Posted by jonluca 10 hours ago
The Exponential Time Hypothesis Is False [pdf] - https://news.ycombinator.com/item?id=50251661
Including the relevant mathematicians and scientists before dumping this onto the public is sure to go a long way to relaxing fears in those communities. I'm not sure how they will deal with accusations of favoritism but at least they are demonstrating a willingness to participate in a process.
I hope the community can express some positivity that will encourage OpenAI and other foundation labs to continue with this collaborative approach.
> It is amazing what you can accomplish if you do not care who gets the credit.
--Harry S. Truman
Jokes aside, this is a thought provoking quote. I do think it's easy to say as a well known figurehead, when the quote and other actions below you may easily be attributed to you, at least partially. But I do agree somewhat, and I think the context around Truman's time (WWII) is a good example of what humanity can accomplish when the stakes at hand supersede the considerations of workers' rights or credit/ownership. Of course this is also a very favorable phrasing for a period of enormous human suffering. I think there is an arms race analogy to be drawn here, though the current situation and stakes are much different.
'A man may do an immense deal of good, if he does not care who gets the credit for it.'
"QI hypothesizes that a Jesuit Priest named Father Strickland deserves primary credit for this family of sayings. This claim is based on the diary entry dated September 21, 1863 written by Sir Mountstuart E. Grant Duff and multiple attributions thereafter. However, similar maxims may have been developed independently."
[0] https://quoteinvestigator.com/2010/12/21/doing-good-selfless
--Albert Einstein (Director, Los Alamos Laboratory)
I still can't see what this means for human understanding and how open would this knowledge be. Who'd ultimately get access to this stuff going forward and what kind of power games would ensue hereon.
It seems like you are doing exactly what you accuse the parent commenter of doing. The only difference, perhaps, is that the commenter seems to extrapolate past progress to future progress, while your own assumption is a lot more tenuous.
> We reached out to external experts and asked them to act as shepherds, organizing groups to understand the new results. They advised three different release strategies
1. They identified relevant experts for each of the discoveries they wanted to release
2. They collaborated with them to determine how to release the results
The effect for the first two (maths, comp sci) was the same because the experts they chose made that decision.
The downside here is actually the third case (physics). Since they only chose 5 scientists (David Gross, Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov) and those scientists chose to keep the results private until they finish their own work. Everyone else who might be interested has to wait.
That was my favouritism aside. Scientists working on similar or adjacent problems that are not included in these kinds of private releases might feel they are not getting a fair chance.
This is a process that will change, but it seems they listened to the anger from the math community and made changes that help address the concerns.
This is like going to a politician's event and seeing him giving away lollipops to toddlers and kissing babies. But it's the same politician caught in corruption and embezzlement scandals.
You look at that and praise how they have redeemed. Other people look at that and see a corrupt politician handing out candy.
People tell us who they are through their actions. If you prove yourself to be capable of morally reprehensible things to the point throughout the years you build a reputation for all the morally reprehensible things you do, does your potential to do morally reprehensible things change if you go way out of your way to let people know that sometimes something's you do aren't morally reprehensible?
Right now you and everyone else is doing the "leave the multi billion dollar company alone" version of the neckbeard "leave the lady be" meme. And you deserved to be chastised for it.
Its the equivalent of you going around telling everyone in the office about how your boss is turning it around because they bought donuts today, after they spent three years telling you you're worthless, they're entitled to taking all the credit for your work and they plan on firing you as soon as they can.
This.
The truth if the matter is that this is still a publicity stunt. This investment of time, effort, and compute is aimed at building a reputation that this company's model is better than the competition's. The previous publicity stunt brew up in their face, and now they seem to be trying to adapt and double down.
All AI is good for is remixing frontier mathematics, there’s no way it could ever make its own. Right?
So Chomsky thought of himself as a philosopher of science more than anything, and his life mission is/was to answer a fascinating question: what kind of creatures are we? There's been a growing consensus going back to at least Darwin that we're separated from the rest of Animalia by our "reason" (!= intuition != understanding != judgement != volition), but he helped popularize an old theory[1] that puts it kind of beautifully: human language is only possible in beings capable of producing an infinite set of meaningful outputs in response to a finite input.[2] And so far, that list includes only two definite members: Homo sapiens sapiens, and computer programs built upon large language models.[3]
So all that to say: yes, I think you're wrong; the programmatic ensembles that brought us today's breakthroughs are an "infinitely deep well". As long as we have questions to ask, they are not theoretically constrained from answering them.
