> math problems are really there to solve a real world problem
I think this is totally wrong. Math problems are almost by definition problems with a particular theory. That theory might be inspired by the real world, but the problem itself is purely theoretical. I can't think of any theoretical problems like this that actually support a practical problem, as opposed to being an internal knot in the theory that indicates something is wrong with it. Not to say that cannot happen - certain optimization problems were historically actually hard to solve and solving them helped us to genuinely optimize a real thing (rather than just explain why the answer we already had was correct, which is much more common). In particular, none of the millennium problems have anything to do with a "real" problem, including the Navier Stokes one.
Agreed, though for the hn audience I want to advocate a bit for the utility of mathematics. The development of applicable mathematics has often not been through the direct means of solving an open problem. It has however often depended on theory which was developed for the purpose of human understanding. It is difficult to pull concepts out of the aether on demand, but when there is a general milieu of human understanding economic applications can be developed in post.
I have in mind GPS, cryptography, numerical fluid simulation, lasers, etc…
Bioinformatics, the underpinnings of llm's in the theories conceptualizing high dimensional vectorspaces, material sciences, MRT's, signal processing..
don't think one gets far with with calculus only there. Probbly also the inner workings of CPUs and GPU's, CAD-kernels..
Probably there is so much domain specific knowledge that makes use of quite some advanced mathemathesis that most just don't know. The sentiment of "not much more needed then calclus" that appeared in this discussion might be explained by this. Curious if people from some of these or other fields are around that could share some mathematical applications they deal with in their work?
Did the theoretical math lead to the invention of GPS, cryptography, lasers, etc? Or did we encounter a real physical problem, then we found that someone had done some theoretical math before that would be useful for this application? If we run into a real physical problem today, can we just have AI invent the math on the spot to solve the problem without a human having done the theoretical math in the past?
My point is that when the consumer application became apparent we already had the required concepts to build the technology on top of. In mathematics it still hasn’t happened that an LLM system has invented a conceptual framework. In most if not of the major AI announcements they’ve worked within known frameworks and assembled ideas across frameworks.
Moreover, it’s not clear that if (and when as I believe) they do, creating technologies with no human understanding of the framework is possible or desirable.
Why wouldn't it be desirable? Is knowledge beyond that a child can understand undesirable because the child can't understand it? I think not, same with anything AI figures out that we can't easily understand ourselves. If GPT-10 Quasar grinds tokens out for 6 months and out pops a warp drive, and even it's executive summary is difficult for anyone to understand, do we get out the pitchforks and burn the data centers or do we go "Sweet, we've got warp drives!"
Why is it always a false dichotomy between two ridiculous extremes? Maybe inventing some dangerous technology benefits from human understanding for a bunch of obvious reasons, like human beings being responsible it goes well?
It might. It might not though. Would a 1300s superintelligence advocate for heliocentricism in the face of all institutional players advocating for geocentrism, or would it create the most refined epicycle model imaginable? I’d guess the latter.
You will find they were inspired by the NP-hard knapsack problem, and inspired a bunch of later research that led to RSA.
I think the tapestry of history would suggest the answer to the question "is math responsible for this invention" a lot more complicated than it appears. For lasers, Einstein proposed the idea based on purely theoretical physics, and it was made possible in 1960. Is that "theoretical math leading to the invention of lasers"? Surely he was at least relying on a lot of additional theoretical work for that. On the other hand, much theoretical that came out of Bell Labs were responses to needs for better vacuum tube technology, better amplifiers, etc., which were a deep collaboration between theory, practice, and tradesman with a strong intuition for how to build with various materials and at varying scales.
>If we run into a real physical problem today, can we just have AI invent the math on the spot to solve the problem without a human having done the theoretical math in the past?
This depends on unanswered questions on what math actually is and it's causal connectivity.
Imagine we have problem A that needs to connect to math solution Z.
The problem is the A -> Z route can only occur in polynomial time in which you need to burn the visible universe to solve. So, that itself is not workable.
As you look at the problem space of A there are a potentially infinite number of paths you could take in the problem topology so again you'd have to brute force the path... mostly unworkable on a lot of problems.
