I think the letter is misguided. So what if the AI labs are misaligned to math?
- But they announced a result before a paper was peer reviewed! The horror! So what? The mathematics community can read the paper once it is written up.
- But their results they publish may not care about conceptual understanding and insight! So what? If that's the mathematics community's goal, then they should sift through the lean proof and reformat the ideas to make them more insightful and develop their own conceptual understanding.
- But they aren't bothering to do literature review to tell the history about how humans contributed to the final result! So what? If it's so important to the mathematical community, they can do that themselves and throw a party every Tuesday in the honor of Luis Martínez-Zoroa and wear jeans on casual Friday in honor of Buckmaster and Alpöge - the left leg for Buckmaster and the right for Alpöge.
An AI giving a definite result of an open problem doesn't decrease the mathematical community's insight or conceptual understanding. They are still free to continue doing their work and pursuing their goals. If it's really so bad, they can just pretend they don't know NS is solved and keep spending their efforts trying to prove it never blows up (or a hand full of them can try to blow it up from scratch).
Guess what! I spend no part of my life working on unsolved math problems. I read some books for pleasure. I work in a hospitable with sick kids. I help my wife raise our kids. My goals are misaligned with the mathematics community! I've done nothing to increase conceptual understanding and insight! So what?
The relevance can be seen from the second link above (the review of the book) which highlights the essential points viz. the importance of Intrinsic vs. Extrinsic Motivation. It is short enough that you can easily go through it. Then apply it to understand why mathematicians are angry.
I don't understand why you can't just articulate the point yourself. It took me a while to guess what you were getting at. Could it be the quote:
Our egos are powerful things. They want to believe that we’re each better than we are, and we want to believe that we’ve mastered our chosen areas – that we’re the best. Whether that’s objectively verifiable or just wishful thinking isn’t the point. If we want to motivate people, we’ll give them ways to become masters or, at the very least, allow them to feel competent in what they’re doing.
In which case, yes, there is a loss of that source of motivation. And that's coming for us all - or rather it's coming for some of us in most professions. Most people are perfectly average in their chosen areas and never got the satisfaction of being at the top of their profession. Yet we still go to work. I imagine it will take some getting use to for Fields Medalists, but I think the average grad student that happened to just love mathematics and never aspired to be a medalist will still like doing math. Magnus Carlsen still became the best chess player ever even though AI's have been better than humans for decades now.
Most sources of intrinsic motivation are unaffected by these developments in AI. It may be the case that extrinsic motivations may be harmed by all of this if there's less money for mathematicians in the math community. The letter lists a lot of reasons to like how the math community does math, and I don't see any real reason they can't just keep doing math that way.
Honestly, I still don't understand the point you're trying to make. Or the realization you're hoping I'll have.
The point viz. understanding intrinsic/extrinsic motivations and how they shape one's behaviour (i.e. SDT) is a nuanced one and so i wanted you to get an overview of it and then see for yourself how applicable it is to the OpenAI/Mathematicians Navier-Stokes issue.
I suggest you go through the SDT wikipedia entry and note in particular how intrinsic and extrinsic motivations are internalised and integrated into a coherent sense of self. This is true for all humans and worth a study to understand what motivates us to do what we do.
To repeat myself from https://news.ycombinator.com/item?id=49680925 "the AI companies behaviour, threatens everybody's Autonomy, nullifies their Mastery/Competence and robs them of Purpose/Relatedness/Belongingness. Nobody should accept this."
Mathematicians will keep doing research with or without AI. But so far they have been doing it in a free environment where there were unsaid-rules/ethics/morals being followed; the most central of which is "do not steal my work; if you use my work give me credit and compensation (if you make money off of it)". This takes care of both one's intrinsic and extrinsic motivation needs which is why all of our scientific practices, societal/economic rules etc. are setup on a system of incentives appropriate to their domain eg. for a researcher doing something original and winning the Nobel Prize/Fields Medal is far more important than making money while for a Business CEO making money is everything.
In the case of Navier-Stokes problem, Name and Fame were everything and Money was a lesser goal. OpenAI with their despicable behaviour have robbed the mathematicians off the above by going behind their backs, without giving them credit and simply throwing a huge amount of resources at the problem. This should not be tolerated.
I think that's just oblivious to what mathematicians actually care about when it comes to "name and fame." Basically no one outside of the mathematics community and its periphery knows who someone like Terrence Tao is, and those outside academia who do know who he is probably don't know one single result that he's proved. The most famous mathematician in America may be James Stewart for authoring the calculus textbook. Mathematicians do not get fame amongst the general public. They want fame within mathematics.
