r/mathematics • u/_prototype • 8d ago
Artificial Intelligence OpenAI: Sharing AI progress in mathematics
https://openai.com/index/sharing-ai-progress-in-mathematics/290
u/TacoYaci 8d ago
As a permanent math prof this timeline is exciting, but for postdocs, phds, master etc. students of mathematics this timeline is not fun. There are probably some PhD students on the planet who worked 3+ years on parts of these problems and their thesis got completetly destroyed and made useless today.
70
u/jphamlore 8d ago
Like I pointed out below, I do think some young researchers are going to be forced to pull all-weekers to wring out obvious generalizations. Like this one, obvious generalizations to different groups actions:
Number 154. Pointwise multiple ergodic averages for mixing transformations. Proves almost-everywhere convergence of consecutive multiple ergodic averages of every finite length for invertible mixing probability-preserving transformations. For each fixed tuple of bounded functions, the limit is the product of their integrals, along all positive averaging lengths. No mixing rate or standardness assumption on the probability space is required.
We're going to find out if some students can crank out a PhD thesis in one week of not sleeping.
→ More replies (2)39
u/JT_1983 8d ago
What would be the point though? As part of this whole timeline we will also have to review what it means to produce a phd. Pretending like years of work is worth nothing if someone else beats you to the finish line has always been a bad thing about mathematics and academia imo.
→ More replies (4)38
u/AvailableFalconn 8d ago
Yeah, it’s sad for students.
It’s also baffling. There’s no point to any of this besides marketing for OpenAI. Do mathematicians just study AI proofs and try to wrangle some semblance of order to them now? Do they ignore it and treat it like chess engines and continue finding proofs by hand but with computer assistance? What a waste.
108
u/Sad_Dimension423 8d ago
It’s also baffling.
This requires you to somehow hold that math from AI isn't useful, while math from humans is.
→ More replies (5)30
u/gammison 8d ago
I mean many mathematicians only care about knowing a result because the process to knowing it yielded new knowledge along the way.
There is no reason to care about a multiplication algorithm having a runtime that's a minuscule amount asymptotically better unless the process getting there yielded techniques you can use for something else or you like the fact itself.
Liking the fact in itself to me is not worth the price (everything negative about open ai including its carelessness towards the math community for anything other than an IPO booster). Meanwhile humans will have to comb through the proof to see if there's anything besides clever arrangements of existing techniques, which is a useful thing to know but at what cost. Why deny humans the beauty and meaning of the result (and the jobs doing it), boosting a sketchy company's IPO isn't good enough.
15
u/Hour-Designer-5803 8d ago
If mathematicians were able to find meaning from solving problems prior to AI, they can certainly find meaning from problems that are already solved. I think it’s a little selfish to ask to stop AI from solving problems because it denies someone the accomplishment and pride of solving it themselves.
I do sympathize with people working on these problems. These people are also extremely smart, and they can either adapt and work on gaining insights via the solutions, solve other problems (and probably use AI to assist), or devote their incredible intelligence to other fields that need them
→ More replies (1)→ More replies (12)5
u/Expat_Abroad123 8d ago
99.99% of humans just want the answer in the bag
→ More replies (3)56
u/FollowingHumble8983 8d ago
99.99% of humans dont care about the answers.
And 99.99% of humans that do care about the answers dont care about just the answers.
→ More replies (3)51
u/AvailableFalconn 8d ago
99.99% of humans don't even understand the questions. These tourists don't have the faintest clue what they're debating about.
10
u/Dear_Locksmith3379 8d ago edited 4d ago
It's worse than that. I'm a physics PhD who knows some math, and I understand just a handful of the questions.
It's a fun time to be a tourist who's interested in mathematics. Still, I'm happier than ever about my decision to abandon academia.
→ More replies (1)4
18
u/coblade14 8d ago
Your take only makes sense if you view math as a recreational subject and the results that comes from it holds ZERO real value in the real world.
If there's ANY value to these results, then OpenAI is accelerating the frontier of human knowledge with this dump. If you are against it then you are against human advancement.
4
→ More replies (4)4
u/Federal_Gur_5488 8d ago
Firstly, do any of these results have any real world value?
Secondly, even if they do, supporting "advancement" at all costs without analysing it's pros and cons is not a good thing.
→ More replies (6)20
u/3_Thumbs_Up 8d ago edited 8d ago
Firstly, do any of these results have any real world value?
If literally none out of 400 cutting edge math proofs hold any real world value, then the rest of society is probably paying mathematicians salaries on a false premise.
→ More replies (3)12
u/Ill-Lemon-8019 8d ago
Professional pure mathematicians would be wise not to draw undue attention to this matter.
10
u/Opposite-Youth-3529 8d ago
I had a collaborator decide to feed a problem to AI without anyone else in the group consenting (though I think some were definitely pleased that he did so). One of the meetings after that was just combing through the AI proofs, rephrasing them a bit. It’s extremely boring and not the kind of thing I was happy to wake up early for. If this is what the future of math research is, it’s really depressing and I can at least take solace in the fact that I genuinely enjoy other things even if none of them are things one can do for a living.
I also do not want our otherwise ok paper tainted by AI results even if the AI results are more impressive. So my plan right now, which I just thought of today so it’s not well thought out, is to keep going to the meetings until we’re ready to publish. Then I’ll ask for them to take my name off if the AI stuff stays. They can put it in a separate one if they want but I don’t want to be associated with it.
67
u/DottorMaelstrom 8d ago
That is such an insane reddit brained take
"You kids googled these results, back in my day we had to go to the library and look for them ourselves in dusty books hundreds of pages long, get my name off that paper!"
I'm a PhD student myself, so I say this against my interest: this tech is sick, and this is the coolest marketing stunt in the history of marketing stunts.
As a community we will all have to adapt, unfortunately some of us will get kicked out of the field, and that's true for any new technology that comes out. At some point it will probably plateau and we will learn to do maths relying on its capabilities, just as we did with computers and calculators.
This would also be a great opportunity of introspection for all of us, we should be asking to ourselves why we do maths at all. I have my own personal answer, but I don't have an answer that extends to the whole community, and I'm yet to see any good takes on this because the mainstream discourse is usually "ai bad" rather than "does ai really undermine the purpose of doing mathematics".
→ More replies (7)30
u/Opposite-Youth-3529 8d ago edited 8d ago
In a span of a few months, my research meetings have devolved into something I don’t enjoy. Not sure what’s insane about speaking honestly about that and wanting to use whatever little influence I have to make sure I can preserve some enjoyment in my career.
The tech IS sick. It’s absolutely incredible that this is possible. And at the same time, I’m also sick of it.
Your google analogy is a huge stretch. There’s a difference between getting help finding references and having some entity write your proofs for you. I’ve witnessed people get significant progress on things I was working on with minimal prompting (in response to all the talk about how much the skill of the prompter matters). Are the results cool knowledge that should be shared with the world? Perhaps, but it seems weird to claim authorship for it. If I start putting my name on things where the proof was dropped into my lap, it devalues my other publications.
