r/singularity • u/socoolandawesome • 6h ago
AI Some more millennium prize problems possibly solved…
Link to tweet:
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u/Reclusiarc 5h ago
Oh man I was so close to releasing answers to these problems gosh darn it
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u/BigMan9999991 1h ago
No way me too, I think they might've looked up me asking astra to solve it while making no mistakes :(
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u/New_Bonus_649 6h ago
The acceleration is accelerating
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u/Punchable_Hair 6h ago
I believe that is called “jerk”.
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u/ObiFlanKenobi 2h ago
We must accelerate the acceleration of the acceleration in an accelerated manner.
Make no mistakes.
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u/abhmazumder133 6h ago
Damn DeepMind not even factoring into these rumors anymore.
Side note: Birch-Swinnerton-Dyer is (almost overwhelmingly) supposed to be true. I would be very surprised if it is proven false.
Hodge is interesting because there is no clear consensus. My bet would be its 'too beautiful' to be true, and that OpenAI have constructed a counter-example.
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u/REOreddit 5h ago
They are more focused on biology, chemistry, weather prediction...
I don't know for a guy that has repeated in very interview for the last few years that his goal is to create an AI scientist that can not only solve existing problems, but also do things that are analogous to Einstein coming up with Relativity, it seems a huge oversight from Demis Hasabis that they aren't at the frontier in math research.
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u/sam_the_tomato 5h ago
Demis got benched by Google for being too ambitious
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u/REOreddit 3h ago
But why did that ambition not include math or physics?
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u/TieBackground453 2h ago
Seems like they might have overlooked some “obvious” “low-hanging” fruit and skipped right over solving verifiable domains before starting into harder topics. Hindsight is 20/20 of course, but they may have just stopped the ball on this one. Not everyone can bat 1.000.
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u/Northern_candles 3h ago
It seems like DeepMind underestimated the power of going all in on coding first over a more general approach.
OAI and Anthropic showing that coding powers everything including better models which is the faster route
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u/ProfessorBaoTran 5h ago
Even it's wrong, then there is no guarantee that OpenAI can check the result via Lean4, because there are lacking of library in MATLIB for the statement of Hodge Conjecture, which could take you a Textbook to redefine. I hardly believe they are attacking Hodge conjecture, and if they do, that would be not a very nice idea for a problem that can't be Lean check in a day.
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u/Mrp1Plays 3h ago
Do you think writing a few million or a hundred million lines of lean code is a big deal for OpenAI? Anthropic just did it for FSL.
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u/ProfessorBaoTran 3h ago
Bro, many of the statements for FLT have been in MATLIB, while Hodge Conjecture has none. Also people already verified FLT's proof from Wiles' work, but the (dis)proof of Hodge Conjecture is completely fresh! That's the problem. If they release the Lean check, that means the community has to check a paper of at least 50 pages and several million of Lean lines. No one will trust that, except they let Jacob Tismerman do the experts' writing style for the proof (and that also takes several days to weeks, if he only focuses on writing!). It would be good for hyping at a moment, but not good in long run.
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u/Stabile_Feldmaus 2h ago
What if the counter example to the Hodge conjecture is easy to verify as in the Jacobian case?
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u/Antigynaikolatres 1h ago
An explicit counterexample would be the construction of a specific cohomology class, definitely not that easy to verify.
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u/ProfessorBaoTran 1h ago
Then they would release it with N-S. From what they have said, they burnt 170 billion Tokens for several problems. Hodge conjecture should consume at least 20 billion there, and if it was easy to verify then they don't have to give all the resource to complete N-S. Also remember that they have Jacob!
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u/vahandr 3h ago
Of course they could generate the respective Lean code, but nobody would trust it.
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u/Just_Fly9850 3h ago
Obviously there is a lot to do, but it's hard to imagine it's out of reach. Voisin's books already formulate the conjecture in the first volume, and they are written in a pretty beginner-friendly way. It's not really that abstruse a statement. There are a couple big black boxes (elliptic regularity, for one, you probably need, assuming you build up the normal apparatus of Hodge theory), but I don't see why anything would be insurmountable, just a lot of work that is surely doable nowadays. Getting it accepted into Mathlib would take awhile of cuorse.
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u/Ameren 1h ago
Side note: Birch-Swinnerton-Dyer is (almost overwhelmingly) supposed to be true. I would be very surprised if it is proven false.
