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Ten advances in mathematics and theoretical computer science

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Re: Ten advances in mathematics and theoretical computer science

#721
post #645
post #388

Earlier quoted context omitted.

Your 'serious' proposal is unlimited global military bombing campaign on civilian infrastructure by the United States (which is currently losing a war using the same strategy) to 'solve safety' preemptively against a 20% number you just made up? And you accuse the 'other side' of 'suicidal apathy'?? You should put down the AI and do some self-reflection on how you came to hold these views.

> You should put down the AI and do some self-reflection on how you came to hold these views. I've been in the field for almost 2 decades, and actively thinking about AI risk for over 15 years. I've always held the controversial opinion that there may come a time where we might unfortunately have to consider using force to protect our civilisation from the threat of ASI, but I've always reframed from openly discussin…

Advocating for nuclear war as a means of 'harm reduction' should be causing you serious cognitive dissonance.

There are dozens of escalating, yet fundamentally less destructive means to prevent a data centers from continuing to operate (if that's the goal). Not starting at those more modest interventions is political malpractice and in opposition to your harm reduction narrative.

Your P(doom) 'probability estimates' are almost certainly based on unbounded exponential growth curves.

Nature abhors such things; I don't make any plans around their existence, and you shouldn't either. Limiting factors always emerge and dominate the curve, tamping it to a logistic at most.

Get involved with real politics by organizing with other human beings that share your values (posting alone and doomsaying is not praxis), or step back from tech and cherish the limited time you have with the people you love.

Re: Ten advances in mathematics and theoretical computer science

#722

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

My wife is working on her PhD in microbiology now, using OpenAI to implement her research ideas. Genetics is just too much data, and she eats through tokens like nobody's business. I thought I was careless with them, but she barely lasts a full day before exhausting her quota. There's definitely a lot of value there, but dealing with the data problem is a big obstacle in biology. I can only imagine what she could get done with more capacity, though...

Re: Ten advances in mathematics and theoretical computer science

#723

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

My wife is working on her PhD in microbiology now, using OpenAI to implement her research ideas. Genetics is just too much data, and she eats through tokens like nobody's business. I thought I was careless with them, but she barely lasts a full day before exhausting her quota. There's definitely a lot of value there, but dealing with the data problem is a big obstacle in biology. I can only imagine what she could get…

What makes it so token hungry? Is she directly using the LLM for genome analysis rather then having it write the data analysis algos?

Re: Ten advances in mathematics and theoretical computer science

#724

Any computable problem will eventually fall to computers. LLMs have made math proofs more computable, in the sense that a computer can both generate potential solutions and check the validity of its solutions on its own, with a reasonable chance of converging on something correct. I assume this was already doable to some extent, but it seems like it’s now exponentially easier. That still doesn’t mean that all math is…

"Any computable problem will eventually fall to computers."

By definition. Its those pesky NP jobbies that get in the way.

Re: Ten advances in mathematics and theoretical computer science

#725

Earlier quoted context omitted.

It sounds like he hasn't verified the results of a problem that he has personally worked on, so how many of these problems have actually been verified?

From what I understand all of them have Lean proofs/certificates thus are basically 100% proven without a doubt.

Besides for what others have mentioned, the lean proof could be proving something else. Given AI’s propensity to hallucinate, seems like someone should check the lean proof actually expresses what it’s claimed to.

Re: Ten advances in mathematics and theoretical computer science

#726

Earlier quoted context omitted.

Isn’t the point more “it’s easy to fall into the trap to believe that predicting when the sigmoid is going to bend is possible and the right heuristic is to instead extrapolate locally”? That aside, I’d question whether applying the Lindy effect in particular to something that’s not really a life expectancy but more a growth rate is credible… or perhaps a bit circular since it “assumes away” the ceiling.

Nobody in this thread is trying to predict when the sigmoid is going to bend. Perhaps they should

It hasn’t bent already? 2022-2024 certainly seemed far more exponential than 2024 to present.

Re: Ten advances in mathematics and theoretical computer science

#727
post #721
post #645

Earlier quoted context omitted.

> You should put down the AI and do some self-reflection on how you came to hold these views. I've been in the field for almost 2 decades, and actively thinking about AI risk for over 15 years. I've always held the controversial opinion that there may come a time where we might unfortunately have to consider using force to protect our civilisation from the threat of ASI, but I've always reframed from openly discussin…

Advocating for nuclear war as a means of 'harm reduction' should be causing you serious cognitive dissonance. There are dozens of escalating, yet fundamentally less destructive means to prevent a data centers from continuing to operate (if that's the goal). Not starting at those more modest interventions is political malpractice and in opposition to your harm reduction narrative. Your P(doom) 'probability estimates'…

> Advocating for nuclear war as a means of 'harm reduction' should be causing you serious cognitive dissonance.