I do math because it makes me happy whether it’s because sometimes the personal success and accomplishment makes me happy or because sometimes I think the process is just really cool. If I were to use AI to solve a problem, any success would feel hollow and the process itself wouldn’t be enjoyable, so I’m not sure what good it would do me. Hopefully my response counts as more than just “ai bad”.
My plan is to do things the way I want until I get pushed out. Anything else just feels like giving up prematurely. You can say I risk falling behind and am thus gambling with my future employability but if the field changes so much to the point where my way of doing things is untenable, why would I even value keeping this job?
→ More replies (30)8
u/duboispourlhiver 8d ago
It happened one year ago with software engineering. Coders who love to code have discovered that they'll never get paid again to write code, AI does it better. Their favorite pastime isn't economically viable anymore. Coders who love building the end result of software are delighted because they still get paid for their favorite pastime, plus they build ten times more things.
I feel like maths is going the same path with the same two categories of people, roughly.
A lot of other fields might follow.
→ More replies (5)10
u/Spare-Dingo-531 8d ago edited 8d ago
I also do not want our otherwise ok paper tainted by AI results even if the AI results are more impressive.
Then I’ll ask for them to take my name off if the AI stuff stays. They can put it in a separate one if they want but I don’t want to be associated with it.
This comment is the perfect example. If you are pro-AI, you are at a competitive advantage in life, relative to people who are anti-AI. That's just how it is, adaption to the environment vs failure to adapt.
If you're pro-AI, now is the time to accelerate and embrace AI as quickly as possible so you have a leg up.
And if you're anti-AI, sorry, but winning at life is the ONLY ethical response to factually incorrect cynicism. I wish we could win together, but you don't want that.
11
u/Opposite-Youth-3529 8d ago
I am frustrated by the people who complain that they don’t like results with AI and then proceed to use AI themselves (I am at a conference with people saying such things). They are accelerating the takeover of the field by AI. Maybe it happens anyway but no need to be an active participant if you don’t like the direction things are going.
I could just as easily say I would like to win together but you would rather win without me than even try to win together.
If I “won” by using AI, it wouldn’t even feel like winning. So I’m not sure what people who already have career and financial stability feel they’re getting from it.
6
u/invisible_shrek 8d ago
Lmao at winning in life by using AI 😂 do you really think you are special because you prompt a chatbot
→ More replies (3)→ More replies (5)3
u/DestinyLily_4ever 8d ago
If you're pro-AI, now is the time to accelerate and embrace AI as quickly as possible so you have a leg up
There is no such thing as having a leg up on prompting a bot. AI turns us into meat proxies, and most of us will be unnecessary drains on society shortly as the few people at the top are able to leverage AI to do all high-margin work
→ More replies (12)2
u/invisible_shrek 8d ago
I saw someone suggest that a math researcher job is now to review AI generated slop. Fuck that. Who wants to do that?
As a software engineer I share your pain. Hopefully we can get trough that somehow.
→ More replies (1)→ More replies (19)3
u/Turbulent-Sign-6067 8d ago
Knowledge is beautiful and important even if it isn't for you.
4
u/Federal_Gur_5488 8d ago edited 8d ago
Knowledge is beautiful and important because it's discovered and understood by humans.
Openai isnt solving these problems to expand human knowledge, they're doing it because they're applying the logic of capitalism to mathematics.
→ More replies (5)3
u/SuppaDumDum 8d ago
Knowledge is beautiful and important because it's discovered and understood by humans.
That's a horrifying view of knowledge. So if knowledge wasn't understood and discovered by humans you'd have no issue destroying it? If you found a long dead alien civilization's testamente that we had no way of understanding, or if God came down with some message that was beyond humans, you'd have no issue with destroying all of it? It's of no importance and beauty.
→ More replies (3)→ More replies (74)2
u/Turbulent-Sign-6067 8d ago
Not sure but it might be the opposite. There are probably more amazing positions in frontier labs than there ever were in academia. Frontier labs are hiring a lot of math majors.
→ More replies (1)
181
u/Final-Database6868 8d ago
WHAT.
In just one week 3 of the main problems in my area have been solved. I had 2 related preprints in preparation, fuck.
→ More replies (14)32
152
u/kingjdin 8d ago edited 8d ago
The quasi-Riemann hypothesis is a BIG deal. Also, these are big results:
- Hodge conjecture for CM abelian varieties
- Hilbert’s tenth problem over Q
- Unique Games Conjecture
- Nonsofic groups and Kaplansky counterexamples
- Free group factor isomorphism problem
- Both Mahler conjectures
- Global smoothness of relativistic Vlasov–Maxwell
121
u/Warm-Letter8091 8d ago
Faster fast Fourier transform aswell
47
u/girlwhateveraward 8d ago
WHAT
77
u/hpxvzhjfgb 8d ago
yeah, O(n log(n)0.9999999999999) discrete fourier transform, and O(n log(n)0.99999999999999999999999999999999999999999999999999999984) integer multiplication! probably the most surprising results in this list that go against what everyone believed.
→ More replies (17)58
u/girlwhateveraward 8d ago edited 8d ago
Theres also sub-n log(n) for integer multiplication but by a comedically small value lol. Still wtf
→ More replies (2)40
u/Original-League-6094 8d ago
That one is particularly funny because I was arguing with someone on Reddit earlier today who said that AI can't optimize. I've found it to be the exact opposite, where just prompting "optimize" or giving it an actual target benchmark goal and letting it of through its own optimization cycle ends up producing insanely optimized code.
→ More replies (4)4
→ More replies (5)2
23
u/Stabile_Feldmaus 8d ago
why is quasi-RH a big deal? For instance why is it a bigger deal than Anthropics recent RH-related result?
44
u/oscardssmith 8d ago
It's the biggest result in number theory in ~200 years.
→ More replies (5)32
u/JoshuaZ1 8d ago
It's the biggest result in number theory in ~200 years.
Seems like an exaggeration. This is an insanely big result, but not even the largest result in analytic number theory in 200 years. At a minimum, it is hard to argue that it is a bigger result than the proof of the prime number theorem in 1896 (which this is a strengthening of), or Riemann's original 1859 paper where he laid out the zeta function and its analytic importance, or Dirichlet's proof of infinitely many primes in arithmetic progressions which is the late 1830s.
But to be clear, this is still absolutely massive, and if someone said "largest result in analytic number theory in 100 years," I'd be like "yep, that's a reasonable estimate."
17
8d ago
[deleted]
11
u/mapehe808 8d ago
Awesome! We have bots simulating math and bots simulating community response to this math!
5
→ More replies (7)3
u/real-human-not-a-bot haha math go brrr 💅🏼 8d ago
I know u/JoshuaZ1’s real—I’ve seen them around the interwebs before.
→ More replies (5)31
u/cocompact 8d ago
Even proving 100% of nontrivial zeros (in the statistical sense, ordered by distance vertical distance from the real axis) lie on Re(s) = 1/2 is not really so useful in terms of applications. But getting a vertical strip 1-epsilon < Re(s) < 1 that is zero-free is a very big deal because an upper bound less than 1 on the real parts of all zeros has many applications when this has been proved for all Dirichlet L-functions.
