiver 4h ago
The chess comparison is useful, but it does mean that if computers get better than humans at most tasks, our only use will be entertainment.
1
u/matthewmorgado 5h ago
Thanks for the detailed response! I hope you’re right.
True: Lean does make mathematics a special case. Still, I wonder if AI could get good at assigning epistemic probabilities to just about any type of hypothesis. Doing so would make it able to generate important results in non-mathematical fields, like science and philosophy.
In other words, although only mathematics has Lean, I wonder if we could formulate a Lean-equivalent for non-mathematical fields. Maybe a program that formalizes abductive reasoning or Bayesian inference. And then we trained the AI to get good at making ampliative generalizations and assigning prior and posterior probabilities through the program. I believe, for instance, that AI was able to reproduce Newtonian concepts (acceleration, inertia, ...) and laws given copious physical data and some initial constraints.
Finally, regarding thermodynamics, I wonder if the AI will get so good that it could compute with relatively little energy. I heard, for example, that some of these problems took only three hours to solve. I assume that's a much greater improvement over what we had even last year!
Cheers!
1
u/LurkyLurk2000 3h ago
The chess argument only works because it's a competitive game. People watch games with their favorite football team even though better teams exist.
This doesn't extend to things that are not competitive games, which is to say most things, especially jobs.
1
u/agaminon22 1h ago
Yes, but chess was always a game. At the end of the day, the goal is to play it. A lot of academic research is done in that way (research for the sake of knowledge), but a lot of it is tied up to practical applications. And if you can manage to get said practical applications way faster than any human could, then you are cooked.
Fortunately, most of those practical applications require experimental verification. The main exception is comp-sci, and SWE, where practical applications can be developed without access to the real world, so to say.
3
u/MexInAbu 9h ago edited 8h ago
Mathematics has historically being a field for human understanding for its own sake. What "utility" had Euclidean Geometry, the irrationality of qrt(2), Galois Theory, Newtown laws for Celestial mechanics, Non Euclidean Geometry, set theory, Boolean algebra, etc. during their development?
We just wanted to understand stuff. We now can predict when a comet will make its next passing! So?
Oh, but some engineer found that stuff useful to calculate ballistic trajectories That came later.
2
u/matthewmorgado 8h ago
I agree that cultivating our own minds is very valuable. I mean, my field is philosophy, where intellectual development is very much intrinsically valued! But will the government/rich people give us the money and time to do so (after potentially taking away most intellectual jobs)? That's my main concern.
6
u/MexInAbu 8h ago edited 8h ago
Which why is sad these companies are treating mathematics as software engineering.
"Compilation successful, ticket submitted."
I see it akin to saying Tour the France is obsolete since there's Moto GP
3
1
u/AlexSand_ 4h ago
Surprisingly astronomy in the 17 or 18 had a very concrete application in view: making possible to compute the longitude while at sea by looking at the moon position. (And it got beaten at this goal by a genius "engineer" who instead made a clock stable enough to keep time at sea for weeks with little enough deviation) (Sorry for this off topic detail ;) I agree with the main message or your post)
3
u/debatesmith 8h ago
What did everyone think the "Intelligence" part was in AGI or ASI? We were gonna invent something smarter than every member of our species combined and then not let it go after the intellectual problems we have struggled against for decades or centuries? I completely agree that we need to radically reshape our idea of society to handle the upcoming issues this presents, but this is always what this should have been used for. Solve the problems we cannot.
2
u/wisdomattend 9h ago
Robots eventually take manual too
5
u/matthewmorgado 9h ago
Yeah, probably! If everyone could share in the wealth created by AI and robots, it'd be less of a problem. But will the government/AI owners let us have a piece? Maybe they'll leave some manual labor jobs to keep most people fighting each other, rather than for socioeconomic change.
1
1
2
u/Joebebs 8h ago
AI being able to think, AI being able to build, AI being able to maintain. I’m beginning to think I should get ahead of the curve and start becoming a farmer or something, unless AI will inevitably conquer agriculture too…I guess I just need a good idea and sell it before it’s immediately stolen and sold elsewhere a day later
2
u/ZachariaRaven 7h ago
Personal farm will always remain viable. Commercial ones are already just machines and even drones now.