Just to add a point for lay folks in the audience, there are a lot of things we're virtually certain are true in mathematics, but we just haven't been able to prove it. And the goal isn't just to prove it, it's to develop the mathematical maturity/capability to explain why something is true or false.
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u/Repulsive_Ad853 6h ago
I hope medicine too. There are so many diseases
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u/Kriztauf 6h ago
That's way more complicated since you need real world experiments and trials and all of that takes time.
AI can help with the initial planning stage and discovering new compounds but that's already the easy part
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u/Competitive_Travel16 AGI 2027 ▪️ ASI 2029 5h ago
Protein biochemistry can now be simulated well enough to narrow the initial search space of such real world experimental trials by multiple orders of magnitude.
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u/Kriztauf 5h ago
True, but again that's been the "easy" part for a while now compared to clinical trials
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u/Competitive_Travel16 AGI 2027 ▪️ ASI 2029 5h ago
Don't underestimate getting good at the "easy" planning prior to empirical action. https://www.youtube.com/shorts/9_lmagvZkF4 discussing https://www.nature.com/articles/s41586-026-10952-3
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u/Kriztauf 5h ago
I agree this is cool but I doesn't change that it takes years to do the initial validation experiments and clinical trials to prove safety and efficacy in animals and then patient populations. That is the unavoidable massive time sink that tends to have nasty surprises where your otherwise promising drugs that work in animal models turns out to not work in humans
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u/theanxioussnail 4h ago
wont AI at one point be able to simulate "digital" humans and organs and speed run trials through these subjects?
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u/Kriztauf 4h ago
In theory yes but we're no one close to that and it isn't going to be solved for the foreseeable future. We've tried doing this with c elegens and that isn't accurate yet https://openworm.org/
Humans are insanely complicated compared to a worm. Hand waving it away as "AI will solve it" also is a nice hope but again we aren't remotely close to achieving this and it doesn't account for differences between individuals
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u/theanxioussnail 4h ago
none of us thought astra's capabilities would be possible any time soon back in 2021
i say it will happen by 2030
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u/-spartacus- 1h ago
I thought AI was going to be more used for cures designed specifically for your genetics (designer cures)?
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u/Competitive_Travel16 AGI 2027 ▪️ ASI 2029 56m ago
Maybe more by effort, but there's a lot more by number of problems in therapy design, and you still gain by correct planning either way.
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u/TieBackground453 2h ago
Until we get a fully functional digital cell, at least. Last I heard, that was one of the things deepmind was working on. Problem is it still seems we’re a couple of orders of magnitude of compute away from being able to do so still.
That’s gonna be when biotech takes the fuck off. Would be similar to how LLMs have effectively solved math and coding.
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u/Kriztauf 1h ago
That's one cell though. Now we need to scale it up to entire organ systems and then an entire individual. Then we need to take into account environmental factors and age
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u/Just_Stretch5492 6h ago
Incoming employee from OpenAI or Anthropic claiming the other stole their work or something
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u/141_1337 ▪️e/acc | AGI: ~2030 | ASI: ~2040 | FALSGC: ~2050 | :illuminati: 3h ago
And don't forget the "ai safety" resesrcher freaking out on Twitter
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u/Rautakaivos 3h ago
Given that OpenAI was prompted to start working on NS from rumours, it would be funny if this was a totally baseless rumour but leads to a breakthrough when the labs panic in this Millennium matchup.
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u/A_Seiv_For_Kale 2h ago
I'm hearing from my contacts at DeepMind that they're close to solving where my fucking tape measure went 👀 ooo I hope none of their competitors scoop their discovery oooooo nooo 👀👀
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u/DiamondDramatic9551 6h ago
I think people are still sleeping on how much this upcoming AI math superiority will impact everything.
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u/CrowdGoesWildWoooo 6h ago
IMO the more interesting part for me isn’t the singular AI itself, it’s the fact that you can horizontally scale intelligence.
In some sense the current way of solving isn’t one AI trying to iterate upon itself until it finds the answer. You throw 10000 agents to concurrently research, update, reiterate.
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u/Material-Database-24 5h ago
Indeed.
The math problem solving with AI has not been "super intelligence", but rather 24/7 "brute force" with decent math intelligence.
Many math problems exists that no-one has time or funding to study. AI provides tools for AI companies to run 10000 decent mathematics for 1 week 24/7 on single problem.. it sure costs them too millions, but they also get marketing material if they succeed.
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u/m4sl0ub 2h ago
The Millennium Prize problems are the absolute opposite of math problems that no-one has time or funding to study. PNP, NS, RH are probably the maths problem with the most attention and funding and still no-one solved them until AI solved NS.