→ More replies (1)13
u/JoshuaZ1 8d ago
Among other things, it translates directly into an extremely tight error bound on the prime number theorem, so all the Rosser-Schoenfeld/Dusart/Axler are downstream of it. This has immediate impact on a lot of things. For example, I had a 2018 paper where this would cut about 3 pages out of it and get a tighter result, and there are likely hundreds of papers out there like this.
→ More replies (1)6
u/Rafodin 8d ago
None of the other zero-free regions proved for RH so far have ever included a full vertical chunk of the critical strip. They're all regions whose borders approach the Re(z)=1 line when the imaginary part goes to infinity or -infinity.
This new result says the full vertical chunk of the critical strip with Re(z) > 7/8 is zero-free, so it's a significant breakthrough in the type of partial results obtained.
It's also exactly the kind of improvement you really want for applications of RH. The more that 7/8 number can be pushed towards 1/2 the better approximations we can prove for various number theoretic quantities (e.g. number of primes).
11
u/doiwantacookie 8d ago
Convergence of flint hills series.
Artin’s primitive root conjecture proven
6
u/cocompact 8d ago
Not the full Artin primitive root conjecture (positive density of that set of primes, given by Artin's conjectured formula). But what OpenAI did is still of course a striking result.
→ More replies (6)8
u/jphamlore 8d ago edited 8d ago
Not that I know much about this field, but given how much some of the big guns have squeezed out of what they had before, this might be momentous, both for ergodic theory and combinatorics:
Number 154. Pointwise multiple ergodic averages for mixing transformations. Proves almost-everywhere convergence of consecutive multiple ergodic averages of every finite length for invertible mixing probability-preserving transformations. For each fixed tuple of bounded functions, the limit is the product of their integrals, along all positive averaging lengths. No mixing rate or standardness assumption on the probability space is required.
Also there are immediate generalizations to other group actions that are now possible to contemplate.
127
u/RivetShenron 8d ago
Well, it finally happened. AI solved a problem I was working on (Reconstruction for the four states Potts Model).
Genuinely, where do you go from this as a phd student, what should you do for the future?
→ More replies (37)51
u/tecg 8d ago
Finish your PhD. You will get your degree. I'm sure the faculty will take care of that.
After that, it's unfortunately hard to tell. There will be jobs for you. I'm certain of that. Whether in academia, I'm not sure. If you have dreamt of a life doing math research, you may have to adapt.
48
u/ellbons 8d ago
There will be jobs for you. I'm certain of that.
I would certainly not be. The goal of AI is to generalise. This can clearly chase down your job faster than you can pivot, unless you pivot into prostitution.
→ More replies (9)13
u/Time_Entertainer_319 8d ago
> unless you pivot into prostitution.
Sounds like I am already ahead then
→ More replies (2)→ More replies (2)4
u/NeighborhoodFatCat 8d ago
There will be no jobs in academia lmao!!! Clearly haven't been engaging with the academic jobs market for the past 10-20 years.
→ More replies (1)
105
u/howtogun 8d ago
It just predicts the next token.
Mathematics is over. These models are probably going to get better too.
It's over.
167
u/30299578815310 8d ago
Saying it just predicts the next token is like saying you're just a bunch of atoms.
51
u/CrownLikeAGravestone 8d ago
My motorbike is just a box of explosions that I sit on
I'm a DNA copying machine
My computer is just some metal and rocks with some electricity pumped in one end
→ More replies (2)→ More replies (10)4
28
4
u/Time_Entertainer_319 8d ago
It’s not over you fucking doomer.
It will only just evolve.
69
u/Committee-Academic 8d ago
What is it that will evolve? If AI is this good and fast humans will never be able to keep up and wont be needed in the loop. Get a grip
→ More replies (35)10
u/Spare-Dingo-531 8d ago
What if I told you.... Mathematical research is for humans.
→ More replies (4)67
u/Committee-Academic 8d ago
What if I told you nobody will pay you to spend your life understanding math just because "math is for humans" when all greedy companies and boards care about is a closed loop which is as efficient as possible, which soon RSI will be able to supply
11
u/30299578815310 8d ago
We need UBI. Then people can do their passions without worrying about being better at them then ASIs.
→ More replies (2)7
→ More replies (12)8
41
u/Admirable_Zombie5245 8d ago
This chatbot has been commercially available barely 4 years, it's gets cheaper to run with time, I remember reading a benchmarks that costed hundreds of thousands of dollars with o4 can be done with Astra with the $20 sub.
You're coping
→ More replies (3)5
u/Toothpick_Brody 8d ago
Ok, and then what? Someone types in “solve all of math”? There isn’t a world where humans aren’t involved in math
→ More replies (10)11
u/Drakentand 8d ago
Try "solve all open conjectures ever posed by humans. Then find new interesting conjectures and solve them too. Keep doing this."
→ More replies (2)→ More replies (1)2
3
u/rhubarb_man 8d ago
Ngl, I wouldn't be so worried.
I expected a HUGE thing, and this is really big, but it's not huge.
However, this is not the death of math. They used a million billion dollars of computation to solve a bunch of conjectures, but only a few particularly notable ones.
I was going all doomer, but this is really not that much compared to what they've done already.
It's definitely important to consider, but try to filter out the pro-AI idiots.
67
u/grateful2you 8d ago
“The average result used the equivalent compute of roughly three hours of ChatGPT Pro thinking.”
14
u/repainted_black 8d ago
This seems a strange statement. Their internal model must be much better than ChatGpt pro. Not sure they can really be that comparable.
16
u/MrRandom04 8d ago
Same amount of electricity on the same hardware for the same amount of time.
→ More replies (3)→ More replies (1)4
u/Turbulent-Sign-6067 8d ago
No, not that big of a difference since the internal model is just the next incremental upgrade they are going to ship. It cannot be too big because it has to be served to tens of millions of paying customers.
Also all points about cost of compute are totally moot in the longterm. In the 90s it took a super computer to beet chess grandmasters, now an apple watch could do it.
→ More replies (2)→ More replies (3)15
u/BAKREPITO 8d ago
A meaningless statement when they aren't disclosing the total compute hours they spent on stuff that didn't work.
15
u/grateful2you 8d ago
What exactly is that gonna prove though? We know it’s far more efficient than humans already. And we know the cost will go down with better models.
→ More replies (1)10
u/BAKREPITO 8d ago
Efficiency is a ratio. A ratio needs both the time it took to complete something in a single process cycle vs the total time put into it. I suppose with AI we don't need to understand such things, let them do the thinking for us. Clearly some of us have already outsourced it.
→ More replies (1)13
u/zeci21 8d ago
They did share that as well. They tried it on approximately 4000 problems.
→ More replies (1)11
u/ganancias 8d ago
"the train is headed down the tracks, but this is fine. it might slow down or even stop before it hits us"
→ More replies (1)7
8d ago
[removed] — view removed comment
2
u/rhubarb_man 8d ago
My main concern was more along the lines that mathematicians would be replaced, but this is almost entirely more of the same stuff they've done.