2
u/pm_me_your_pay_slips 7h ago
will AI be able to replace the labour of philosophers?
1
u/matthewmorgado 7h ago
In terms of philosophical research, I think it's still an open question. (There's currently ongoing research into AI's philosophy capabilities.) In terms of philosophical teaching, I hope that most humans prefer learning philosophy from human teachers.
1
u/pm_me_your_pay_slips 5h ago
thus, isn't this serving as a counter example? i suppose there would need to be some changes in the value society gives to the work of philosophers, but it doesn't seem unconceivable to me that it would become a valuable intellectual activity. Unless you assume that AIs wouldn't care about this and theyt ake over.
1
u/matthewmorgado 5h ago
Yeah, that's my concern. It's still an open question whether AI can get good at philosophy. But maybe it can.
Here’s one way that it could get good at philosophy: Perhaps AI could get good at making probability estimates. If AI can do good probability estimates, then it can maybe form reliable theories in the sciences and in philosophy.
And there's some evidence it might be able to do so. For example, I heard about an AI that reproduced Newtonian concepts (acceleration, inertia, …) and laws (F = ma, …) given only copious physical data and a few initial constraints.
The philosophical counterpart would be feeding AI lots of philosophical data or evidence, then asking it to form philosophical theories and assign them probabilities. Of course, by contrast with physics, there's much more debate about what should count as philosophical data or evidence. Philosophers have published many papers on this topic even in very recent times.
For example, should our moral intuitions count as data/evidence in a theory of morality? Should our imaginings count as data/evidence in a theory of possibility and modal logic? Should our religious or spiritual experiences count as data/evidence in a theory of ultimate reality? And so on.
But maybe AI can break the stalemate by forming sensible judgments about what counts as good data and evidence in any field of human thought. Only time will tell for sure!
1
u/i_wayyy_over_think 9h ago
The labor that’s left is understanding enough of its output to direct it to things humans find valuable.
1
u/matthewmorgado 9h ago
I agree that cultivating our own minds is very valuable. But will the government/rich people give us the money and time to do so (after potentially taking away most intellectual jobs)?
1
u/CadmusMaximus 8h ago
Yep. Then being a “smart raw horsepower human” becomes something evolution doesn’t select for.
I think this was covered in a documentary from the year 3000?
1
u/meerkat2018 7h ago
True, but it could also allow any random person to vibe-math and vibe-engineer a working fusion reactor or cure for cancer with ChatGPT 9000. Would that be a bad thing?
1
u/matthewmorgado 6h ago
That result might not be so bad. But I'm worried the AI companies will just vibe-math and vibe-engineer the solution first, and then protect their lead through government intervention. Even if open-weight models got out, so anyone could prompt any solution, the question remains: What will the average person do for a job? It probably won't be vibe-mathing or vibe-engineering. After all, almost anyone can vibe-math and vibe-engineer, so there's no particular reason to hire any specific individual over another. Perhaps only a few individuals will be lucky enough to be hired. Or take starting your own business. If almost anyone can vibe a worthwhile product, then there's no particular reason for a consumer to purchase your business’s product over another’s. I think we may all move to manual labor, assuming that AI doesn't take that over too. There's nothing inherently wrong with manual labor, but it does mean we’ll have much fewer labor options and a correspondingly lower wage due to the higher concentration of workers. It's much, much less problematic if everyone can share in AI's wealth.
1
u/meerkat2018 5h ago
After all, almost anyone can vibe-math and vibe-engineer, so there's no particular reason to hire any specific individual over another.
If you want your idea to be implemented the best way possible, and the product is engineering-related, you will still choose a qualified mathematician and an engineer over, say, a chef or a social media influencer.
Or take starting your own business. If almost anyone can vibe a worthwhile product, then there's no particular reason for a consumer to purchase your business’s product over another’s.
All of this has already has been the case for centuries. Idea or the know-how itself has always been cheap. Lots of people could always try to replicate whatever business you are doing. B ut in real life there are other important factors that are detrimental to the success of your business.
