There is a real, undeniable possibility of AI becoming better at mathematics in the same way that it became better at chess and Go, and in such a scenario, one may expect the community's response to be comparable.
Stockfish does not steal research or scoop researchers.
The concentration of computing resources and capital should be examined by the math community.
Frames could literally cost 1 dollar (only happened after china entered this market), but good luck finding ones like this with good lenses.
You need to buy from one supplier who intentionally offers cheapest frames for 50+ dollars and those frames look like crap. The ones that look better (even if same plastic) cost 500+ dollars - and all due to price gouging.
For lenses I am not sure, but suspect something similar.
Fielmann in Germany has been offering very reasonably priced glasses and frames for ages.
- I think competitive open models are just an artifact of the AI race we're witnessing right now. What's the incentive for a company to spend billions researching, developing, and training a model, only to release it for free? Leading to the next point.
- Even if open models are good enough to be competitive, how are we going to run them? Doing so locally is next to impossible and I don't see that changing. The capabilities of models that you can run locally will always get better, of course, but the level of quality that is considered essential for work will always stay pinned at "near-frontier". Datacenters will always have better optimization and economies of scale, the industry will consolidate over time and eventually we'll end up with a handful of companies that operate the hardware serving 95% of all inference needs.
I'm not convinced that we can reach the fantasy world that they're trying to sell without killing the entire planet, but if we somehow do I don't see how we can avoid the world turning into a dystopian hellscape. We would need extremely radical interventions to avoid that scenario, such that these models and the hardware to run them would be owned and governed democratically, i.e. the end of capitalism.
And a lot of people are using trailing edge models just fine already.
> [...] but the level of quality that is considered essential for work will always stay pinned at "near-frontier".
Why? When we'll finally all write our software in Lean and prove it correct and prove it fast, it won't matter that a slightly more clever model could have found a slightly nicer proof or whatever.
Just like today people happily use Python for many programs, even though rewriting in C might give you a performance boost. Good enough is often good enough.
If that's your only objection: in a few years you can prove Rieman's hypothesis on your smartphone, no need for any trillionaires to give you permission. Does that make any change to your argument, or did it not actually matter?
For the latter: I assume that having a whole data centre will always be an advantage. I am saying that for a fixed target, like proving the Rieman hypothesis from scratch, the required hardware will shrink.
And, yes, the Rieman hypothesis hasn't been proven yet. So to take your fears into account, replace my example with something they've already done, like constructing a solution to the Navier-Stokes-problem.
Yes, but to what point the hardware will shrink? There are several orders of magnitude of difference in what in your mind AI will become and what more conservative people believe. You take your view as granted...
Tech companies are as much the topic of this post as AI, I think that's the immediacy.
There's a single answer to that question: yes, math very much has an impact without humans in the loop.
Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.
You give your AI the problem, like 'make this computer program faster and more reliable', and it'll go off and do the math necessary to make it so.
For all we know, P vs NP will never be resolved neither by human nor AI, and the world will just keep turning.
I am saying that applications supplied and supply an inexhaustible amount of good problems and questions to consider. Purely theoretical concerns also supply some questions, but even if that well dries up for some reason, applications persist.
As the US has offshored manufacturing, the number of patents issued for those processes has fallen. Innovation occurs where the foundational understanding is applied; they arise from a desire to do the required work more efficiently.
Similarly in math, attempting to solve a problem leads to new questions. IF you actually do the work.
You need to have done enough of the work to know what the correct next question are, or you need to rely on AI for everything.
The main situation I can think of where better calculations have a really visible effect is video and image compression, and that stuff is very far away from mathematical proof territory.
t. low information voter.
If you tell someone they can't use a matrix multiplication with better asymptotic performance than n^2.3755 from 1990 they're going to shrug and not care.
I’ve watched quite a lot of YouTube videos where two machines compete, so you may not be completely right here
Top chess engine championship is pretty fun to watch.
In other videos he's called out the influence that this and similar games have had on human players in recent years, particularly around square denial and thorn pawn strategies.
