Funnily enough, there’s a good chance Truman never said those words; the earliest known attribution of the quote to him is from a Time magazine article written in 1988. It’s not in any of his personal writing or speeches.

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I think, sadly, these fields will collapse further into a tighter in-group. Anyone outside that group will find it increasingly hard to penetrate. Talent won’t get you there anymore.

I'm happy to relax for six months, and ask Qwen-8-E2B on my Nintendo 3DS for the solution.

I'm not sure why you think that someone who believes that this is inevitable is just someone who assumes they'd be in the "have" rather the "have not" category.

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.

> What is weird is criticizing people who acknowledge good things because of past bad things when nothing anyone said here, that I can see, anything close to "they are redeemed rejoice!"

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?

Wrong, these companies have shown time and time again they are irredeemably misaligned with our interests.

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.

I would have found it a lot more impressive if they just empowered scientists through some kind of grant rather than to internalize all this. It sets the tone for what's to come and inevitably if what they find is juicy enough it will not be published. For instance once they start working on materials science (if they aren't already).

I hope it gets us somewhere new. You can hope that and appreciate it hasn't yet though. (I'm not part of their IPO)

It's parasitic on humans and it's not an infinitely deep well. Wrong?

:/

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?)

I think the question is rather, what will happen to human beings when any possible personal intellectual accomplishment will no longer be seen as interesting or relevant by other human beings when AI can do most of it?

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 would be a very exciting experiment. I doubt you could find enough vintage training data to train a LLM enough to do it without it being contaminated by anachronistic data in the weights, but I would be absolutely amazed if it could reproduce that.

whether the original authors would have produced their work without building off from the work of other mathematicians.

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.

success and failure of anthropic are both good for open weight models

There are so many just barely sub-exponential function shapes between 2^(n / sqrt ln n) {this result} and 2^(log n) {polynomial time}!

The challenge is the initial reduction from an arbitrary problem in NP to the problem you want to prove NP-complete.

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.

Iirc, there's a big difference between the computational complexity of what a transformer can solve and what it can solve in practice; what it can solve in practice tends to come from things like singular learning theory (which describes the forms of generalizations that a given ML algorithm can make), but I think (iirc) that transformers can compute a pretty broad class of O(N^2) functions?

For the umpteenth time a transformer is an arbitrary turning machine due to the fact that it has a theoretically limitless tape (the context).

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.

At certain temperatures water is indeed not wet.

Anyone credible? A nontrivial number of people also believe that humans used to ride dinosaurs around like in the Flintstones.

No, it is famously a pointless internet debate with no settled answer. There is no scientific definition of what can or can't be wet, saying that wetness only applies to surfaces is just an opinion. It's an entirely linguistic question, and most people would say water is wet. If you want more than descriptivism, the common definition is something like 'containing or being covered with liquid', and I think most people would agree that a mass of water contains water.

Stick your head in it and breathe. You'll know.

The question was

> 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.

That's not that how that works btw. The incompleteness is a property of the algorithm which does the proofs, not the theorems. If a theorem is true it has a proof and a program which proves it (printf("the proof verbatim")). But no computer program can successfully prove all theorems. The space of potential proofs is too big to search systematically, but you can still get lucky.

Either P=NP or not. Hoping one way or the other changes nothing. Nor does it change how efficient computing is, nor does it have any effect on cryptography. Discovering a vastly more efficient means of factoring primes--perhaps via quantum computing--would do that. But just learning that P=NP does nothing to further such a discovery. Almost certainly, if P=NP, the exponents and/or constants in a polynomial factoring algorithm would be galactic. (FWIW, Knuth believes that P=NP and that it has no practical consequences.)

Not really. P=NP but the degree of the polynomial is Grahams number doesn't let people into your bank account

it could make lots of compute way more efficient, not sure why it is catastrophe..

Why? Nature doesn't care if people are making financial transactions based on flawed cryptography.

Yes, but it has also been known for 50+ years that QED has a Landau pole and might be UV trivial or inconsistent, whereas QCD has asymptotic freedom and is thus controlled at UV.