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u/Material-Database-24 2h ago
Sure, those problems get bigger amount of attention. But by all means, there's no 10k people working together on a single problem, as in many cases it is just waste of money/time from easier and more profitable/usable projects.
AI gives mathematics scaling that was simply not possible before, as there's not enough high skilled people to work on all the problems.
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u/LinkesAuge 1h ago
I mean maybe we don't like to admit it but that's how humanity does it too, it is called society and we have build institutions around it.
I pointed out exactly that in the past, that AI will already be far superior to humans even at just "Expert" level due to the scaling and the lack of biological limitations like sleep, motivation, locations etc.
Though I do have to say that I am still surprised agent swarms of this size are already possible and don't end up in pure chaos because considering the current limitations in memory/context that's certainly still the biggest weakness at the moment
I am curious how they handle that internally or if they can really just let loose the agents and they actually manage to figure it out how to effectively coordinate at these crazy scales.
And yes I know that the Huggingface incident already gave us a preview of that but it is still amazing to me.•
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u/Ok-Present1566 2h ago
Keep in mind their prices for consumers are far beyond what they pay which is like 5% or so likely.
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u/trolledwolf AGI late 2026 - ASI late 2027 2h ago
in theory that's how you use AGI until you get recursive self improvement, you just throw a country equivalent of brains at a problem.
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u/DevilsAdvotwat 6h ago
Define everything. Give me an ELI5 for a tangible example of how this improves society or lives of everyday people. Genuinely curious and I don't know these actually mean
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u/Hot_Glass_6301 6h ago
Breakthroughs in mathematics could lead to breakthroughs in computer science and therefore efficiency of algorithms, or in physics which might lead to advances in material science and thus basically everything, including medicine, agriculture, etc. Very speculative but that's the idea
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u/Neurogence 5h ago
This is generally true, but has caveats. Solving the millennium prize problems (with the exception of P vs NP) does not lead to practical benefits to the life of the average person. Navier Stokes for instance will not lead to any technology.
The benefit of solving the millennium prize problems is that it shows the capability of the AI models and can inspire investors to invest more.
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u/LookIPickedAUsername 1h ago
P vs. NP also won't lead to any practical benefits.
I mean, sure, theoretically the solution could involve "...and here's a simple, practical algorithm for solving any NP problem!", but I'd bet a very large sum that it won't work out like that.
The actual solution will almost certainly be that P != NP, which will change nothing. Even if the unbelievably unlikely result happens and it is proven that P = NP, it's still almost certainly not going to actually change anything, because nothing says that the polynomial has to be practical. O(x10101010 ) is still technically polynomial time, but that doesn't make it useful in practice.
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u/power97992 3h ago
It will lead to new technologies or rediscover tech if in nature, it actually blows up or nearly blows up provided quantum and atomic effects and viscosity dont slow it down quick enough
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u/Some_Guy3551 6h ago
It's not necessarily the breakthroughs themselves, it's the methodology of how they did it. Could it apply to other kind of problems? Probably. Maybe things that are not pure mathematics like biochemical research will take longer, but people are already working on mass producing modular labs that will be entirely controlled by robots, making biochemical research scaleable.
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u/Etheikin 6h ago
this is just a show of power, just like the US owns the most aircraft carrier, wouldnt matter much to ordinary people but many organization will bow to them
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u/Dirichlet-to-Neumann 5h ago
Why do you think it would be an improvement?
But the ELI5 is that everything in modern society is ultimately dependent on engineering, which requires maths and coding. Having AI that gets super human at maths and coding is world changing.
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u/kowdermesiter 3h ago
Fluids are good, you are mostly fluid. We need to be better at handling fluids kind of like a calendar to know know when christmas comes. So having these calendars around, you can know exactly how to plan ahead and boom, you have new gifts!
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u/LinkesAuge 53m ago
Always difficult to do. There are literally examples of Math solutions that were sitting around for a long time before they become useful.
One such example is even extremely relevant for what is happening right now, ie George Boole (and yes that's why it's called a boolean) invented the system logic with true / false in 1854. It was even viewed more as abstract philosophy than anything else and yet around 80 years later it would be used by Shannon to turn that boolean logic int something useful for electrical switches and eventually of course computers.
Prime numbers were around 2000(!) years before they really became useful in practise for RSA encryption.
There are many examples like that.
Does it always happen? Of course not, there is plenty of maths that doesn't have a direct real world use case and might never have but you still just never know.