Of course, this invites some obvious follow-ups on practicality; even the most impassioned ASI boomer wouldn't argue that the exact ensembles used here could answer every question in the universe. But A) that's possible because some infinities are bigger than others, and B) the exact same caveat applies to humans, whose cognitive capabilities are thoroughly determined by accidents of biology, culture, and episteme. The latter is the thrust of Chomsky's famous debate with Foucault, which is absolutely worth a watch for anyone who hasn't seen it (starting around ~18:00, AFAIR): https://youtu.be/3wfNl2L0Gf8?t=1080
---
TL;DR: I ultimately disagree on both points, yes. In the ways that matter, machines are no more constrained than animals.
[1]: https://en.wikipedia.org/wiki/Wilhelm_von_Humboldt
[2]: Many animals are capable of communication, often quite complex and fascinating communication at that; even flora and fungi communicate! But language is qualitatively distinct. You may have heard this in the pithy-yet-mindbending sentiment "we've taught many apes to communicate with sign language, but none of them have ever asked a question."
[3]: It's no surprise in hindsight that trying to build better autocorrect got us to AGI; I find it unspeakably tragic that Chomsky never got the chance to see how thoroughly he's been vindicated, in this regard. He had his stroke mere months into the singularity, and had a quite negative view of the approach before then.
Language to humans is a symbolic mapping of labels to reality based on actual experience.
"Language" to LLMs is just a string of tokens to manipulate based on relationships harvested from recorded human experience.
It doesn't mean anything other than 1s and 0s - it's not a language because the LLM isn't communicating with you, just as the sum of humanity isn't communicating with you.
It's just a really good "choose your own adventure" book.
In LLMs that's a bounded infinity though, the models themselves have only so many bits and the activations are also limited. Once you reach the same state twice the model is looping and it won't break out of that loop. I've seen such loops across tens of thousands of tokens so I'm not sure to what degree the infinite output rule holds true. It would be an interesting experiment to try to figure out to what extent the 'busy beaver' can be kept busy before it degenerates to looping or nonsense.
I'm also unaware of the quality of the consultation with the relevant mathematicians, colour me skeptical there.
> "The external collaborations will follow four principles... until Anthropic, Google, DeepSeek, Google and dozens of Chinese companies all make the same offering, in which case we will rediscover and re-implement all of the things you hate about traditional academic advancement and publishing, except because our companies are run by people even more mercurial and self-absorbed than university presidents, we'll wind up supporting even fewer people to do it."
Edit: it turns out you've been doing this frequently, so I've banned the account.
If you don't want to be banned, you're welcome to email hn@ycombinator.com and give us reason to believe that you'll follow the rules in the future. They're here: https://news.ycombinator.com/newsguidelines.html.
Only time will tell if OpenAI or the other labs continue to play nice. I think it might help if we applaud when they act pro-social rather than just jeer when they falter.
What makes you believe stillpointlab is a shill instead of a person who has a specific opinion on this topic?
[0]:
> We give a deterministic algorithm for exactly counting the satisfying assignments of an arbitrary k-CNF formula. For every fixed k ⩾ 2, on a formula with n variables and m clauses, our algorithm uses $poly_k (n, m)$ space and runs in time $(n + m)^{O_k(1)} 2^{n/(\log n)^{1/2 + o(1)}}$
The dominant term there is (roughly) $2^{n / (\log n)^{0.5}}$, so still superpolynomial but less than exponential. Fucking wild.
[0] https://github.com/openai/math/blob/main/preprints/The-Expon...
Turns out the 'opne' in open AI wasn't referring to open source, but open problems!
A very different thing is proposing a framework and in it identifying interesting questions. So far AI has only worked within existing frameworks addressing problems already posed. That may change in the future, but it would be a genuine and qualitative evolution.
Are there any good accounts to follow (platform agnostic) that give occasional updates on the intersection of AI and math that aren't too dumbed down, i.e. that a layperson can appreciate?
Also glad to see that one of the authors of the paper stating it is also in the loop here.
2026 is weird.
More comments in https://blog.kolen.dev/link/openai-shepherds
1. How much did it cost?
2. Would an equivalent allocation to incentivize human effort have borne the same results?
3. Post IPO, will Open AI continue allocating similar levels of capital to further these causes?
#2 is particularly important to answer, given research grants have been getting cut elsewhere: see U.C.L.A's research grant cuts from last year and Terrence Tao's attempt to raise funds (about $60k) by collaborating with Open AI earlier this year [1].