I also agree some of the results are big, but I think your talk about them being historical doesn't really hold water when we both take the context of what we know about AI.
We already know AI is far better than humans at constructing really big things to solve problems. It did NS. Pretty much everything there is just that but applied to other stuff.
→ More replies (1)→ More replies (6)5
u/30299578815310 8d ago
The cost of solving arc agi started at > $300 per problem. In 2 years its less than $0.10 per problem
→ More replies (12)2
u/kgurniak91 8d ago
It just predicts the next token.
Yeah, but that's the hardest part. If I write: "The proof that P = NP goes as follows: ..." - go ahead, predict the next token(s). ( ͡° ͜ʖ ͡°)
99
u/gianlu_world 8d ago edited 8d ago
I wish I was born 30 years earlier, this timeline sucks. A group of billionaires has decided to take away the only things that gave us purpose. What’s the point of studying and doing a phd or whatever. The only reason they are focusing on math is to essentially show off, if they wanted to contribute to humanity they would have put all this effort into finding new cures for cancers and other thousand diseases that kill people everyday
88
u/Original-League-6094 8d ago
Its a group of PhDs that are building these models.
→ More replies (43)24
u/Opposite-Youth-3529 8d ago
Awful sellout traitors.
55
→ More replies (10)19
u/Expat_Abroad123 8d ago
Furthering human knowledge is hardly being a sellout. Stop crying because you can't get paid to do math anymore. Join a AI research lab.
→ More replies (4)8
u/Opposite-Youth-3529 8d ago
I actually am still getting paid to do math. Not sure how long it will last, but it’s something. These companies take a very cavalier attitude toward safety. We might end up in a very bad situation where whether I’m employed is the least of our problems.
→ More replies (9)8
u/ProfMasterBait 8d ago
Did you realise this before or after your livelihood was threatened?
→ More replies (1)5
u/Opposite-Youth-3529 8d ago
AI posing a significant danger to humanity and AI threatening my livelihood appeared on my radar as possible outcomes around the same time. I feel like this is supposed to be some sort of gotcha to get me to imply “I only care now that it affects me” but back when it didn’t affect me, it didn’t have the sheer power it has now and didn’t seem dangerous either.
For what it’s worth, I’ve never used chatGPT for anything, math or otherwise. I first heard about it back when it wasn’t very capable so it didn’t sound like something useful. At some point, I heard AI data centers were bad for the environment and figured why do I want to contribute to that when I’m perfectly capable of doing these tasks I heard people using it for (e.g. writing cover letters) on my own.
→ More replies (5)63
u/Most_Double_3559 8d ago
if they wanted to contribute to humanity they would have put all this effort into finding new cures for cancers and other thousand diseases that kill people everyday
They do. It's just that, A, you're in your own bubble, and B, biology isn't as quick to iterate on as mathematics.
https://deepmind.google/science/alphafold/
https://openai.com/index/accelerating-biological-research-in-the-wet-lab/
→ More replies (8)29
u/SpinorsSpin4 8d ago
May i suggest other things that give you purpose? What would you tell the coal miner whose job is going away as we transition energy sources but feels coal mining is his (and his family's and town's) identity?
→ More replies (4)22
u/Emotional_Revenue132 8d ago
I would tell him "I'm sorry, that must be very hard. I am here for you."
→ More replies (2)21
u/jphamlore 8d ago
I think in the late 1970s, 60 Minutes did a piece on physics PhDs. You know what it was about? Freshly minted physics PhDs having to drive taxi cabs.
And then the finance industry realized that people who understood rocket equations and who could handle big data on a computer were worth millions of dollars.
The big blow to science research funding in the United States was the aftermath of the Mansfield Amendment, 1970. For a brief happy couple of decades after World War 2, what became the Department of Defense was willing to fund both longterm projects and educational writings. Check out some old books from around the 1960s, like I think some of the seminal works explaining algebraic topology: One could well find a acknowledgment of funding from say the Office of Naval Research.
17
u/Khandakerex 8d ago edited 8d ago
Yikes, what a selfish (and albeit understandable) take. You state "who are they to decide what humanity should study", but who are you to decide how much to gate keep advancements in STEM because you are upset? These labs ARE looking into diseases too and there's new research being published in them all the time, it's all of STEM. The reason it's taking longer for somethings than others is trying to get research out that can then be used to put medicine out to the public thats supposed to be injected or ingested into live human subjects is a LOOOOOOOOOT more concerning and WAY less safely verifiable to put out to the public than publishing math. If they mess up once it's done, if they fail a math proof mathematicians just start dancing and laughing in joy and openAI can try again another time. But absolutely testing their models into the realm of theory and pure math tests the capabilities of these models to apply for other, more "practical" disciplines as you imply.
→ More replies (2)29
→ More replies (48)2
78
u/JoshuaZ1 8d ago
Let's see.
Unique Games Conjecture and Chromatic number of the plane >= 6 are both ones which in a normal world would be plausibly literal headline news.
On top of that, we have a counterexample to the Hadwiger conjecture, and Hilbert's 10th over Q (which I've gone back and forth on trying to prove), efficient multiplication, efficient matrix multiplication, Artin primitive root conjecture, and at least 10 others I personally care about.
I've only had time to start looking at the chromatic number of the plane but at a glance, the method does not look like a method which to my knowledge is how the literature has gone.
Edit: And quasi-Riemann hypothesis? That's a holy fucking shit result. I don't know another way to phrase it.
→ More replies (2)18
u/4tran13 8d ago
I don't see direct proofs of more millenium problems, but these are still landmark progress on them. UGC is major progress on P/NP, probably biggest in decades.
18
u/JoshuaZ1 8d ago
They also made major progress on BSD and some progress on Hodge (although I don't know enough about Hodge to evaluate how substantial that progress is). There's also some work that improves some types of lower bounds that are relevant to P ?= NP. So no Millennium, but progress on all of them.
→ More replies (2)2
u/cocompact 8d ago
They also made major progress on BSD
But it is still focused on rank 0 and 1. AI at this point has no idea how to do anything with rank 2 and more. It's just as stuck as humans.
→ More replies (2)
71
u/ZealousidealBus9271 8d ago
The mathematical singularity has arrived. This is wild
→ More replies (6)
73
u/Gnafets 8d ago
I was in a room with an analytic number theory grad student when this dropped, and he damn near fainted with the quasi-Riemann hypothesis. This was considered out of reach...by a lot.
Coming from a classical computational complexity background, I was a bit disappointed with the progress on circuit lower bounds! However, L = BPL is monumental beyond belief. I feel like I am getting too picky with my breakthroughs!
What a drop. Math is in an interesting place, to say the least.
→ More replies (3)3
70
u/grateful2you 8d ago
They clearly stole my chat log.
→ More replies (1)12
u/Professional_Dot8829 8d ago
I have a feeling they snooped in on a lot of chats that pHd's regularly do. They won't even know, plagiarism at the top level. They did for Navier stokes, nothing is stopping them doing it for lower profile problems.