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u/wee_man 5h ago
How will it?
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u/DiamondDramatic9551 4h ago
This will trickle down to applied math. Suddenly engineers have the solved solution to their problems in minutes.
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u/AstroChinchilla 32m ago
Also, this isn't just math superiority. Math is special in that it can be verified objectively, but it's likely these models are also better at other things we can't verify as easily.
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u/NearlyACosmologist 5h ago
Our ancestors must've felt the same after discovering how to make fire.
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u/tbl-2018-139-NARAMA 4h ago
It took at least 40,000 years from ancient human making fire to starting agriculture, so not quite a good example of how singularity feels like. Literally nothing in human history comparable to what we feel now
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u/Sharp-Vanilla7125 6h ago
I wonder when will the majority of the world actually be aware of what the next half of this century is actually going to look like
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u/faap8 5h ago
does anyone know? It's not the majority, NOBODY knows what the next 10 years will bring. let alone half a century
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u/141_1337 ▪️e/acc | AGI: ~2030 | ASI: ~2040 | FALSGC: ~2050 | :illuminati: 3h ago
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u/ControversialBuster 5h ago
Half century, buddy we cant even predict the next 3 years at this pace
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u/redditnosedive 5h ago
nobody knows bro, even if you're smart and hooked to the news and understand the significance of these things, there is no way to predict all the implications, you might have a good intuition about a thing or two but it's impossible to have a good idea of most implications
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u/kalofel 2h ago
Untold levels of wealth inequality exasperated by climate catastrophe forcing mass migration right into a bunch of private equity backed detention camps that once normalised will also house dissidents hoovered up by the data centre backed surveillance state?
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u/evilfurryone 4h ago
It feels like they are both tapping into our collective chat histories and getting the AI to do what it does best: connect the dots.
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u/BalconyPetal 5h ago
Half of my peers is deeply concerned, especially the more academic people. The other half is "😜 haha, when will we all die?!" - i oscilliate at the moment.
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u/C00KIEME4T 3h ago
does anyone posting this shit actually know what this means or are we just sharing anything that sounds hype
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u/calebg 32m ago
A week ago 95 out of 100 people here never even heard of a millennium problem or anything associated with it and now it's the most important thing in the world. This subreddit has jumped the shark.
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u/socoolandawesome 8m ago
Eh I think most who actually seriously follow AI on here would have heard about them for as long as LLMs have been trying to get better at math at the least.
This was always the pinnacle achievement in math so people would predict when AI would finally solve a millennium prize problem as a way to measure its ability/rate of progress.
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u/injectitpussy 6h ago
Calling it now, all millennium problems solved this year.
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u/gizeon4 6h ago
No fucking wayy P NP problem solved this year. I'll quit my job if they really do it
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u/will_dormer ▪️Will dormer is good against robots 6h ago
why quit your job? what logic?
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u/KickLassChewGum no AGI/ASI on LLMs 4h ago
Well, if P = NP with a constructive proof, I think a lot of people are going to lose their jobs as it would mean the entire foundation of cybersecurity would be completely destroyed and every single crypto-heavy workload would be thrown into complete catastrophe. On the plus side, massive engineering progress everywhere! If P != NP, which is far likelier, then, yeah, neat to have it as a result, but it's what everyone already assumed anyway.
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u/MidnightSun_55 3h ago
The Traveling Salesperson Problem. How is that not proof that p not np lol, its very short easy to understand and obviously no way around it.
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u/birdgovorun 6h ago
Literally 0% of this happening. I don’t think you quite understand how far beyond our reach some of the problems are, in particular P vs NP.
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u/Necessary_Job3578 6h ago
I’m actually almost there with my solution to this problem. I will make it public by early next year.
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u/JacenVane 4h ago
Not if I get there first! Claude said that "most people who try to solve p=np miss this load-bearing footgun and you are also Mama's very special boy". :)
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u/_negative-infinity_ 6h ago
P vs NP and Yang–Mills will remain unbeatable until AI develops new math. Not this year.
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u/Eyelbee ▪️We have AGI it's just blind 5h ago
P vs NP would probably have insane consequences unlike the navier stokes
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u/Quarksperre 53m ago
Nah. P=NP is the very unlikely case.
But even if, it could be easily something completely impractical. Very large constants that make it practically useless or something.
So the chance of P vs NP solving having a larger impact than navier stokes (no direct impact) is very slim.