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.

Computational biochemistry is what I'm currently pursuing, but I'm pretty new to the field so take everything I say with a grain of salt: Biochemistry is a really really really tricky problem, for a couple reasons:

1. Biology has a very nasty habit of not cleanly abstracting. It's not like we can treat every protein as a "diffuse mass" without losing a ton of important interactions. This is unlike something like CFD where you can treat a mass of water molecules with certain constants. Think of something like cancer: a small mutation to a DNA strand can cascade into a tumor. You have to deal with the mutation happening at an atomic level while scaling to a whole organism (yes I know there's models that can approximate this, but they can't capture all the interactions).

2. This brings us to modelling at the atomic level. To model a system of atoms with the Schrödinger equation, it naively scales O(6^n) per particle. Note that means every nucleus and electron, so if you have say 10 carbon atoms and 22 hydrogen you're already at 10^127 operations. We can cut corners a bit and end up with something like CCSD which scales O(n^7), or cut more corners and scale O(n^3) for DFT. DFT is pretty much the last method where bond forming and breaking is modelled, so after more corner cutting you lose losing reactions, which are important for understanding why something is happening. Most protein folding simulations (moreso prior to alphafold) run a very crude approximation that models atoms as balls on springs (things like AMBER and CHARMM), which obviously can't handle reactions.

3. If this wasn't bad enough, you also can only move through time at about 1 femtosecond (10^-15), so it takes a ton of simulation steps to get even a nanosecond in. Forget millisecond or second lengths where things start to happen.

So, while the math of the physics exists, computationally it's practically intractible. There's some exciting work with something called Machine Learning Interatomic Potentials (MLIP) which approximate DFT using a neural network which are about 1000x faster than DFT, and iirc scale much more linearly (look at things like MACE and orbmol if you're curious). So we're making progress, but we've gone from so ridiculously impossible to pretty much impossible for large systems.

I have a couple ideas about developing custom microchips to make this faster, which is why I'm pursuing this, but there's still a massive way to go!

Are there efforts into building "autonomous laboratories"? Not sure if the idea is practical but it seems like a direction things might go in, where you give an advanced model, or a swarm with a leader, free reign to run experiments day and night.

That seems like the way to go. Also tokamaks etc

Until the over-RL'd models cook up a bioweapon to game BioBench, yes.

This person thinks there's a 98.7% chance of AI extinction and that we should nuke data centers. I'm not sure that they're an unbiased observer.

They do that to make it easier for readers to verify the statement (which is entirely contained in that file) separately from the proof (which is spread over thousands of files and github can't even show them all).

Proof is at https://github.com/openai/math/tree/main/lean/OAI/Algorithms...

https://github.com/openai/math/blob/7ef5c0cc5ca4b0e072b7a050...

looks like the real proof is in this file

I was confused too, but it looks like https://github.com/openai/math/blob/main/lean/ComparatorChal... (with the sorry at the end) is just the problem statement; the actual proof is a big pile of lean in the Algorithms folder, with the final theorem stated here https://github.com/openai/math/blob/7ef5c0cc5ca4b0e072b7a050...

How much effort do you put into prompting it? Are you asking it one shot with a simple prompt? Are you giving it to multiple agents and giving them a workspace to collaborate in? You might give it to a trusted colleague who does not know the solution along with an agreement to jointly publish, ask them to go through the process of solving it with agentic support, and then compare your solutions.

Edit: to be clear, I completely believe your experience - just pointing out that it might be interesting for you to actually “try” to solve it thoroughly with the tools, though it is obviously hard to do that in a fair way when you know the solution.

Iirc some of the prior math discoveries involved very very very heavy handed guidance to force the AI to discard prior assumptions, and to try many avenues with MAX effort. So ya models don’t behave like ground breaking theoreticians by default.

Ha, I had a similar little test problem, but the frontier models are now smart enough to read enough online of what I posted here and there to piece together the answer. And someone else has written the paper in the meantime and got it accepted for publishing.