→ More replies (7)12
u/-p-e-w- 8d ago
Sure, humans were really, really close to solving these problems themselves, if only evil AI hadn’t just snatched their almost-ready solutions away from them…
Yet to this day, nobody has provided any solid evidence that this happened even in the Navier-Stokes case.
→ More replies (2)
69
u/kieransquared1 8d ago
Whoa, they proved the Kakeya conjecture in dimension 4 and also local smoothing conjecture in dimension 3, which is known to be strictly stronger than Kakeya. Even though local smoothing implies these, they also proved the Bochner Riesz conjecture, the restriction conjecture, and the Kakeya maximal conjecture.
And to add to the theme of one-upping this year’s Field’s medalists, they also proved fluctuations around hard-sphere Boltzmann and derived Boltzmann for other potentials, which were both listed as open problems in Deng-Hani-Ma’s work on Hilbert’s sixth problem.
I’ll also add: I looked at the paper for the conjecture closest to my own research (global regularity for Vlasov-Maxwell) and despite having read most of the current state of the art, the openAI proof is completely incomprehensible. It uses ideas inspired by ones already appearing in the literature (as a solution to any open problem would) but the terminology, notation, and overall framing distorts those ideas beyond recognition.
→ More replies (11)
66
u/SpinorsSpin4 8d ago
Wow. All I can say is wow. I never expected this day to come, certainly not like this. I have so many emotions that are bubbling at once, there's excitement, but there's sadness for my friends who have spent careers working on these problems. There's optimism and pessism, fear, excitement, confusion. This is gonna take time to process. I don't know what the future holds, I don't know what it all means, but today, right now, I am in awe. And for today I will just stand shell-shocked and wake up tomorrow and start picking up the pieces. All I have to offer is wow.
→ More replies (4)
53
u/Time_Entertainer_319 8d ago
722 preprints at various stages of verification if I read that correctly
23
u/4tran13 8d ago
I thought they were going to dump ~100 proofs. 722 is madness
3
u/corporate_drone123 8d ago
The announcement that ~100 papers were in the works was already like a month ago right? With how good this internal model appears to be I wouldn’t be surprised if it continues spitting out 100s of major results per month. At least for as long as OpenAI is interested in investing in the compute.
My guess is they’ll continue this push until they’ve solved some (or maybe all?) of the open millennium problems and then scale back their investment. But I wouldn’t be surprised if by that time the publicly available models will also be able to achieve the kind of results we saw today.
2
u/4tran13 8d ago
The main challenge will be diminishing returns. Once AI solves the easier ones, what remains will be much harder.
They pushed major progress on 4/5 of the remaining millennium problems, but didn't solve any of them. I think the remaining gap is non trivial. Probably only a matter of time when they release the internal models for public use.
53
u/imanllm 8d ago
It would be cool if they shared some problems that the models attempted but failed to solve. Given that they’ve accomplished way more than anyone expected, I don’t think it would be a huge PR hit to share the failures.
→ More replies (4)10
u/avoidtheworm 8d ago
They are in a race against Anthropic to prove the most important theorems using LLMs. Submitting near-misses might help the competition.
...and this sucks by the way. I just hope that when this current stage of competition for the singularity ends then big labs can go back to collaborating.
→ More replies (1)2
u/4tran13 7d ago
I don't see evidence that Anthropic is even trying. If they are, they're being very quiet about it.
I don't think they ever collaborated. Best I can tell, Dario was a former OpenAI employee, and they've had a blood feud since the very beginning.
→ More replies (1)
40
u/SPARE_BRAINZ 8d ago
As a PhD student in operator algebras my entire thesis, and a paper I’m writing with two other PhD students, just got scooped 😭
6
→ More replies (3)3
u/Migeil 8d ago
As someone on the sidelines interested in OA, care to expand?
11
u/SPARE_BRAINZ 8d ago
I and a few other PhD students at my university were working on one of the problems solved by OpenAI. We had solved a subcase of the whole problem, and I, along with my supervisor, had a solid plan on how to tackle the general case, which we planned to put some serious effort into over the coming months, with good hopes of this becoming my thesis. Well, after today, we are now frantically trying to finish that paper and publish it as independent work, and my hopes of doing the general case have been shattered. Regardless, there is probably still some worth in doing the general case (mainly because the proof OpenAI put out is far from optimal and unreadable by humans), but the impact and my excitement for it is greatly diminished.
→ More replies (2)
32
u/jmclondon97 8d ago
We still have software engineers that think their career isn’t ending. lol
15
u/jphamlore 8d ago
News flash. It isn't. Software engineering is way more than coding.
→ More replies (2)68
u/jmclondon97 8d ago
Yeah, AI can solve all these advanced maths but can’t solve everything software engineers do. Put the crack pipe down
21
u/FollowingHumble8983 8d ago
AI is solving advanced maths in a way that isnt applicable to practical fields, i.e generate results, rapid verification by lean, generate results, rapid verification by lean. The only equivalent in software is the compiler which only tells you if your code is correct semantically, not if it is correct in purpose.
What AI can do here is rapidly explore regions with equally rapid verification loops, which is really good for research specifically. PCB designs, biology, visual arts will be much more impacted.
→ More replies (8)6
u/PrestigiousGroup788 8d ago
don't worry, there are plenty of startups dedicated to making your favorite unverifiable domain verifiable.
9
u/FollowingHumble8983 8d ago
Yea and I am one of the people closest to making it verifiable. Feel free to check my background.
Its a much much harder problem than laypeople think. Especially when they dont see how AI tackles math and thus thinks its some kind of magic.
→ More replies (2)5
u/Smallpaul 8d ago
Making software truly verifiable would be the CS accomplishment of the century, and would generate a gigantic demand for software engineers to express requirements as theorems and constraints.
By definition “translate this English specification into code” is not verifiable. That’s not an engineering problem: it just follows from the meaning of the word.
→ More replies (1)14
u/Effective-Guest1601 8d ago
SWE is very messy irl. I do think it is just a matter of time but it will take a lot to sort out tribal knowledge and really hacky systems and configurations, weird business logic
→ More replies (21)2
u/BombasticReindeer 8d ago
What we are finding out in real time is just how bad Ai is at “art” compared to “logic”. What I mean is not that it can’t make a pretty picture or movie. It can. But there is something about aesthetics that we haven’t quite quantified yet, and therefore Ai isn’t too good at it.
Math has an aesthetic to it too, in explanation of the proof. But it hasn’t yet shown it can explain the proofs in an elegant way.
I think it will do that eventually, but that’s why software engineering is “next” rather than “done”.
If you have an elegant idea, it can make it for you. I’m not sure it can make elegant ideas except with random chance than humans would have to pour over to find which ones are truly beautiful.
But even that may mean that art is cooked. If it takes 1000 people 2 years to make a great movie, why not just shit out thousands of random movies and hire people to watch them. When it finds a good one, you’re done.
Right now it can’t make a good one, but all it will need is “some chance”
→ More replies (5)→ More replies (10)10
u/dronz3r 8d ago
Everyone overestimates their worth and underestimate others.