There is no bound on the amibitions of AI. AI is set to replace anything done by people, and there won't be any room left for people. There isn't any task done by humans that AI won't be better at.
This is not a tenable outcome.
We should never have built machines with agency, rather than optimization processes that operate as subroutines of humans.
We haven't quite crossed that bridge, but we do appear to be standing on it.
Do you really think making labor obsolete and giving humans back their time is such a bad thing?
In the short term, AI is disempowering the vast majority of people in favor of a very small subset. In the also way too short term, AI is disempowering all people.
I believe we will distribute the fruits of AI's labor at the very least to the extend where everyone can live comfortably.
No one has an interest in putting large parts of society on the streets in some sort of dystopia.
Historically though, technological improvement has lead to large increases of living standards for the overwhelming majority of people, so I think that past trends support the utopian view more than the doomer view.
I am not assuming humans don't remain in control, but rather, I am not axiomatically assuming there's any inherent reason we will.
We have precedents of people warning about existential risks in the past, when the warnings turned out to be false, or overblown. In some cases, such overblown warnings led to serious negatives for society (demonization of nuclear power).
Those counterfactuals are important, though. We do have a history of averted disasters, albeit not as large. Ozone hole, Y2K, think about things that seemed overblown at the time, and consider whether they were actually overblown or whether there was a concerted effort to successfully avert them.
No, the argument is instead that the person claiming that humanity is going to be destroyed is making a fairly extraordinary claim and that requires fairly extraordinary evidence.
Or, in other words, we have tons of evidence already as for why the world ended is a fairly far out there prediction, given all the crazy people making these predictions keep turning out to be wrong.
So, you can make your extraordinary claim if you want, but really the burden is entirely on you to prove your extraordinary claim, and everyone else is free to remain on the default and completely normal end of the prediction spectrum, of believing that the world isn't going to end.
And when people do tricks like this, they are running away from the fact that they are making a wild completely out-there prediction, and hiding behind that by trying to come up with reasons as for why evidence doesn't matter and actually the burden of proof is shifted to those who have the default and boring prediction of the world not ending.
Its not a counterargument to basically anything, except as to avoid having to deal with actual evidence.
It is an argument that seems almost tailor made to have to ignore mountains of evidence against you.
In any other contexts the supposed "rationalists" would be fully in agreement that having evidence matters, and that not having any works against you.
So, in order to fight against this severe issue with their arguments, they have to invent a reason as for why the entire concept of evidence itself doesn't apply to them and they get to ignore normal evidentiary requirements.
Wow.
Only on HN.
Also apparently not from the US? Or Russia?
This does not reflect what I see in my government.
I'd guess horses today have on average a better life than back then.
I am much more than my job. If I receive basic income, please replace my job ASAP!
And if I don't receive a basic income in a world where AI is capable of replacing all human jobs, then the problem is not AI, but the powers that be.
And if I don't receive enough, then again: the problem is not AI, but powers that be. And there are various solutions for that... and none of them are helped by me being anti-AI.
The limit is inflation.
Theyre never going to use that power to provide basic income for everybody. You cannot wave a wand to make them do that. Theyre going to use that power to accumulate even more resources and raw materials and impoverish/expel the "useless" labor.
Realistically our leverage over the powers that be is mostly about our labor and our ability to withdraw it.
That's not necessarily true. Technology gives more power to everyone. The rise of factories historically did not give more power to the powers that were at the time (the aristocracy), but instead lifted the masses from poverty (after some initial turbulent period).
> Theyre never going to use that power to provide basic income for everybody. You cannot wave a wand to make them do that. Theyre going to use that power to accumulate even more resources and raw materials and impoverish/expel the "useless" labor.
Contrary to leftist propaganda, the rich are not some cartoon villains and psychopaths that abuse people just for fun. The reason why the rich currently exploit the poor is because doing so provides them with significant material gains. Once they can obtain the same or even better material gains by "exploiting" robotic labor instead of human labor, the logical outcome is not further abuse and exploitation of other humans, but simply indifference.