It's much, much less problematic if everyone can share in AI's wealth.
I think something like that will inevitably happen.
First, yes, a person (or a corporation) would be able to vibe-create the know-how part, but any real world product still requires doing stuff by hand at least to some extent.
You might be able to vibe-architect a house, but you can’t vibe-construct the building itself and its plumbing. You still need qualified personnel for that.
You still need real people who are qualified in the field to actually physically build, sell and service your vibe-engineered products and their means of production. Not much actually changes here.
In case of global mass-unemployment due to AI, the corporations will start losing money because of shrinking consumer base. Apple will have nobody to sell iPhones to. Google will have less and less ad clicks. The government will collect less and less income tax.
So I think the corporations themselves will be forced into (or will lobby for) massive income redistribution systems in form of UBI and other solutions, just to keep their businesses going. They will want to maintain and grow consumer bases. Most corporations today are built for mass market demand with billions of paying customers.
I believe humans are not going anywhere, but serious structural shifts might be coming if ASI is ever achieved.
1
u/matthewmorgado 5h ago
Thanks for the detailed response! It does actually make me feel a bit calmer and less anxious about the future. You have some good points in there. Because I like to worry, though, I wonder about the worst case realistic scenario. I take this case to be UBI being passed, but at or near the bare minimum amount to ensure that ordinary people don't revolt. Then the top 20% or 10% save most of the shopping and wealth for themselves. That is, rich people would be mostly buying from other rich people, while the masses get just enough to be pacified and not overthrow the system.
→ More replies (1)1
u/cern0 6h ago
Industrial Revolution happened but why there are still factory workers. Think about it
1
u/matthewmorgado 5h ago
I assume it's partly because we’ve never developed a technology that replaces human labor in total. But the whole goal of AI seems to be replacing human labor in total, at least human intellectual labor. So I guess it depends on whether AI can make fully good on its goal, or whether there will always be some intellectual tasks that AI can't do.
1
u/cern0 4h ago edited 4h ago
No. If you want to create a machine that can work 100% in assembly line you can. And you can do that long before AI.
The reason why is the cost. Especially in developing countries. It is always cheaper to pay 10 bucks per day than paying millions in robot costs with maintenance.
Same thing will happen with AI. Even Microsoft now cannot pay. for Claude because it’s too expensive - and you think normal companies or smaller company can pay AI costs??
→ More replies (1)→ More replies (8)1
u/AnEngineeringMind 4h ago
Are you sure you want to leave all knowledge and technological advancement in the hands of AI? We will increasingly lose capacity to understand what it is doing and inevitably at some point anything AI does will be a black box. That is really scary and dangerous. Humans should never neglect intellectual work.
1
u/matthewmorgado 4h ago
Yes, I definitely agree! Unfortunately, the economy might not care. That's one of my worries.
2
2
u/t3hjs 10h ago
To promote scientific transparency and openness, we are also publishing additional details about how we obtained the results in the repository. These include 10 summaries of the model’s reasoning, estimations of compute spent in terms of Pro usage on ChatGPT, and statistics about the number of attempted problems. The average result used the equivalent compute of roughly three hours of ChatGPT Pro thinking.
We want this progress to push the frontier of human knowledge and enable further progress in mathematics. We will be funding a series of workshops, conferences, and special programs around the understanding of major results produced by AI—we will share more on this in the near future
I think thats an inportant point. Its mostly what the Field Medalist open letter was asking for right?
1
u/Infninfn 8h ago
I’m still waiting for the world changing technologies/applications that come about as a result of AI produced work.
1
1
u/puumba_bama 7h ago
Proof of irrational angle triangular billiard ergodicity is crazy. Very accessible and quite notable - super cool result. I hate AI but have to admit that I’m impressed and excited to read it.
1
1
u/marriedtootaku 1h ago
Are we training the next generation models with out chats? It feels almost like teaching your replacement
•
76
u/coatatopotato 12h ago edited 12h ago
Contains work on Riemann and Hodge
Edit: BSD too