If the mathematical community identifies Luis Martínez-Zoroa or Buckmaster and Alpöge as the last human in the chain before NS was solved, and internally attaches their names to it, that will be enough for most mathematicians. Mathematicians write the textbooks. Some other mathematician is still free to consolidate OpenAI's proof into a better proof, put it in a popular graduate textbook, and gives it the name "The Martínez-Zoroa Theorem", and then whenever an undergraduate PDE textbook mentions NS, they say, "according to The Martínez-Zoroa Theorem...", and then Martínez-Zoroa gets a Fields Medal for his contributions to his theorem.
The case you're making seems to be that no one in the mathematics community would feel satisfied with that because at the end of the day everyone would know Martínez-Zoroa didn't solve NS. OpenAI did. And it wouldn't matter if Open AI paid to erect a 50 foot statue of Martínez-Zoroa in front of a museum of the history of NS in which every single mathematician who ever contributed anything to NS was publicized and celebrated and glorified and deified and credited and thanked. It wouldn't matter because maybe what mathematicians actually wanted wasn't credit for what they did do but that at the end of the museum tour the final display would talk about the human who solved NS. No matter how much credit you give mathematicians, no mathematician will now ever be able to claim "I solved NS" because OpenAI beat them to it.
If that's the case, then the letter is misguided. It's pretending that the problem is that AI is misaligned with the goals of mathematics. That's not the problem. The problem is that no matter how ethically it behaves, humans are going to be pissed that there is a non-human thing that is better at math than them. And I'm also pissed that we are creating this thing that's going to be better than humans at a whole bunch of things and it's going to cause a bunch of people to outsource their humanity to an AI. I'm pissed about that. But I'm not trying to pretend that AI can somehow eventually win me over if only it was more aligned with me when I know full well that its alignment has nothing to do with my loathing of it.
This is just making up stuff, setting up strawmen and knocking them down by oneself which is meaningless. There is nothing much to infer from the above verbiage other than "living in you own fantasy".
To repeat myself for the umpteenth time, the real issue is;
AI companies are stealing our hard-won lifelong research findings, which we were already sharing freely, without attribution/credit and building upon them without informed consent nor compensation.
The AI companies behaviour is the problem, not the technology itself.
Ironically, by engaging in these sort of shenanigans, OpenAI is effectively killing the "Goose that laid the Golden Eggs". viz. Researchers were giving away their hard-earned highly specialized knowledge freely to the models in the hope that it will help them get quicker to the result. But now everybody is going to lockdown their research findings and will stop sharing it with the models to the overall detriment of advancement of Science.
This whole discussion is basically a field demanding that their field be preserved for them alone to discover. No competition allowed besides the monks of mathematics.
You can invent whatever fantasy you like. I hope more honest people will read the letter (from the fields medalists and other endorsers) and consider it on its merits.
Here's the thing. I read the letter. I'm considering it on its merits. And it has very little. They made great arguments for why it's a good thing that the mathematical community operates the way they do. They could have made a good argument for why practitioners within the mathematical community shouldn't be seduced by the power of AI and should continue to build mathematics they way they do now. Ignoring AI as a tool, but perhaps not ignoring the results coming out of it, builds understanding and skill and develops humans. I'd be all for a letter that calls on humanity to not give up their humanity to AI tools. To not become lazy and overly dependent on them.
The letter makes no arguments why AI companies proving a bunch of results quickly at all affects the ability of mathematicians to do what they want to do. It's just a giant self-congratulatory list of all the wonderful things the mathematical community does and notes that AI companies aren't doing the same thing.
It's not enough for them that they are still free to pursue all the goals they outline in that letter to their hearts content. They want to make sure everyone else doing mathematics also sets aside their own goals and pursue theirs. I distrust AI as a technology regardless of alignment. And I've learned to just not use them and focus on the things in my life that matter to me. It turns out that I'm still free to pursue the things in my life that are meaningful regardless of the existence of LLMs.
The communique from the mathematicians when shorn of polite language is blunt viz.
AI companies are stealing our hard-won lifelong research findings, which we were already sharing freely, without attribution/credit and building upon them without informed consent nor compensation.
It should now be clear that the AI companies behaviour i.e. backstabbing the mathematicians and stealing their life's work is the problem and not the usage of AI itself.
I also pointed you to Self-Determination Theory(SDT) to understand Intrinsic/Extrinsic Motivations that drives Mathematicians (and also Scientists/Researchers/Knowledge-workers) to spend their entire lives in the pursuit of knowledge. From SDT it can be seen that the AI companies behaviour, threatens everybody's Autonomy, nullifies their Mastery/Competence and robs them of Purpose/Relatedness/Belongingness. Nobody should accept this.
A) According to the letter, mathematicians most value:
- mathematicians developing their mastery
- developing mathematics that provides insights and can be eventually synthesized down conceptually to textbook theories
- caring for students and fostering their growth
- human mathematicians getting credit for doing important work
- etc.
B) According to the letter, AI labs aren't trying to do any of these.