How about swarm of agents controling a fleet of humanoids and automated construction vehicles?

Definitely. It will let some smooth-talker with a vibe-coded website raise billions for "Nuclear Fusion AI". Then they can use AI to squeeze your team with lawsuits until you agree to sell cheap, and maybe keep you on as an employee to build it.

I mean, you never know. If we could have simulation models with excellent fidelity, then AI could do all the research and iterations and come up with something very plausible. Cutting down physical world experimental iterations/prototyping.

So effectively, you would spend the first 1000 experiments inside a computer simulation and move to the physical world only when you had enough confidence.

Nothing could go wrong

The thing that I've not fully groked here (might be relevant) is that OAI is generating "paper" proofs first, and only then formalizes them in Lean as a separate step. They've as far as I'm aware not said anywhere how many write ups failed formalization due to a bug in the proof. If we assume that number is low, models would be quite good at one-shotting math proofs. Then it depends if you can replicate the math RL training for chemistry/biology/medicine. Is there enough data out there for that? No idea.

Exactly my thoughts.

I find that unless the outcome I'm looking for from the model is almost binary and easily verifiable, it is basically faster to do the work myself.

Assumptions made by the models multiply and by the non-deterministic nature (dbf, similar to work by humans) I'll have something end up light years away from where it should be. During a normal workflow, I have to contend with every line I write forcing a very tight feedback loop... I suppose I could also sit there and spend 9 hours writing out a "perfect spec" but we've already tried that with waterfall development!

So, not sure if its the models, rather the class of problems I'm applying them to... but it is a bit ironic they are allegedly able to solve these conjectures but not stop to ask about assumptions.

1. This has not been my experience

2. We dont have the actual frontier models

internal unpublished models + large swarm of agents (>2000)

I don't understand this dialogue, which seems to repeat with every result of this sort. Of course this is interesting! And of course the answer tells us something! And of course we also want to understand where it came from! None of this is in contradiction!

Knowing the answer to Fermat’s Last Theorem wasn’t valuable. But the pursuit of it led to many developments in other fields of mathematics that were valuable (where value is measured in terms of $).

I disagree. We climb mountains for the sake of it, and the rest of the world benefits because the gear improves and makes adjacent, non-for-the-sake-of-it activities safer.

We chase open problems for the sake of it, and others sometimes support us in doing so because the paths we pave along the way end up being useful for them for adjacent purposes. If you get the answer for free, you might have scratched the itch, but nothing was built for others to use, no fodder was found for the next great question.

Nobody pays mathematicians for solving famous problems. Famous problems are how mathematicians orient themselves while they do the other things that they're paid for (maintaining a useful community, mostly). All this does is deprive them of a navigational tool.

> Imagine a programmer telling their boss it’s not about working software it’s about the journey of writing the code. Good luck getting hired.

Your formulation is a little bit exaggerated, but I (and many, though far from all, programmers) would agree with the following more "tame" formulation:

Getting software to solve a business problem in an elegant and maintainable way means that we got the abstractions right. Similarly, if a software can easily and elegantly be modified to cope with new business problems, it is also a strong sign that we got the abstractions right. In this sense, the business problems that the software solves are indeed just waypoints on the journey of finding the proper elegant abstractions for putting the business problems into code.

Turning these novel insights about "good" abstractions into code and programming languages enables the team to iterate faster and generate business value faster. So, appreciating that it indeed all about the journey means a commitment towards an approach to accelerate the rate with which the team can turn business insights into code and code into business value.

I know that many managers do hate such a formulation, but I stand behind it.

Completely wrong.

Often a problem is important because we have no idea how to solve it, which means we need to develop new machinery to solve it. That new machinery can then be used to do things we couldn't do before. Stimulating the development of that machinery is the most important part of the problem.

You should remember that mathematicians and programmers working for a company have different jobs with very different goals.

This is such a short sighted take. Number theory was considered beautifully useless for centuries, and now it’s the backbone of the cryptography that secures every bank transaction. We don't know where the pursuit of knowledge will take us.