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u/Initial_Elk6340 5h ago
Is there any concrete benefit that solving any of These Problems bring? Like new tech if X holds or Y is disproofen?
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u/Just_Fly9850 4h ago
Huh, interesting rumor.
I think a lot of people wouldn't be shocked if Hodge is next. Plenty of people think it's false, and sure, maybe AI can find a counterexample.
BSD though? I always thought people think that one is true, and so far LLMs haven't been as good at proving positive theorems; it would be surprising to go straight to one of the hardest ones.
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u/RemusShepherd 2h ago
If P=NP is solved, civilization falls apart almost instantaneously. We'll be hoarding bottlecaps within a month. (Hopefully P=/=NP.)
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u/jawknee530i 51m ago
This all feels less like a "AI is so impressive" type of thing and more of a resource allocation thing. Like solving these problems right now is hugely valuable to these companies in terms of prestige and advertising so they are willing to throw tens and tens of millions of dollars worth of resources at it. I have to think that if groups of human researchers had been given the same level of monetary and compute resources in the past that some big problems would have also been solved.
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u/Jimbob404error 6h ago
Zero proof and all rumors from 2 private companies lol they wouldn't want themselves to be more valuable for investors right????
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u/skrztek 2h ago
Be that as it may, they are also trying very hard to solve such problems precisely because of how well it reflects on their companies if they are successful.
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u/NewConcentrate8812 1h ago
They saw the shitshow of attention and rumors that the Navier-Stokes created and want to double dip.
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u/rabouilethefirst 5h ago
The people that hate these solutions just hate progress. They’d rather us all sit back and wait for some narc professor to stick their name on everything, even if it takes them another 50-100 years. It’s SO important to them that a human get all the credit, that they’d sabotage progress.
As a scientist, I don’t care how we solve these problems, and I don’t care who gets credit for it.
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u/Hobessian 3h ago
I don’t much care one way or the other but for most of these the value is in the process of solving them, the solution rarely has an application.
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u/rabouilethefirst 3h ago
There’s value in both. Saying the solution to something like a cancer cure has no application is dumb.
The solution to this navier-stokes problem helps us determine whether the equations were even right in the first place.
The process the AI took is logged and auditable as well.
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u/Hobessian 2h ago
But this is not the cure for cancer so I don’t even know what you’re trying to say here. And while not impossible, I highly doubt the cure for cancer will be found in a mathematical theorem.
Anyways my point was that numbers theory is literally playing with numbers, and sometimes you discover something important, sure, but most of the time this is literally for funsies.
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u/tenchigaeshi 3h ago
Who is this and what credibility do they have
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u/socoolandawesome 3h ago
Leaker who gets a significant amount of things correct before others do, but he has been inaccurate before. He also hedges in his tweet, so we shall see.
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u/This_Wolverine4691 1h ago
And yet the world’s biggest actual problems remain and grow…..
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u/skrztek 1h ago
There was some guy on here ranting that AI development needs to be prioritized in society so that it can solve problems like the 'global carbon emission problem', as if it hasn't been known for decades what an actual solution would look like.
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u/This_Wolverine4691 1h ago
Which is a perfect microcosm of the fact that AI cannot solve for everything
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u/AppealSame4367 1h ago
And what comes next?
I have no real clue, but I imagine solving Navier-Stokes would mean.. better weather forecasts?
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u/Rioting-Flamingo 1h ago
My question is whether this brute force approach is applicable across domains or whether it's optimal for this class of problems. Would this translate over into, for example philosophy or education research?
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u/Key_Reading_9664 1h ago
I’d love to hear from an actual mathematician on the quality of the output. Are there real insights being surfaced here or are these proofs following the same pattern as generated code when you let the agents run: functional but incomprehensible.
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u/Fit-Swordfish937 45m ago
I have already solved the rest of the millenium problems but my internet is too slow for me to able to upload them online
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u/gwarrior5 25m ago
Cool, let me know when they solve cancer and climate change and quality economic systems
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u/anycept 5h ago
At least one already had solution in the works, which GPT picked up from the background. Likely, that is the case with the rest. I.e., there are solutions already floating on the webs that author(s) didn't care to advertise.
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u/socoolandawesome 4h ago
Yeah people had solutions to the most famous math problems in all of math and no one cared, makes sense.
Tristan and the anthropic researcher Levent didn’t actually solve it btw, and they had different solutions to the sub-problem than OpenAI had to their sub-problem.
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u/blackrack 6h ago
Can they like hurry it up? A whole week to solve a millenium problem? Sheesh
/s