Align AI and Mathematics–To Something Else
liorpachter.wordpress.com
liorpachter.wordpress.com
Not sure quite what animates the absurd hatred of one of the least greedy groups of people on the planet, but it certainly isn’t experience. To anyone with any, it just looks like absurd derangement.
All threads on this topic (i.e. Mathematicians and AI) are overrun by bots/shills/vested interests/etc. astroturfing for the companies.
It is just Propaganda and attempting to manipulate Public Opinion.
This just reads like a rancorous rant.
In any human group there will always be issues on how we treat each other dependent on time/context/culture. But while not condoning it, this issue is orthogonal to that of misaligned AI.
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.
The above is true for "misaligned AI" in all the Sciences. It is time the Scientific Community got together and sued the hell out of the AI companies.
It is called common decency/etiquette, having ethics/morals and not plagiarising/stealing others work.
No, there is no such requirement. Deal.
It is the accepted way to use each other's works in the scientific community. That is why citations/references/bibliographies exist.
There's never been such a consideration that one should not work on a problem that someone else is working on or has worked on. Nor do I think it's something that should be true. Mathematics exists and is supported to benefit society, not to pamper mathematicians.
That is not what i meant at all. This is your erroneous take.
In any scientific community when people work on the same problems, if they are aware of the others work, they usually cooperate/share their findings especially if the problem is a long-standing nobel-prize/fields-medal worthy one. If one builds their approach based on others then there definitely is a citation/reference acknowledging others contributions.
This is the ethical accepted practice since the dawn of the scientific age because "standing on the shoulders of giants" and building from there is how science advances.
EVERY.SINGLE.TIME. No shit, why would they want something disruptive to fuck with the way elite academia operates? And obviously I am talking about the "Master of the Universe" types atop the Ivory Tower. They have been A-OK, with privately-funded professorships, partnering with book publishers to milk students with single-access codes and never-ending "new" editions to their books, summer salary grants, partnering with all sorts of private companies as contractors, and/or milking on the tenure tit while the average adjunct lecturer at a local college/university struggles to make ends-meet and has 150 students in a lecture.
The author talks about his UC Berkeley years. That UC Berkeley that opened and operated for nearly a century as a public institution educating California's true middle class up until the 1960 Donahoe Master Plan, but slowly progressed to gate-keep "normies" out and pivoted to a model of elitism that is absolutely and catastrophically broken.
Fuck off.
The best example of this is James Stewart's Calculus textbooks. It is priced so high and made him so much money that he built a $24 million "Integral House"!
Where the money from your Stewart calculus book goes - https://www.mprnews.org/story/2011/04/18/where-the-money-fro...
The House That Calculus Built - https://www.fastcompany.com/3052267/the-house-that-calculus-...
PS: Just to be clear, the above has got nothing to do with mathematicians and their work. It just goes to show how bad the textbook publishing industry is in shafting students that you can make money off of them by selling centuries old well-known mathematics.
The poor altruistic AI companies like OpenAI will unleash math understanding and theorems for free for humanity!
- 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 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.
As i have mentioned in my other comments here;
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.
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.
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.
I am capable of having a conversation with you on a great many topics. What you aren't capable of, apparently, is forcing me to want to have the one you want to have.
As far as calling names:
"Your comment is ... disingenuous."
"you are being disingenuously clueless or cluelessly disingenuous."
and now:
"I had imagined i was interacting with somebody who could understand the larger picture"
... Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions. ...
The inference should be clear.
Hence we need to start with the underlying psychological motivations and then see how it explains observed behaviour. And it is not even complicated but somewhat obvious. The fact that you (many others) refuse to address this is why i question your (and theirs) motivations/agenda.
As regards your last few lines regarding "calling names" they are all only w.r.t. to the issues being discussed and are just rhetorical/descriptive judgements on your comments.
But because of the bad behaviour (plagiarism, going-behind-the-back etc.) and incentives misalignment, AI companies are currently not aligned with that.
There is also the structural problem of generating proofs at a rapid pace just because you can but then have no way for "proof digestion" which is the key in the mathematical process. See Terence Tao's writings - https://teorth.github.io/tao-web/ai-views.html
Why can't the mathematicians that value their own community remain aloof from what AI companies are doing. Can't they continue to take their time digesting proofs, gaining insights, and attributing credit to mathematicians doing good work. Here's how I perceive the situation:
Before:
- mathematicians digest current results and develop insights
- insights lead to new results
- new results give mathematicians an opportunity to credit those insights
Now:
- AI companies release a bunch of potentially uncredited proofs
- mathematicians digest these results and gain insights
- mathematicians recapitulate AI proofs in terms of their deeper insights and theory
- mathematicians give credit for these new insights and progress in understanding, even though the binary true-false status of theorems were already determined beforehand.
If the true-false status itself isn't real mathematics, then mathematicians still can do the real mathematics after the fact and continue to celebrate each others' work. The only thing they lose is the ability to attribute a human to deciding the true-false status, which isn't real math anyways (though maybe valuable for motivation). What they gain is efficiency. Every mathematician working towards proving NS won't blow up can now shift their resources to understanding why it can blowup.
Perhaps the letter is implying that the mathematical community itself will become misaligned with how mathematics is currently done. I'm unpersuaded it's entirely the AI companies' fault if that happens. AI may create a lot of temptations for individual mathematicians to become lazy, but that seems like something the mathematical community needs to resolve for itself. Every institution needs to take a lot of self-ownership here. I'm also annoyed about parents complaining about their own children being addicted to their phones as if it isn't in their own power to determine if their children have phones in the first place. I think this letter would be better directed at universities and journals. They should be holding their own institutions to account if they feel like they are adopting the mentalities of the AI companies and no longer faithfully executing the values of mathematics.
The truly valuable stuff is coming up with new ideas, that is, new techniques that allow for breakthroughs. That is rare, is done by only a handful of people in any decade, and is very, very hard. When you study a book on the history of math, you see the names of people that created brand new techniques which allowed them to solve problems no one else could solve.
But you still have that 99.9% that needs jobs, and they need to publish, but what they are doing can be mostly replaced by AI.
The specific situation with Navier-Stokes really highlights this. Mathematicians came up with the technique, but the AI managed to apply it faster than even the technique inventors. So it appears that AI is now good enough to be doing the workmanlike stuff, which is the bread and butter of a lot of mathematicians that are just trying to get their publications in so they are not fired.
I do think this creates real problems for the field and that some changes are necessary.
1) Keep the average mathematician employed doing redundant mathematics just to have capable humans around. Every now and then you get one of those mathematicians actually developing new ideas, but most departments will entirely be just for show. It's doable though. College sports is able to keep itself going along these lines (and I mean the track, softball, and polo type sports).
2) You get unemployed mathematicians who were still developing their abilities. And as a result you lose the institutions that generate the mathematicians that contribute new ideas.
You get to keep the handful of exceptional mathematicians that are developing new ideas, and that's survivable if you happen to be a Fields medalist. None of this really has to do with the AI companies aligning themselves to giving credit and developing insights. If AI companies became aligned to that, then the AI's would be replacing the Fields medalists, too.
For a nice introduction, see Why We Do What We Do: Understanding Self-Motivation by Edward Deci - https://thorprojects.com/2020/05/04/book-review-why-we-do-wh...
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.
Also see my other comment here https://news.ycombinator.com/item?id=49695418
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.
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.
My other comment is relevant here - https://news.ycombinator.com/item?id=49710169
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.