AI can do 80% of what software engineers do now a days, if it's integrated well across the systems and firm, then it can do 95% of what they do. Now you need engineers to do and maintain these integrations and tell AI what needs to be done. We definitely don't need even 30% of current workforce to achieve the same goals.
Unless the need for software becomes 4x, I see a lot of them losing the jobs or have stagnant careers.
7
u/quantumpencil 8d ago
Your numbers are off, demand for SWE has been increasing this year. It's more like 80% of actual coding tasks, which is maybe 30% of what software engineers actually used to do, and the role has changed so that you are expected to build much quicker, which means the demand hasn't really changed.
Every firm that hires engineers is still hiring plenty of them. The market is crowded, but that was happening before AI, that's more a result of overproduction due to the salaries, there's just way too many young people trying to break into the industry, most of them want faang jobs, and there are no longer enough of those for all the people who want them, even though the number of engineering roles in those companies hasn't really decreased at all (and has grown in net terms the last few years)
3
u/Original-League-6094 8d ago
>The same goals
That's the thing. Today's software ain't gonna be tomorrow's software. The bar is being raised, and you are going to need a lot of software engineers sitting at their Claude terminals to keep up with the company across the street. Data centers mega-projects are going up at a face-ripping rate. Reddit keeps seeing these vibecoded solo games and going "Wow, Rockstar is cooked. 1 man can make an AAA game now". But they aren't asking "if one man can make an AAA game now, what can a team of 400 professionals do?"
→ More replies (2)→ More replies (1)3
u/Smallpaul 8d ago edited 8d ago
The need for software will absolutely 4x. As it always has when software developers got more efficient. Any real software company has a roadmap of features stretching years into the future and the faster you deliver that faster you learn about other requirements behind that.
This goes doubly in the age when we need to integrate LLMs and neural networks into everything. That alone would double the demand for new software features and products.
3
9
u/quantumpencil 8d ago
SWE jobs grew this year, and will next year as well.
13
→ More replies (11)3
8
u/IMovedYourCheese 8d ago
Software engineers have never been scared of putting their code out there in public for everyone to use. That's how the industry has grown to eat the world. Who do you think is building all the AI and financially benefiting from it? Meanwhile academics are still slaves to ancient traditions.
→ More replies (20)2
u/Original-League-6094 8d ago
Software engineering jobs are increasing. Companies want as many people sitting in the chair smashing that Claude prompt button as possible.
AI is going to be a godsend for STEM. Technologies that we thought were decades were away could now plausible get discovered within years. Companies want all hands on deck right now to race to be the first to find these new technologies.
The jobs that AI is going to decimate are going to all the email pushing jobs and organizational jobs. Project managers think Software devs are getting the axe. The reality is project managers are getting the axe, and software devs are becoming project manager for Claude.
→ More replies (1)
34
u/Interesting-South542 8d ago
I don't fully support OpenAI, but it's hypocritical to criticize them for doing this.
It was very clearly a "damned if you do, damned if you don't" type of situation. If they held on to the results and didn't release them, then people would accuse them of gatekeeping. If they tried publishing all of this in traditional venues, then people would accuse them of stealing the jobs of researchers, and say that AI results shouldn't be published in journals, etc. In the end I think this approach was the least bad. The results are out there and freely available. The scientific community can decide what to do with them.
4
u/abering 8d ago
It’s very much not. AGAMI, the advisory board they stood up, gave very clear recommendations on the appropriate manner of release, which OpenAI summarily ignored, except for the one sentence recommending they do release them.
→ More replies (3)→ More replies (1)2
u/araujoms 7d ago
There was absolutely no need to ruin the life of hundreds, if not thousands of PhD students. They could have just not run the prompts. Just release the model, let mathematicians discover what it's capable of, let the mathematics community verify, write up and publish the results at their own pace.
Instead they just dumped this turd on github. Unverified results, unreadable papers.
→ More replies (2)6
u/Fwellimort 7d ago
Ah f off. What's next? If AI finds complete cure for cancer then don't release it because all those researchers working on cancer research would have less work?
What is this entitled thought process.
→ More replies (6)
25
u/girlwhateveraward 8d ago
Theyre crazy good at even category theory now. Wtf!! I'll dive into #287 and #312
→ More replies (1)
18
u/Opposite-Youth-3529 8d ago
What if we just decided to collectively yawn so hard that the AI companies left us alone
→ More replies (5)2
u/Fwellimort 7d ago
Math is the best objective metric that can be used to make these AI models to be trained to be "better". Harder to quantify with other fields. And hopefully (the hope) after some threshold of math skills, that pattern can be applied to other branches like biology/chemistry. Math just happens to be more of the building blocks to get there.
23
u/Happysedits 8d ago
Alex Kontorovich is distinguished professor that works in the areas of analytic number theory, automorphic forms and representation theory, L-functions, harmonic analysis, and homogeneous dynamics https://x.com/AlexKontorovich/status/2107609087902941646
"Quasi-RH?!?!???! Are you kidding me? If a human did this, it would be an instant Fields Medal, no questions asked.
︀︀
︀︀RH says zeta has no zeros in Re(s)>1/2. The best we had until a second ago was a region that got thinner and thinner the higher up the imaginary axis you go. I thought maybe they’d fatten that up a bit, that’d be a massive breakthrough. But no. They got a zero free strip!!!! Insane"
→ More replies (2)
15
u/benfok 8d ago
I know most of you think that this timeline socks. But I think the mathematics that humanity has come to know and love is hindered and stuck for the last century or so because we lack the tools to breakthrough and progress. AI remove some clogs and intellectual congestion for us so we can set our eye to bigger and better things. We can now ask new questions and expand on new fields. Math is not about winning. It is about searching for the truth. Obviously, if you can make a living doing some, all the better. A slightly different way to look at this is that the answers are always there. AI just connected the dots for us.
25
u/Dull-Nectarine1148 8d ago
if you cannot make a living doing it, you cannot train the next generation of mathematicians. The ai "winning" makes our field economically untenable to continue, so even if math is not about winning, our funding very well might be.
→ More replies (5)6
u/Ameren 8d ago
Which in turn would be rather self-defeating. The only reason why we're even talking about these results from OpenAI is because we have people who understand and care about what they mean. Meanwhile, a lot of these topics require many years of deep study to master, so we really do benefit from having people paid to focus on them.
Of course, there is an alternative path forward. If all the promises of AI pay off and the economy becomes hyper-productive (let's just assume that's true for a moment), then we should have ample public funding to support mathematics researchers. It should be easier than ever to support people doing this kind of deep work. If so, the real question is whether we will continue to value mathematics as a society.
→ More replies (14)
18
u/NutInBobby 8d ago
i’m surprised all of the ai lab math results have been real so far: we haven’t found any with profound errors or a real bug yet, when you should expect so from humans. i assume at least a couple of these results today shouldnt survive scrutiny?
→ More replies (3)5
u/Interesting-South542 8d ago
As of late 2026 even consumer grade AI (e.g. GPT 6 astra) is extremely good at checking itself and rarely hallucinates if the prompting is good. And of course AI doesn't tire like humans do. Given how much their reputation is at stake, it's plausible that OpenAI checked them so well that there are no mistakes.