The breakthroughs tend to occur when somewhere in between A and Z there is another mathematical construct M that can link them together. M was very likely discovered something so completely and wildly different you would never link them by brute force. By M existing you narrow the problem space to NP time. M might have sat in the toolbox 100 years unused before that point.
If this is the viewpoint of mathematics, why does it make a difference that human or AI solve it? And forget about "understanding", because "understanding" in mathematical sense means in a very narrow way: top experts of math in certain field would understand and accept it (my estimation is that ~100 people in the world would understand Fermat's Last Theorem proof). Mathematicians could spend the whole year digesting FLT and "convince" the public that this is correct, and for most people (including math PHDs and professors), FLT is correct because some smart people say it is.
As an aside, it's amusing that this conversation is a re-statement of a main point in TFA:
> However, math problems are really there to solve a real world problem.
vs
> That theory might be inspired by the real world, but the problem itself is purely theoretical.
From TFA:
> In my essay The Two Cultures of Mathematics a quarter of a century ago, and which can be summarized by saying that there is a spectrum of attitudes in mathematics to the relationship between problem-solving and conceptual understanding.
The author thinks this letter was choosing only one of them as the "right" approach whereas the better stance is "porque no los dos?"
I only just skimmed the referenced essay, but a priori I don’t think “problem-solving” as Gowers uses it has anything to do with real-world practicality. The problems under consideration are entirely theoretical, regardless of which “culture” a mathematician belongs to.
You're right, but I also may have quoted poorly to give the impression that the first post was only about real-world problems. It goes on to point those out as an infinite source of theoretical problems, which sounded to me like an emphasis on the problem-solving culture.
The reply to that seems to say there are theoretical problems not necessarily connected to real-world problems, which I interpreted as an emphasis on the conceptual understanding aspect.
I may have misinterpreted either or both of them though!
If we are talking about pure/theoretical mathematics, then the vast majority of the problems people pose and solve have at best tangential relationship with applications, and a big part even is only related to other math problems. Of course quite a bit of mathematics historically emerged as this kind of intellectual endeavour to find applications later, but there is neither a way to predict which ones are that and how to get them, nor is there indication of this thing going on to the same proportion nowadays as it was, considering the mathematical production is much higher. In mathematics human mathematicians have to decide which problems matter, it does not come from somewhere.
Solving "real" problems in theoretical mathematics (as in problems directly related to applications) is a very small proportion compared to the vast majority of math work that does not. So if we are discussing about the future of mathematics as a field, we have to understand what the field of theoretical mathematics is actually about.
"The FT’s Gillian Tett reported that a senior financier’s New York firm now seeks out humanities students, because “AI-native” Stem graduates are entering the job market with “alarmingly shallow ideas”."*
I don't advocate for the dichotomy of stem and humanities. A good counterecample from the 20th century being Ernst Mach (Mach-speeds are named after him) and his work in phenomenology ("bodies do not produce sensations, sensations produce bodies")
Your incatation of contextless 'technological progress' still kinda calls for a quote like the above
Technological progress is not bottlenecked by most of the millennium prize problems or erdos problems per se, or most of the rest open problems in theoretical math, ie that merely knowing the solution of them will help applications in some manner. I doubt the solution of such problems has any direct effect on technology progress at all, at least in any deterministic, foreseeable manner.
In fact, the relationship between theoretical mathematics and "real physical problems" is bidirectional, as in "real physical problems" informs to some degree some problems that may be interesting to research on in theoretical math, and at the same time pure mathematical research that is developed completely independent may find applications at some point. And even theoretical mathematicians working close to applications are mostly dealing with problems not directly addressing applications. Eg maybe they study properties of a certain function that arises often in application without any view to solving a specific "real physical problem" with it, and somebody after may find that useful for some application after some point, but that could be one out of 50 papers (random number) and it is hard to predict that. There is of course some work more related to specific real problems, but that's most often not what theoretical math is about, and not what these new developments with erdos problems, navier stokes etc are about.
So what could (in a chaotic sense) have effect in application is mathematical theories developed along the way of solving these pure math problems, which brings us back to the question of what happens if we remove this friction and if AI can do more than construct examples and proofs, ie actually build theories (autonomously or humans+AI). If anything, it is through building theories that mathematical progress germinates applied sciences, as this is the process that develops mathematical tools that can be taken up later, including whole mathematical fields. Building mathematical theories is a heavily social process, and it is the community that basically decides which directions are important to follow.