Conclusion) The result is that AI is not competing with them in their goals of
- mathematicians developing their mastery
- developing mathematics that provides insights and can be eventually synthesized down conceptually to textbook theories
- caring for students and fostering their growth
- human mathematicians getting credit for doing important work
- etc.
The upshot is that mathematicians still have autonomy to pursue those goals, develop mastery at achieving those goals, and remain part of a community of others pursuing them. The only mathematician who loses these sources of motivation is the one who embraces the use of AI and personally abandons those goals.
The real crisis will come if AI does try to align itself with the goals of the mathematical community and if AI turns out to be better at developing insight, training students, writing comprehensible textbooks, etc. Then the top mathematicians will truly provide little value to their community.
You have conveniently left out the spirit of the mathematicians communique and are only trying to argue its letter which is what makes me think you are being disingenuously clueless or cluelessly disingenuous.
To repeat myself again, the crux of the problem is;
AI companies are stealing our hard-won lifelong research findings, which we were already sharing freely, without attribution/credit and building upon them without informed consent nor compensation.
The AI companies are robbing the mathematicians by not involving them in major decisions about solving the leading/promising research problems in their domain. They are the ones who have identified the problems, its importance, promising approaches of attack etc. which have all been freely shared and which the AI companies have used to build their models.
For example, in the Navier-Stokes case, OpenAI could have easily informed the mathematicians like so, "hey, your research approach looks promising, do you have any objections to us using your research in our models and throwing a lot of compute resources at it so that we can finally solve it?" Every mathematician would have jumped at the chance since that is what he was doing anyway but at a small scale and far slower pace.
Instead OpenAI went behind the mathematicians back while building upon his and others work without attribution/credit nor compensation. This is plagiarism, cheating and despicable behaviour and should not be tolerated by anybody.
Yes. Everything I've said and want to say is about this letter.
Let me try to summarize this discussion in a way that an overly obsequious AI would never dare:
- I argue that the arguments in the letter are bad.
- You mysteriously assign me homework on the topic of human motivation.
- Confused, I reiterate the points made in the letter, and I make arguments against them
- You ignore my arguments, call names, and then defend the letter by making points that the letter doesn't make.
- I ignore your points, because they aren't the points made in the letter. And my original post was about why the letter was misguided.
- You call names. You feel like your points are valid. You then claim that the letter is valid because your points are valid.
- I keep disagreeing with the letter.
- You call names again, because why am I so obsessed with talking about the letter. I must be an idiot, or an evil lying phony, or an evil lying idiot-phony because I keep bringing the conversation back to the letter on a thread about the letter.
I had imagined i was interacting with somebody who could understand the larger picture given only the key points. Apparently that was wrong and i need to spell out every detail.
I didn't call you names but implied that you had an agenda and were masking it by trying to debate the literal words in the original communique from 25 fields medalists which was written to be politically correct. Apparently asking you to "focus on the spirit and not the letter" of the communique was too much. So i highlighted it, repeated myself three/four times and yet nothing seems to have worked to aid comprehension.
I point to a most important and relevant psychological theory viz. SDT, which explains how one's behaviour is influenced by intrinsic and extrinsic motivations and ask you to think about how they might explain why the mathematicians are angry at the current situation of AI companies shafting them. I even used specific terminology from SDT to highlight its applicability in this case. Apparently this is too much "home work" (and needed thinking) and one needs to spoon-feed everything without assuming any human intelligence/curiosity/initiative at the other end.
It seems my attempt to show the larger context and situate it in actual psychological research has been of no avail though not for want of trying.
Shouldn't the AI companies know by now that all mathematical knowledge belongs to the mathematical community? Hopefully this letter knocks some sense into them.
Spot on. They now feel threatened that there's multiple challengers to their intellectual monopoly. This is their "whaaahhh... whaaahhhh... private company bad, now," but where OK when Halliburton, Boeing, General Dynamics, Monsanto, Open Society Foundation, Tides Foundation and many other shitty and scummy private and so-called "non-profit" entities were funding their shit. Now their entire business model is changing. Is not that it'll completely collapse, it's just changing and they are throwing a bitchy fit.
The opposite of malicious is not honest. Nor do I see how motivations fall on a binary. The user submitting an AI proof can be honest, or malicious, or careless, or overzealous, or incompetent, or a whole bunch of other things. As far as the AI's motivations, "malicious" is just as much an anthropomorphism as "honest" and both descriptions are absurd. Nor do I really understand how any proof, regardless of its origin can be called honest. I think their definition of a "malicious" proof makes sense, but I don't see at all why an AI generated proof necessarily meets that definition.
What I'm not seeing reported on much is if the result reveals any new techniques or ideas that advance mathematics - which is what we usually hear is the reason to work on these problems. Or does the resolution of NS just add a fact to the list without any new understanding.