[1] https://www.nytimes.com/2026/10/16/us/math-ai-terence-tao.ht...
There are lots of reasons I believe this. One is that frontier AIs are very clearly superhuman on shorter problems (as can be seen on benchmarks like FrontierMath, or just by playing with them yourself if you have a source for difficult problems)--so these achievements are "just" scaling that advantage to research-sized problems. Second, AI is also clearly superhuman in its knowledge across fields, so it can make connections and combine techniques that humans won't be able to access. Third, these problems are famous and have withstood efforts of many of the best humans, in many cases being considered unapproachable.
Altogether it seems like AI is not only smarter but also more cost efficient that humans for math-adjacemt problem solving. I'm not saying that AI is superior at everything in math, eg theory building, but I think it's really unlikely you could get any group of humans that could compete with OpenAI's latest results.
However there are truly superhuman vehicles, spaceships and submarines, that can carry humans where no human could go alive.
I don't know if these AIs are superhuman in the way of planes or in the way of spaceships. I also don't know if they can do everything we can do by talking or if they have some limits.
I mean, a plane can fly but not reach a branch and stay still on it. A small drone, almost. My coding agents sometimes can't do the obvious but is it because of some intrinsic limitation or because my instructions are bad? So far my experience is that they are superhuman like cars or trains, not yet as planes.
>2. Would an equivalent allocation to incentivize human effort have borne the same results?
Unlike their initial massive brute-force run that solved the Navier–Stokes Millennium Prize Problem, most of their subsequent breakthrough results in mathematics have come from a single prompt to a single AI agent, using approximately 3 hours of ChatGPT Pro-equivalent thinking compute per result on average.
2. most probably no, the AI doesnt rest and its very very fast.
3. also no, they are doing this for aura farming which then will result in more money for them, the money will dry as soon as this stops working.
We're now at stage where we can turn energy into thought to generate expertise on demand.
I think the scarier alternative may be OpenAI forever gating their super-frontier models, capturing a significant portion of the sciences and leveraging it for equity in businesses that build on scientific advances. e.g. "Hey CATL, how about you guve us 5% equity in exchange for a battery chemistry breakthrough our AI has found?".
It's roughly equivalent to the playbook Palantir had for the public sector when they marketed themselves as a company that had cracked data science. At least that's what they've been pitching back then. I can't find a lot on public disclosed deals based on that.
2. it wouldn't happen so who cares?
3. no, but models will be better, it'll be cheaper to do
It's not a snark. The scale of VC philanthropy is unprecedented and it fuels itself. All of it will eventually, one way or another, become open. Long story short – there is nothing to complain about.
That's so insane to me. This top mathematician (and colleagues) at her pinnacle spent years proving it in three dims and now OAI proves it in every dimension...
(which is somewhat valid). Though I think a far more interesting thing would be whether AI given the corpus of 19th century mathematics and physics reproduce what Ramanujam or what Einstein did.
IMO that there is any work at all to build from is the result of a long tradition of taking the next step. Professor to student and so on. The danger of AI here is we get to take a leap, say, 10 steps - but then there is no more tradition to have the fortitude and mentoring necessary to continue the progress.
It all gets derailed while betting on RSI and never having to do math research again (but if an advanced theorem is proven, and no one alive is competent enough to comprehend it, does it even matter that we get to call it solved?)
They know that value creation is a dead end sooner or later..
It's all well and good to say that we should just go on these journeys for our own enrichment, but even so they will just be doing it alone...or else not do it at all because they need a shared human effort surrounding them to do it, and therefore end up depressed and immersed in drugs or media all day.
Of course we're awed at what AI can do now, because all of us observing it have had the luxury of having such opportunities before AI. I got my PhD before AI and I found satisfaction in participating in a shared math community, which I wouldn't have done if I were starting my PhD now, because I would find the current academic environment unacceptable and useless.
That's rhetorical, right? Of course mathematicians built on what older mathematicians built and OpenAI's machine built on that. The real question whether OpenAI's machine has contributed something others will in turn build on.
The most important component in the time bound is of the form 2^{n / polylog(n)}, which is subexponential. But if you have reduction from another problem that increases instance size quadratically, the algorithm for the other problem is no longer subexponential. Which means we are still essentially in the same neighborhood as before.
It's a huge result if true, and probably the first major AI result that affects the papers I read. But since the boundary in the hypothesis was kind of arbitrary, breaching it should not significantly change our intuition on complexity classes.