If you're referring to the "nuke the data centers" line in my bio, that's tongue in cheek. It's an expression of my sentiment towards AI at the extreme.

To be clear, I don't think any country should seriously be considering dropping nukes on data centers. Targeted strikes on data centers operated by rogue private companies or nation states is acceptable to me – assuming pre-warning of intent and appropriate regulatory foreshadowing.

I suspect we agree this is reasonable?

> Your P(doom) 'probability estimates' are almost certainly based on unbounded exponential growth curves.

> Nature abhors such things; I don't make any plans around their existence, and you shouldn't either. Limiting factors always emerge and dominate the curve, tamping it to a logistic at most.

No, they're not based on unbounded exponential growth curves at all... I'm actually somewhat skeptical of claims that there could exist an intelligence that far exceeds our own. My assumption is really just that AI will be far faster, far more knowledgable, far more persistent and marginally more generally intelligent than the average human. The first three are already true, the forth we're getting to.

We're on an exponential curve right now and I suspect the rate of progress will accelerate some more as a result of RSI. This will likely continue for 2-3 years (if we have that long) before starting to flatten out.

As for my doom prediction, my median concerns are around around the destabilising nature of ASI.

If it can be controlled then it will concentrate power like never before, and I believe this will destabilise civilisation. I can go into more detail here if you wish.

However, I'd still put these destabilisation risks at under 50% in total. My concern more broadly is the majority of ASI outcomes are doom scenarios. It's extremely hard to imagine a world in which you have a magic box that can grant any wish that intelligence can grant, but which we have a functional civilisation. You have to basically assume all potentially dangerous wishes won't be granted and probability the only feasible way to do that is restrict who can make the wishes – but then you have the concentrate of power risk.

I largely agree with the premise "If Anyone Builds It, Everyone Dies", so we must try to avoid building it. I think we can build ASI safely, but we're clearly not on the path right now and I suspect it might take decades (or more) to figure out how we can build ASI with an extremely high probability of a good outcome.

> Get involved with real politics by organizing with other human beings that share your values (posting alone and doomsaying is not praxis), or step back from tech and cherish the limited time you have with the people you love.

I do this. I've been writing endless comments more recently urging people worrying about their jobs/careers to stop and just spend the next few years with those they love.

I don't think we realistically have a chance of diverting from this path at this point. I have made peace with this but it makes me very sad and haunts my dreams almost every night.

Re: Ten advances in mathematics and theoretical computer science

#729

Any computable problem will eventually fall to computers. LLMs have made math proofs more computable, in the sense that a computer can both generate potential solutions and check the validity of its solutions on its own, with a reasonable chance of converging on something correct. I assume this was already doable to some extent, but it seems like it’s now exponentially easier. That still doesn’t mean that all math is…

In my opinion, after seein the Jacobian conjecture go, the Riemann hypothesis only has about a year left.

I’m not sure if people just aren’t as aware, but the Jacobian conjecture practically was on par with those other great problems.

Re: Ten advances in mathematics and theoretical computer science

#730
post #623

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

There are many math problems that are simply puzzles: intellectually interesting but nothing worth of value depends on it. To me it would be more impressive if we could define hard problems that need to be solved up front and see how the models deal with that. The results OpenAI demonstrated are impressive, but it also looks like they threw a lot of compute at it just to get results. How many tokens did they waste on…

"To me it would be more impressive if we could define hard problems that need to be solved up front and see how the models deal with that."

I was recently listening to BBC Radio 4's episode on the Poincare Conjecture[1] and the guests on the program were discussing how the problem that looked deceptively simple eluded the great mathematicians of the time (including Poincare himself) for nearly a century and how Grigori Perelman cleverly came up with the proof. It took other mathematicians working in groups years after Perelman's publication to understand and validate his proof. The mathematicians on the program were speaking of highly of his proofs and admiring the originality of his work. This made me think of one neat experiment where if we cut-off a frontier model's training data 2002 or anytime before Perelman posted his proofs on arXiv and check if it can come up with the solution by itself. That would surely be a great signal to see if these LLMs aren't just solving interesting puzzles and that they can came up with something truly novel.

P.S I highly recommend Misha Green's "Perfect Rigor" for anyone interested in the history of the problem and the genius behind the proofs of the conjecture - Perleman. I found it an entertaining read and could digest its description of the problem as a layperson (with undergrad level math).

[1] https://www.bbc.co.uk/programmes/p0038x8l

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