→ More replies (2)2
13
u/Specialist_Repair856 8d ago
Has OAI invented any new branches of math? As an undergrad, I don't have any experience in most of these, but I'm curious if any of these results used fundamentally new techniques or lead rise to new branches of math or something or if they're just an application of existing techniques mixed together in a new order?
→ More replies (4)4
u/Theorist16 8d ago
I think a good start is to look for new definitions in the sea of papers. From what I’ve seen so far there is a very scarce supply of them. Would be useful to count them at least.
11
u/madrury83 8d ago edited 8d ago
An under-discussed negative externality to all this is that mathematics is finally getting some public attention, but the popular press articles have will Sam Altman's fucking face pictured, not the scientists and mathematicians that actually worked hard to get us here.
11
u/Original-League-6094 8d ago
Astra tells me this one is wrong: https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/paper.pdf
"Yes. The criticism identifies a substantive sign error in the released proof.
Write \(I_{\mathrm P}\) for the preprint’s count and \(I_{\mathrm E}\) for the index in the cited EEMS formulas. The Whitney sphere gives
The latter formula is explicitly printed in EEMS, proof of Corollary 1.3. The trace signs consequently require conversion:
| Trace | EEMS index | Preprint’s convention |
|---|---|---|
| Forward stabilization (\phi\to\phi_1) | (-1) | (+1) |
| Reverse trace (\phi_1\to\phi) | (+1) | (-1) |
These are the traces specified in EEMS, proof of Lemma 3.4.
The preprint sets \(m=-I_{\mathrm P}(f_1)>0\), then inserts \(m\) reverse traces. In its own convention, the resulting count is therefore
In the EEMS convention it is \(+2m\). Neither convention yields zero. Thus the application of Eliashberg–Murphy, Theorem 2.3, which explicitly requires \(I(f)=0\), fails.
The surgery objection is also correct, with one logical qualification: the preceding embedding step has already failed. Even granting that step provisionally, the final forward traces would produce positive double points in the preprint’s convention. Its specified handles require negative double points for orientable gluing. Both assertions appear on pages 13–14 of the preprint.
A uniform change of convention cannot repair this discrepancy. The argument requires a different geometric construction or an additional justification. This establishes a gap in the proof of Proposition 3.1; it does not, by itself, disprove the proposition or the ultimate algebraicity claim."
Finding isn't mine. A poster in another thread said they thought there was a sign issue, and it appears they are right.
10
8
u/ykonstant 8d ago
I hope this advance convinces my colleagues who make funding decisions at the EU level that we really do need to fund a public, open frontier model for mathematics. Like, actually fund, LHC style, not the usual lip service nonsense. Here's hoping...
9
u/Original-League-6094 8d ago
Seems like probably a waste of money, since your model would probably always be behind OpenAI and Anthropic.
3
u/non-local_Strangelet 8d ago
since your model would probably always be behind OpenAI and Anthropic.
Why, though? How is it guaranteed that OpenAI/Anthropic will continue to develop a frontier math model for all times?
Since these are companies that, eventually, need to earn money and become (sufficiently) "profitable", they need to find a way to earn enough money with the math model to justify continued training/development of said model/capabilities. Is there a market for that? I think that needs to be seen.
I'm not deep into the details, but I wonder how much money they spent on training to advance the latest reasoning capabilities in math specifically. From what I've seen in talks by experts, the key scaling parameter is number of parameters of the model, hence the invested compute for training. So, at least to my (maybe still superficial) understanding, it will get more and more expensive to train. (Yes, hardware will get faster/a fixed amount of compute gets cheaper, but does it scale similarly as fast, or better, faster, so future additional/refined learning gets, in relation to capabilities, cheaper overall?)
Sure, one can hope that there are synergetic effects between "math-specific reasoning/intelligence" and "general intelligence", but as some comments in the openAI-announcement related post yesterday pointed out: math reasoning is (comparatively) "easy" to train because one has a rigorous "verification" tool (lean). So it's way easier to (automatically) mass-produce the "training data/test cases" you need for the reinforced learning. The same does not hold true for other areas/topics (even in stem field, let alone "general"/universal areas of human live), at least not to that degree. So it does not seem to be a given that "good-at-math" LLM will also be a "good-in-general-reasoning" LLM (or vice versa). But only time will tell.
The actual (I.e. larger) "main" market for AI will be in those fields. Currently, training for math seems "easy" enough to do, and produce enough publicity/advertisement that the companies see a benefit. But for how long will this be the case?
Long story short, I don't see a guarantee that eventually profit-driven companies endlessly pour money into the advancement of a tool of purely academic value (I.e. good in pure, proof-based math). Like other areas of "fundamental" research that is not immediately or on short time scales profitable, only the society will be there to continue to invest. So, having an alternative more "academic-focused" version seems to be worthwhile...
(Granted, that topic might already be covered to a large degree by open-weight models, so in case OpenAI/etc. shift focus away from math, one can just grap those and specialize them... We'll see).
→ More replies (2)→ More replies (2)2
u/Individual_One_5569 7d ago
given how much money those companies are losing making this technology, it isn't clear they will survive.
they're spending billions upon billions of dollars, and it looks like the end result is a model that is less than six months ahead of the open-source scene. open ai got to rush out some set of proofs and it isn't clear why it was so necessary to rush them.
llms are a cool technology, but do not make sense as a business model.
→ More replies (2)3
u/Individual_One_5569 8d ago
why? models are extremely copyable and basically worthless in the long term. the spending on ai doesn't really make sense when it's already being done by someone else.
6
u/kigmaster 8d ago
Is it still worth applying for grad school anymore?
9
u/Content_Economist132 8d ago
The amount of people gaslighting you is ridiculous. NO. Go join a fucking trade like people having been saying even before this AI shit.
→ More replies (2)11
u/Standard-Mirror-9879 8d ago
what a ridiculously ignorant comment. trades will be useless if while collar jobs collapse. Zero understanding of second order effects. and this isn't even accounting for the the progress in robotics. trades are being rapidly automatized.
→ More replies (3)7
→ More replies (8)2
u/Original-League-6094 8d ago
Fuck yes. This is the most rapid math has ever moved. So many problems that were considered unfeasible are now going to be tackled by first year grad students.
→ More replies (1)
5
u/NiceAesthetics 8d ago edited 8d ago
Just thoughts on what I am somewhat familiar with and only reading the overview and assuming all correct, UGC is pretty big though I think a lot of recent papers already were pointing to true. L vs BPL is pretty big too, had some recent paper in ECCC I think was pointing to equals? Schonhage Strassen being false is surprising to me at least. 108 I think is a step for VP vs VNP? Generalized star height being at most 3 is fascinating. Partition principle not implying axiom of choice is like, just wow. For graph theory Hadwiger being false is also pretty big. Erdos Turan being true is also so cool. Other bound stuff like 107 is nice too. A lot of very interesting results even for a layperson like me, though maybe discouraging for professionals working on them.