In the usual approach, you assume a nondeterministic Turing machine (or equivalent) that solves the problem and a time bound (which can be an arbitrarily large polynomial). You then create a boolean expression that can be satisfied if and only if the Turing machine accepts the original problem instance. Unfortunately all constructions so far have included the time bound as a factor of the size of the expression.
Anyways, most of the times, SAT can be solved quickly, but not always, so getting the answer from Astra in polynomial time doesn't prove much unless you can also prove that it always does, no matter the input.
A single transformer step is simply O(1) (for a particular parameter size), but it applied a potentially infinite number of times.
Thus while a single transformer cannot solve any problem, a transformer system applied in the normal way can solve any computable problem.
So if you use the context not as a tape in itself, but as an io channel to read/write an infinite tape, the context for any given step can remain fixed in size, and so the step itself can be O(1).
Everyone agrees that water is wet (P!=NP), but no one can prove it. In the meantime, a whole field of computer science was built on a stronger belief (ETH): that water, at its worst, soaks. Turns out, even at its worst, water only makes things damp. It's still wet. That said, this finding did produce a new measurement of wetness.
Do you accept
- Moshe Y. Vardi [1]
- Anil Nerode [2]
- Donald Knuth [3]
to be credible? Source for the statements that they consider P=NP to be possible: [4]
And you may include me in the list of credible P=NP believers because treat myself as a credible authority, i.e. when I ask myself whether something is right, I consider myself to be much more credible than some famous scientist. ;-)
(to be very clear: the previous paragraph is rather a clear statement against this kind of "hero worship" with respect to mathematical or scientific problems. One should consider the evidence by oneself instead of believing in P!=NP because lots of computer scientists claim all the time that this is likely true, or consider P=NP now to be possible just because some famous computer scientists consider it to be possible)
---
[1] https://en.wikipedia.org/w/index.php?title=Moshe_Vardi&oldid...
[2] https://en.wikipedia.org/w/index.php?title=Anil_Nerode&oldid...
[3] https://en.wikipedia.org/w/index.php?title=Donald_Knuth&oldi...
[4] https://en.wikipedia.org/w/index.php?title=P_versus_NP_probl...
> to be very clear: the previous paragraph is rather a clear statement against this kind of "hero worship" with respect to mathematical or scientific problems.
No, it's an irrational rejection of the notion of expertise. The experts are not "heroes", they are simply people who have done vastly more study than folks like you or me. e.g., if Magnus Carlsen looks at a complex chess position and says that white is winning, I will trust his judgment far more than my own.
That sounds particularly relevant in how AI-assisted/driven mathematical research is changing the game, where previous assumptions based on human experience/effort are being overturned unexpectedly.
My thesis was around showing implications of few different hardness conjectures. So grounded was ETH that I introduced it in a side note as Conjecture 0 after Conjectures 1 and 2. I don't think it's easy to express how substantial of a Bayesian update this is all around.
> does this update your priors significantly in the direction of P=NP?
My answer is no ... and Aaronson's answer would also be no ... clearly he doesn't view a change from 3% to 5% to be significant ... his response downplayed the significance of !ETH in re NP?=P. So apparently you downvoted me for simply stating my own opinion while you completely misunderstood what it was an opinion of.
Would be funny if the most famous problem turns out be an example though
EDIT: I am wrong (it's been a while) but there is nuance.
I said any computer program fails to prove some true statements. In fact, some 'true' statements cannot be proven by any program, as others have said.
But for those statements G, you can prove 'G is true if our system is consistent', just not 'G is true'.
So when we say G is 'true', we are really just asserting the consistency axiom that our computer program is denied.
I'm saying it'd be funny if Riemann were true but not proveable.
Though I guess it's actually funnier. If Riemann were false then there would be a counterexample, so it's clearly within existing axioms.
So if one can prove that Riemann isn't proveable in our current axioms then it has to be true.
G is independent of your original system T (cannot be proven true or false).
If you create T+ with added consistency axiom, then G is true and provable.
But G is never true and unprovable in the same system.
It's a lot like is/ought or theology.
absolutely insane
I am not certain on the extend of this proof but QED is probably not sound on it's own and we have been using that even longer. lambda phi^4 behind symmetry breaking and the higgs is strongly believed to be unsound on its own.
More to the point, QCD has been experimentally tested both at UV (deep inelastic scattering) and at IR, while the physical meaning of testing QED at UV Landau pole regime is unclear.
(only half tongue-in-cheek)