Technological progress is bottlenecked by the fact that there are many mathematical problems for which currently there are no known practical methods of solution.
Because even with supercomputers the equations that describe many physical systems cannot be solved, research and development is still based on a lot of empirical methods, i.e. things must be physically built and measured, because mathematical computations cannot predict their properties with sufficient accuracy.
So if some miraculous algorithms would be discovered for the approximate solution of the systems of equations that are insoluble for now, that could accelerate technological progress a lot in certain domains, especially for the discovery of new materials or chemical substances with desirable properties.
AI can also introduce its own "bad friction", or it (ppl?) can bypass good friction without necessarily directly be removed by ai, eg bikeshedding, slowly pivoting towards directions and problems that ai is better in tackling, because that can produce these accelerated results vs fields and problems that ai may not be able tackle as well and thus the output there is poor, demotivating people from following these fields and missing important insights from them. Of course this could have the opposite effect, depending on which direction the whole hype can go, or not happen at all if ai will be able to tackle everything equally well.
>Humans only invest in solving problems that matter one way or another.
Fermat's Last Theorem was one of the most famous open problems in math for centuries, and it has no direct applicability to any tangible problems here in the physical world.
Oh some few. No right triangle with rational sides has area equal to a perfect square depends on N=4 for instance.
And it can be used to form other theorems that are terribly actionable. Every elliptical curve over Q is modular, which has consequences throughout number theory.
But yes, none of those are very tangible, until applied to problem solutions that are tangible.
Not really. I can't imagine a realistic solution that would affect, say, how we actually model a real fluid. Hypothetically we could find out that a whole class of real fluids are not modelled by Navier-Stokes at all, but I don't think that's remotely likely, nobody familiar with the problem expects it.
None of the things you mention are guaranteed to increase the probability of correctness. You can run the LLM output through as many deterministic programs as you like, but "the query plan runs in acceptable time" is not something you can verify with such a tool. Nobody knows how the LLM does it, so they cannot know how to make the LLM do it better.
Even if the query plan was not generated by an llm, you can't verify it will run in an acceptable time. This is one of the biggest unsolved problems in databases
From a completely technical perspective, we have a rough idea how the LLMs work, and improving a system requires measuring outcomes and you don't necessarily need to understand the mechanism.
EXPLAIN ANALYZE against data that's similar in size to prod checks a query written by an LLM as good as anything we can write... but, yes, you're right, we still didn't solve the halting problem - neither the LLMs.
Work is a necessary evil. If it is not necessary, then it is just a regular evil. There are no credible arguments that going to the moon is necessary, or supports some other necessary goal.
Of course by work, I mean work directed by somebody else to serve their ends, in exchange for money to live your own life. If we could afford to have people work five hours a week and still maintain a functioning society, then surely it is a moral obligation for us to do that. If you decide you want or need to do some kind of voluntary work to keep your mental health intact, so much the better. And if those happy people want to voluntarily commit some of their energy to going to the moon for no reason, then good for them.
I really cannot imagine taking your position. Working less is the pretty much the only thing we should be putting energy into.
Good for you. And I hope you never get laid off, burned out, or anything else.
I however do not get my fulfillment via work. I work to live, and I do [mostly] enjoy my work. However I have a very long todo list that I'm not getting done in part because I don't have the time to work on it (and in part because I don't have the money for the tools/parts I need)
> If we could afford to have people work five hours a week and still maintain a functioning society, then surely it is a moral obligation for us to do that.
I wonder what this would look like. I feel like nearly all of mankinds greatest achievements are due to our current structure of employment or at being forced to do something at the behest of someone elses ends.
> I feel like nearly all of mankinds greatest achievements are due to our current structure of employment or at being forced to do something at the behest of someone elses ends.
like out-of-control global warming, depletion of freshwater reserves, destruction of soil, mass surveillance, extremely uneven distribution of resources. I mean all previous innovations which were supposed to allow working less somehow never materialized in working less, and the quality of life improvements are greatly questionable, basically keeping the production-consumption machinery takes up all the surplus it produces, while depleting the resources we have.
The great achievements we have are much like the Moai statues on the Easter Island.