My understanding is that it’s proof by counterexample, so the main thing to study would be the implications of the counterexample. The technique used to find it sounds like a lot of brute force. But I’m not a mathematician, and maybe the AI used some clever techniques to narrow in on it.
Boo hoo. OpenAI got the result only days ago. It makes perfect sense for them to take the win in marketing, and it's fine if they take a few months putting together the paper and present it more productively later. The scientific community didn't get the result themselves, so it isn't theirs to be bossing everyone else around about.
I don't care much for AI myself, or smart phones either, for that matter. I would be content if NS remained a mystery for another 100 years - or forever. But goodness, does the "scientific community" need to take a deep breath and count down from 10.
Was it a marketing win though? My takeaway is: if you're doing groundbreaking work with openAI's models and they find out, at best they'll outspend you and scoop you. At worst they'll steal your chat history.
That's a completely different matter. And does it matter to my point if they were successful or not? That's ex-post analysis. It seems clear that ex-ante, they wanted this to be a marketing win. The original poster complained that they wanted a marketing win.
My point is: why shouldn't they want a marketing win from this. What obligation does a non-academic institution have to follow the traditions of academia? Its result doesn't belong to academia. And if academia wants to subject OpenAI to their own internal processes and give them marching orders, it just isn't going to work and maybe - who knows - it'll even further erode their own legitimacy. Does anyone actually believe that NS would have been resolved in the 2020's if we lived in a parallel world where LLM's were never invented? Would Buckmaster have gotten as far as he did without LLM's doing a lot of the work for him? We can complain about AI companies contributing to mathematics, but are we complaining about Terence Tao using AI in his research? When Tao publishes something are we all going to go to war against him because maybe other mathematicians' prompts went into training the AI that Tao used?
In the hypothetical, when he becomes famous, someone making prints for $20 is $1,980 less than what he would be getting now so the damage is $1,980 per print.
Both the purchasers of the print and the photographer are part of society. Under your proposal, some purchasers will spends $20 on a print that they would of have been willing to spend more than $2000 for, so the purchaser gained at least $1980 of excess value while the photographer gains $20. In your view, how is a purchaser of art gaining $1980 of value helping society?
The cost of buying the encyclopedia becomes disposable income to be used on other consumer goods. In that sense in shows up in lots of other companies profit-and-loss statements.
And at the speed at which the solar system is orbiting the galaxy, I don't know that it would even look much like like the planets are orbiting the sun.
> The difference with the Copernican stuff is that you can fly a satellite (e.g. Voyager) to the edge of the solar system, look back, and see the planets orbiting the sun.
Or you can put the satellite in the back of a truck and back the truck out of your garage and see the sun orbiting the earth. Yet it remains sane to put anywhere in the center depending on your context.
If you have a reasonable grasp of Newtonian gravity you would also be unable to conclude that. A wrestler flailing a skinny guy around, from the POV of the skinny guy, is still definitely not the skinny guy flailing the wrestler about. I don't see what's to argue here. Given all facts, then there is no POV that results in the conclusion the sun goes round the earth. Just like how there's no placement of the camera that results in you claiming I'm pushing the earth away.
I agree with the example of human agents because we can acknowledge concepts like will, choice, agency, etc. But none of those ideas are present in Newton's laws of motions.
Will, choice, and agency are unnecessary for explaining the example. It can be described simply by the forces exerted. The locations of the observers or sensing equipment matter little in this case, though they do become problematic when attempting discern whether heliocentric model fits unaided observations from a planetary surface.
Am I wrong to think that because equal and opposite forces are always present, names have to be given to phenomena that are not present in the formal math itself?
- But they announced a result before a paper was peer reviewed! The horror! So what? The mathematics community can read the paper once it is written up.
- But their results they publish may not care about conceptual understanding and insight! So what? If that's the mathematics community's goal, then they should sift through the lean proof and reformat the ideas to make them more insightful and develop their own conceptual understanding.
- But they aren't bothering to do literature review to tell the history about how humans contributed to the final result! So what? If it's so important to the mathematical community, they can do that themselves and throw a party every Tuesday in the honor of Luis Martínez-Zoroa and wear jeans on casual Friday in honor of Buckmaster and Alpöge - the left leg for Buckmaster and the right for Alpöge.
An AI giving a definite result of an open problem doesn't decrease the mathematical community's insight or conceptual understanding. They are still free to continue doing their work and pursuing their goals. If it's really so bad, they can just pretend they don't know NS is solved and keep spending their efforts trying to prove it never blows up (or a hand full of them can try to blow it up from scratch).
Guess what! I spend no part of my life working on unsolved math problems. I read some books for pleasure. I work in a hospitable with sick kids. I help my wife raise our kids. My goals are misaligned with the mathematics community! I've done nothing to increase conceptual understanding and insight! So what?
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