> Realistically our leverage over the powers that be is mostly about our labor and our ability to withdraw it.
That is (partly) true, but only in the current economic system. Widespread human-level AI changes the equation, and not necessarily in favor of those who are currently rich. You are applying capitalist and socialist analysis to a system that transcends those terms (AI post-scarcity economy).
Did not give more power to everyone. At best you could say that it shifted power from landed gentry to industrialists. Even that switchover was less of a change than you'd think.
The practical upshot of the beginning of industrialization was very negative. The enclosure movement stripped families of their land to push them to work in the factories where they would never go willingly. The famines in Ireland and Ukraine were both triggered by redirecting grain to export in order to fund domestic industrial expansion.
The most brutal two wars in human history were that brutal precisely because industrialization made it possible.
>instead lifted the masses from poverty (after some initial turbulent period).
What lifted the masses from poverty wasnt the factories it was the labor movement which occurred in response to horrific working conditions and the reliance those factory workers had on mass labor (specifically coal mining which was incredibly labor intensive and a key economic chokepoint).
The whole of that is glossed over by right wing libertarian propaganda but that last part is particularly underemphasized.
>Contrary to leftist propaganda, the rich are not some cartoon villains and psychopaths
Do you look at peter thiel and elon musk or the robber barons and see anything else?
The few billionaires ive encountered personally were no less sociopathic but they kept it hidden better. Power corrupts. Immense wealth corrupts. That isnt a leftist thing, that's a human thing.
>The reason why the rich currently exploit the poor is because doing so provides them with significant material gains. Once they can obtain the same or even better material gains by "exploiting" robotic labor instead of human labor, the logical outcome is not further abuse
False. It just shifts the focus of their exploitation from human labor to natural resources.
They'll fight over oil and minerals and gas and water resources and at best leave us to rot (homelessness will skyrocket) and at worst they'll find some excuse to exterminate those of us they particularly dislike (Gaza serves as a model here).
The world economy's reliance on human labor has been the best inducement to peace there is. It's no coincidence that all of the countries in the world with lots of natural resources and no industry are the biggest shitholes and vice versa.
>That is (partly) true, but only in the current economic system. Widespread human-level AI changes the equation, and not necessarily in favor of those who are currently rich.
Human level AI (assuming it ever happens) will simply make the fight over natural resources that much more intense because labor will matter that much less.
You're living at the tail end of a relatively golden period in a country where labor was the economic bottleneck and natural resources were relatively plentiful. Venezuela and Angola and Iraq are models of what happens when that equation is reversed.
Nobody gives a shit about appeasing the people who live in those countries, their labor is virtually worthless. They are a model for how the rest of us will be treated in a world where human labor loses its value.
Compare the standard of living in 1850 vs. 1950. Even of relatively poor people. I rest my case. Technology is the main force that improves human wellbeing. There are of course also other factors, but they are less important.
> The practical upshot of the beginning of industrialization was very negative. The enclosure movement stripped families of their land to push them to work in the factories where they would never go willingly. The famines in Ireland and Ukraine were both triggered by redirecting grain to export in order to fund domestic industrial expansion.
Yes, that's what I mean by "initial turbulent period". Perhaps the same will happen with AI, but it will be worth it in the end. Don't give up prematurely!
> What lifted the masses from poverty wasnt the factories it was the labor movement which occurred in response to horrific working conditions and the reliance those factory workers had on mass labor (specifically coal mining which was incredibly labor intensive and a key economic chokepoint).
It was not one or the other. It was both. The rise from poverty would not be possible if factories were not developed. And I am not saying that in the AI world we would not have to fight for our rights. Of course we would. But the problem is not AI, just like historically the problem were not the actual machines in factories.
> False. It just shifts the focus of their exploitation from human labor to natural resources.
Exploiting more natural resources is the only way to increase standard of living of humanity. I am OK with that. Resources don't have feelings, and ecology is not more important than human wellbeing.
> The world economy's reliance on human labor has been the best inducement to peace there is. It's no coincidence that all of the countries in the world with lots of natural resources and no industry are the biggest shitholes and vice versa.