> I mean all previous innovations which were supposed to allow working less somehow never materialized in working less, and the quality of life improvements are greatly questionable,
The bone evidence of pre-Columbian Indians in America is one of periodic starvation. For the colonists, the bone evidence is one of extremely hard labor and short lives.
America's poor have a higher standard of living than medieval kings.
You could enslave someone and yet give them a greater standard of living than a medieval king. That would not mean that it is acceptable, or even better.
I suspect most of them would find being my slave better. By modern standards it would not be acceptable or better, but all evidence I've seen suggest most people in medieval days would consider then loss of freedom not that big of a deal (partially this is about how little freedom many of them had)
> I feel like nearly all of mankinds greatest achievements are due to our current structure of employment
Woah, really? More than cheap fuel, scientific research, social welfare, political work towards peace?
The only good thing I can think of that is actually directly caused by the way we employ people is that some things (delivery, food) are very cheap, cheaper than they would be if people worked at a sustainable rate. But that comes at the immense cost of the health and wellbeing of a vast underclass of people.
Nobody is talking about slavery here. You need to do something to feed yourself, otherwise you are making somebody else a slave to feed you. As a society there are some very disabled people we can accept this for, but when someone isn't supporting themselves that is enslaving someone else.
Not sure this reply makes much sense. I said that if we (humans) become more productive, i.e. that we can produce sufficient food/water/shelter/whatever with less effort, then the first goal after that should be to reduce the amount of drudgery the average person has to put up with, rather than (say) keeping the amount of drudgery the same and spaffing a bunch of fuel into space. I'm not sure where in that you see someone being enslaved to feed me.
Incidentally, we tolerate this kind of "slavery" just fine when we charge people rent for basic shelter. The cost of maintaining the asset (the house) is far less than the cost we actually charge people, so in your sense when I pay rent I am being enslaved by the landlord to support their lifestyle.
Finally, you brought up slavery. The guy I'm replying to just said "work is good". I don't think it's good that we make people destroy their bodies in amazon fulfilment centers. People know what's good for them, if they want to do work let them do the work they want. But to say "no, you have to do the work I want you to do" under the hypothesis that we have plenty of stuff to go around (and we absolutely do) is just sick.
Right, and as a consequence lots of very important software (orders of magnitude more important than tailwind) does not have full-time employees. Good for them if they can manage it, but it's a gravy train.
Given how hard it is to build any form of financially sustainable model around an open source project I think we should actively celebrate anyone who manages to build a model that works, not dismiss it as a "gravy train".
I really just think they got lucky, I don't see anything to celebrate. It's like celebrating one of your friends winning the lottery - good for them, but it's not really an indication the system is working well at all.
Their point was more that, if every 'weekly download count after a new release' (or whatever record) is consistently being broken on each new release due to generally increasing popularity, then it doesn't make sense to imply causality between the messaging around this particular release and its already-expected record-breaking status.
But that is perfectly consistent with the downloads incrementally going up all the time. It doesn't say anything about whether the recent policy changes increased that rate.
Excuse you? What I originally said was "I don't understand your comment". They posted a clarification, and the clarification still doesn't make sense. No, I haven't read the download numbers. How is that going "well akshually"?
No, it doesn't. If the claim is just that download numbers are not consistently trending upwards, they should have just said that. I would have no trouble understanding that. What they actually said is "Libreoffice didn't say the numbers were going up, they claimed a specific record." Well, so what? Nobody said Libreoffice said that! The OP said that, because if it's true, then it's not surprising that the latest stat (release or not) is the highest ever. Nobody in the thread so far has said anything that contradicts "the numbers were going up anyway, therefore the record might not be to do with the AI policy".
The numbers graph is spiky and I can imagine you could argue either way that they are generally trending up or not. But that's irrelevant!
This objection is completely meaningless unless the download numbers follow a consistent upwards trend. You are simplifying the new record to a boolean, but most people still find meaning in extraordinary events happening, even if they follow a general trend.
So I fail to see this discussion as anything but sophistry until anyone demonstrates that the download numbers are totally ordinary. It's typical HN contrarianism without any value, because it's enough to argue for the possibility of something, even when the data for checking it is easily accessible.