Thinking in such a utilitarian way feels like a flavor of Meditations on Moloch.[1] Just look at how short-term, quarter-to-quarter thinking is affecting the economy and the lived experience of every human on earth. It’s horrible.

[1] https://slatestarcodex.com/2014/07/30/meditations-on-moloch/

"Knowing the answer" means more than knowing the value of a single yes/no bit.

Knowing the answer is valuable, but it's not everything. We also want to understand why. The four-color theorem has a computer proof, so we know it's true, but we learned much less from that than we do from a human-understandable proof.

Many of the OpenAI results can be made human-understandable, so it's better than the four-color theorem example.

If you were a math grad student, would you rather your advisor be telling you to LLM maxx your ideas or working with you and giving you ideas on your thesis personally? I know my answer.

> If knowing the answer is not valuable then asking the question wasn’t valuable to begin with.

Let's say it's possible to know an alien civilization exists 100 million light years away from their waste heat. But that's all we know and it's unlikely we'll ever interact with them.

Was the question of whether we're alone still "valuable"? Wouldn't a lot of philosophy and even some physics fail to meet your definition of valuable?

> Imagine a programmer telling their boss it’s not about working software it’s about the journey of writing the code. Good luck getting hired.

Imagine the next version of Claude Code or Codex no longer hands you source code and instead turns a natural language prompt directly into a compiled binary that passes the test suite. Would this programmer's boss ship the binary straight to production and dispense with the company's git repo altogether? After all, the goal at the end of the day is shipped software that produces value, not human-readable source code.

I would love to hear what these fat cats say in private.

This is a cop out argument.

I've worked in ML since 1994. I've been very impressed with the progress of models lately. I read "The Coming Technological Singularity" when it was first written and dedicated my career to seeing these sorts of things coming true.

That doesn't mean that their exponential improvement will change faster than light travel. Therefore, to deliver a human being to the surface of another planet (let's say Proxima Centauri at ~4 ly away) with enough resources to create a stable colony means we'll travel at less than the speed of light. Even with a solar assist, the best we can do right now is less than 1% the speed of light in an unmanned probe. People are working on alternatives, but those are not the sort of technology you just pop in a space ship and send for 400 years to a neighboring star. How do you support a population for 400 years?

As an alternative, let's just make humans like tardigrades, capable of shrivelling up and surviving high-radiation, low-moisture environments. Then we can take 10K years to get to a remote location. As a bonus, the resulting humans can survive in a much wider range of conditions so we have many more target systems to consider. Oh, but that's human engineering- are you sure that we'll just be able to genetically modify people (technologically and morally) at that level any time soon? A single person died in an early gene therapy trial and it shut down the field for 10+ years.

Basically, what you're arguing is that exponential growth in AI (not a given) will unlock huge material sciences and biological advances. While possible, it's unlikely to combine in a way that suggests "we should send people to other solar systems".

biological material of humans? you'll have to expand your argument here. Are you reconstituting the material on the other end? If you have that technology, do you need a robot to tell a human the story of earth? Why not just upload it directly?

I honestly think they are both finite lol.

I wonder if the best statement we can make for future AI discoveries is that, ideally, they will allow us to move up the Kardashev scale faster.

The new faster multiplication algorithms are both galactic, are they not?

It does not seem surprising to me at all that AI can find new galactic algorithms that are not of any direct use (at best they can guide us to find better solutions that are non-galactic).

What would be surprising and interesting is if AI can find a new floating point multiply-add that is 2X faster per operation than the current fastest chip implementations. That would immediately have billion+ dollar implications. The teams who already work on this have excellent approaches and invest enormous amounts into tiny improvements already; there are probably not much low-hanging fruit there (proponents of using AI for chip design improvements have impressive claims, but unclear that any of those really worked out in reality).

If we had really good understanding of physics, couldn't we find out how to make a room temperature superconductor (or prove it can't exist)?

Or is such understanding reliant in experimentation because there are "hidden constants" we can't figure out with math alone?

Huh? I'm not sure that makes any sense.