The reason why some countries become shitholes is mostly ideological (extremist political or religious ideologies take hold of the population). Every shithole country is non-democratic (communist, totalitarian, fascist, theocratic etc..). This is not a problem of natural resources. It is a problem of people, their education, their beliefs/ideology, or, as capitalists say, "human capital" is the main problem here. AI could help here too, especially with education.
But yes, if people themselves are largely ignorant and extremist, no amount of resources and human-level AI robots will help them make a well-functioning society. You could drop masses of AGI robots into Afghanistan tomorrow, and people will just use them to kill or oppress each other more effectively, instead of using them to start building an AGI utopia...
Chess is only valuable as an entertainment. So no one really gains anything from computers becoming really good at chess.
But with math, everyone in the world would gain from computers becoming really, really good at it.
There's lots of problems like that. Eg if we prove P != NP, that won't have much of an immediate effect either.
However, there's also plenty of problems whose solutions will have practical effects, some even immediate.
Sure. But do you know which ones they are? Or do we discover later that they were valuable?
Your argument would be 100x more convincing if you gave an example.
I will try: a super-compressor that made my 100Mb web app into a 5 kb binary bundle would immediately speed up my work. Can/will AI move human understanding or machine capabilities on this front?
A browser without security vulnerabilities would be wonderful. I think LLMs are already helping with this a lot, but a lot of complexity remains.
A right to privacy in society would be amazing (see the UN Declararion of Human Rights). AI is eroding this.
So I tried but I’m not very impressed with my list. Do you have one?
This has nothing to do with mathematics.
> So I tried but I’m not very impressed with my list. Do you have one?
Look into operations research. Or narrower, you can look at improvements in linear programming solvers and mixed integer linear programming.
(These are examples of areas that have seen mathematical improvements in applications recently. I don't think good AI has been around for long enough to contribute much to progress there, yet.)
Take the Navier-Stoke problem for example. Knowing that there are solutions that "blow up" probably doesn't have a lot of practical applications. Such solutions couldn't happen in a real system. But the process of finding that proof could result in increased understanding of how turbulence works, or new techniques for solving non-linear partial differential equations (which has a lot of applications in science and engineering).
Sure. And AIs can use ideas from AI published proofs in one domain to inspire other domains just fine. Nothing changes here.
AI’s solutions are like the answers section to practice problems at the back of a textbook. Answer is 42, so what?You have to attempt the problem yourself, that’s the whole point of the exercise.
As an engineer I’m happy to use AI for math. If I publish a paper that way, very common these days, I think it’s still problematic. My paper would include something I didn’t come up with and I don’t really understand.
I think this is a good time to properly discuss these things because AI is coming for everything. Mathematics and Software were just the first two.
Yes, you might not get new human capabilities. But your applications still work better.
I think the error you're making is that you're assuming these systems have the same mathematical capability as humans (or better). But that's not the case, nor would an informed prediction be that they surely will get there soon enough if technological evolution keeps apace. That would be akin to believing a hiker will reach the moon if they will just keep ascending the mountain. "But look, they are making such good progress!"
I'm not convinced of that.
It is one possible outcome but there are also other possible outcomes.
What makes you think these companies (and I'm not a fan of all their motives) are not interested in developing research? The motives may be self-serving, but it is undoubtedly and objectively accelerating research.
Part of the point of the letter is that it is quite possible to act in a way that is a net negative to research. The most obvious case is when the companies violate ethical standards in research.
The subtler case, the one for maths in particular, is what happens when you fail to follow well-established patterns for making maths research productive. Tao himself spelled out how that can look in https://mathstodon.xyz/@tao/117207856734787448 (which notably came before any of the news on Navier–Stokes).
Sorry, but this is backwards. Mathematicians are the ones coming to the table asking for money from the taxpayer. This is the context we are speaking in. Mathematicians speaking with the taxpayers who fund them. It's not a great strategy to get offended or speak from a high horse. If the taxpayer is not getting it, patiently explain why you think this art project should remain funded at the same level instead of spending it on something else.