I think the confusion is that robrain somehow understood smokel's objection as being "all-time total downloads obviously increase over time, so this is meaningless", rather than what smokel actually said which was "the number of weekly downloads has simply been increasing over time". Which is why robrain quoted LibreOffice's "This is the highest number of downloads in the first week”, to counter the idea (which nobody suggested) that the record was just about all-time cumulative downloads going up.
That's then what tempfile was questioning how it contradicted smokel's claim (because it doesn't, just an imagined claim). Your points, that if the number of weekly downloads isn't actually consistently increasing then this could still be meaningful, are valid - but irrelevant to tempfile who was wasn't arguing that this is meaningless; you should argue that to smokel instead.
It isn't relevant whether they were promised that. Indeed I think the assumption must be that they were not promised that, since otherwise the author asking if they were would not make much sense.
If OpenAI did use the conversations from Buckmaster and Alpoge, then not disclosing it, explicitly, is plagiarism. If they planned to use that plagiarism to pressure the authors to publish, that is even more unethical. What the terms of use say does not make it any more or less ethical.
If you use their consumer subs, you get subsidized tokens in exchange for them having full access to your data. Those are the T&Cs. Have something secretive? Get a commercial sub with zdr.
(And if memory serves, there is also the opt out from training on consumer subscriptions). Its not plagiarism if you make your data available for the purpose of training their LLMs. It is you giving away your IP for some tokens.
That's absolutely right. Why the downvotes? If OpenAI are using but not acknowledging the work of others that's plagiarism. If they don't know for sure, but aren't performing due dilligence to make sure they aren't, that's also plagiarism.
It's not as simple.
All our chats are being used by both labs for their future product (unless signed by ZDR).
Where should the acknowledgement begin? Who should be acknowledged? The whole world? All the 2B users of AI?
If I know person A is working on problem B.
I am free to work on problem B too. Why should person A be limited to working on it.
I can imagine excuses for unknowing plagiarism in this case. What is described in the article seems much more serious: a research program that was only initiated following reports of the author's similar program. In this case no excuses of "I didn't know" can apply, it is not like this revealed some obscure work from the 1980s nobody could reasonably have foreseen. And as far as I can tell this program was only really initiated to apply pressure to the researchers, without their knowledge/consent. It looks very weird.
Your comment was greyed out when I saw it earlier, maybe you missed some downvotes?
About the plagiarism issue, I model it as OpenAI being an advisor and their AI a PhD student. If the advisor puts their name on a paper behind that of their PhD and it turns out the PhD copied the text of the paper from somewhere else the advisor is also responsible of plagiarism, not just the student. The least the advisor can do is withdraw their authorship from the paper.
But, yeah, point well made: it could be much worse than that. Like an advisor instructing a student to copy someone else's paper.
I think "greyed out" just means "0 points or less", so if you get 1 downvote without any upvotes it'll be greyed out. For instance your initial reply to me is now greyed out, and I have since observed a few upvotes and downvotes on my original comment (the downvotes apparently from people who aren't willing/able to justify why).
Personally I don't like thinking of LLMs like a PhD student, because most PhD students remember where they learned things from, while LLMs essentially cannot. I think of it a bit more like someone using a search tool carelessly. Although in this case it is apparently more like deliberate misuse than carelessness.
Isn't the reason obvious? You said the jury is supposed to lack domain knowledge. Domain knowledge apparently includes knowing the possible sentence. The given example is a case where knowing the possible sentence would alter the verdict given by any reasonable person. Therefore the jury should have knowledge of the possible sentence. What is unclear about that?
What's surprising about this is that you can get the bullshit machine to produce correct externally validate citations. It's not particularly hard either—it's one of the first things you build when you give an LLM access to a body of documents/search. So for a large public service to whiff like this is certainly a stain on their credibility.
On the other hands it's a boost to their credibility that they make their mistakes easier to evaluate than their competition does. It would be worse if they had a similar error rate without openly providing references. Kudos to Perplexity for including more empirical attack surface.
By training it on a whole bunch of examples with valid external citations, to the point where it's able to hallucinate something that's valid. Of course, it won't always work, which is the point of TFA.
I don't think this is an answer. I'm basically claiming there is an uncontrollable error probability, and I think you agree with that. The person I'm replying to implies it can always be reduced (maybe even to zero).
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