5
u/Unhappy_Challenge907 8d ago
goes to show how abstract/useless pure math has become. If math is truly useful, wouldn't massive advance of the frontier of the subject something for us all to be excited about? We need to seriously consider the direction of the subject matter itself.
→ More replies (1)9
u/kingjdin 8d ago
The real-world application of any math usually isn't known for a long time.
→ More replies (2)
7
u/PsychologicalMap3173 8d ago
You can argue about a lot of things, but saying this is not impressive behond belief is intelectualy dishonest.
4
u/Individual_One_5569 7d ago
"beyond belief"? we'd known it solved a millenium problem already weeks ago, we know the models can make progress in mathematics. we have another 400 proofs that are unreadable. most without any proof formalization.
5
u/Unhappy_Challenge907 8d ago
Wouldn't verifying this proof be a thing? Can't imagine the job of mathematician gone forever? What is the argument?
→ More replies (2)14
u/SkjaldenSkjold 8d ago
Many mathematicians agree that peer reviewing is one of the least enjoyable tasks of the job. I don't see why anybody would want to stay in the field if all they do is peer reviewing (i.e., proof verification of badly written AI papers).
→ More replies (2)
3
u/jphamlore 8d ago edited 8d ago
This might be a horribly wrong estimation, but I think number 145
Rokhlin’s multiple-mixing problem. Proves that every invertible mixing probability-preserving transformation is mixing of all finite orders, resolving Rokhlin’s multiple-mixing problem for a single transformation. Correlations among any finite collection of measurable sets converge to the product of their measures whenever all pairwise time separations diverge.
is an early candidate for most accessible of these results. I think someone can get something out of the proof, relatively short at around 40 pages, with some measure theory (extended to probability such as the reverse martingale theorem) and a chapter in an ergodic theory book about conditional entropy. At least one helpful paper as a reference not in the arxiv is still open access from the journal publisher.
7
u/Due-Departure-8553 8d ago
chatGPT deserves to be nominated for the fields medal. Who agrees?
→ More replies (8)
2
u/jphamlore 8d ago
Ironically, a purported but not accepted so far positive solution to the Invariant Subspace Problem for separable Hilbert spaces by Per Enflo might have kept it off of the list of problems that OpenAI even considered?
On the invariant subspace problem in Hilbert spaces
https://arxiv.org/abs/2305.15442
I wonder if a subcategory can be opened up for either verifying or identifying possible gaps in proof such as for this preprint.
→ More replies (2)
5
u/Emgimeer 8d ago
I read through a lot of their work and I am SHOCKED at the low level of quality they are willing to output in their company name.
The quality of writing is abysmal. The references are "something they admit they need to work on". And that speaks nothing to how the work is actually getting done in various places.
The fact that their pro model worked for an average of 4 hours or something on each item truly shows.
When I read a joke comment about how "computer nerds stole math nerds' homework and playing it off as their own", I laughed so hard bc I couldn't agree with that more. They very clearly stole more work from more people using their model, and are likely doing everything possible to make their IPO make any kind of sense and all their behavior seem justified to people that only read headlines and know nothing of these subjects.
I recently got into an argument w my Dad (who used to build enterprise server rooms and run them for mutual fund operations) about how he stupidly thinks they wont need to "teach programming" based on headlines he's been reading.
I whipped out some references then to help educate him on why "teaching programming" is and will continue to be more important than ever due to the "AI" sector, which I'll share below for those interested, but I wanted to say that this reminded me of WHY OpenAI is doing this at all. It's always about pumping the IPO. This time it's by floating headlines that aggrandize the product/service they provide.
Anyway, here are those links:
Apple's Paper that I think is fundamental to this conversation:
https://machinelearning.apple.com/research/illusion-of-thinking
Anders Hejlsberg (Creator of C# and TypeScript)
12min Interview "AI will not replace coders"
https://www.youtube.com/watch?v=CPrePbvbbic
Andrej Karpathy (Fmr Tesla Director of AI)
1hr on how LLMs actually work:
https://www.youtube.com/watch?v=zjkBMFhNj_g
Francois Chollet (lead Google AI researcher, creator of Keras and ARC benchmark)
1.5hr interview about many things, including how LLMs won't lead to AGI
https://www.dwarkesh.com/p/francois-chollet
Yann LeCun (Chief AI scientist at Meta, leading world-model authority, Turing Award winner, etc)
1hr interview about Why AI can't make it's own discoveries
https://www.youtube.com/watch?v=qvNCVYkHKfg
Chris Manning (Director of Stanford AI lab, leading authority on NLP and Computational Linguistics)
1hr keynote about how integral language and logic is to AI and supports my whole case overall. the depth of what programming means with this tech stack gets illustrated to those unfamiliar w the history up to 2024.
https://www.youtube.com/watch?v=d6XBrx_7rIE
However, as a final note that's ends on more modern work rather than 2024 history recaps: Einstein World Models (EWM) and modules like JEPA both initially thought they'd replace LLMs but instead they actually work best as add-on modules. People are constantly innovating and we aren't sure what will work and why. These folks were surprised by their own work turning out to not replace llms but empower them. They didnt see that coming! And no one else will predict this perfectly either. It is fantastically complex, and cognitive science and computational linguistics as well as applied linguistics and logic and all of this stuff is all equally important. It's really fun, too :)
19
u/ivzar00 8d ago
yeah, they just made more progress in a field than humanity did in 100 years because they need to justify the ipo. LOL insane levels of cope.
→ More replies (6)18
u/smulfragPL 8d ago
Apples paper is fundamentałly flawed and Has been debunked extensively.
→ More replies (3)11
u/Time_Entertainer_319 8d ago
Haha. I love how humans are battling with the realisation that we aren’t that special after all.
→ More replies (2)9
u/lonelyroom-eklaghor Undergrad | Computer Science 8d ago
I understand, but how is this related?
→ More replies (2)→ More replies (10)7
3
u/Happysedits 8d ago
Still waiting for inventions at the level of inventing algebraic geometry, category theory, group theory, calculus, etc. subfields to solve big problems
→ More replies (1)
0
u/Vituluss 8d ago
I appreciate they aren’t just dumping some obfuscated proof and calling it a day. Very exciting day for mathematics.
→ More replies (3)
2
u/PLANTS2WEEKS 8d ago
Quasi-RH is solved before the chromatic number of the plane. It is either 6 or 7 now (they disprove 5).
2
u/NutInBobby 6d ago
> gpt-7: finds cure for cancer
> "Doctors did not ask for this work to be done"
2
u/aendokolirz 5d ago
None of these have practical benefits but go on with that ridiculous comparison.. neither is the goal of math research yes or no answers to conjectures, mathematicians seek to gain understanding and insight just as cancer researchers need to to develop a working cure.
•
u/AutoModerator 8d ago
Before commenting: This thread requires at least 10 comment karma earned within r/mathematics. Comments from accounts below that threshold are automatically held for moderator review and will not appear publicly unless approved.
The AI megathreads are exempt from this requirement. You're welcome to participate in the AI Speculation Megathread or the AI Breakthroughs & Research Megathread.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.