Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0].
Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a painting could.
He also criticized the public's craze for "rushing" into it, and complained that this technical "progress" was weakening the arts.
I have listened quite a few interviews with Tao and I see him being very careful about criticizing AI. He very often emphasizes the usefulness of it. Where he is critical has a lot of merit. One of the points I clearly remember him saying that having AI be able to solve many of the open problems, regardless of how important there are (there are many open problems that are not that important) greatly reduces the problem space for mathematics students to give new problems to work on.
In a parallel thread omnicognate correctly pointed out that for AI companies it's a direct commercial loss to pour all this money into bruteforcing the solutions to these problems, and that a lot of times the solutions by themselves are not directly commercially valuable. They are doing it for stock price, trying to lure in private capital in preparation for IPOs.
Their models are good, but they are not the moat because Chinese models are good too, so what they are doing, in my opinion, is more harm than good. Mathematics is a science by humans for humans.
> One of the points I clearly remember him saying that having AI be able to solve many of the open problems, regardless of how important there are (there are many open problems that are not that important) greatly reduces the problem space for mathematics students to give new problems to work on.
The crux of the argument perhaps. It suggests that too many people are currently studying mathematics without making much progress.
>I have listened quite a few interviews with Tao and I see him being very careful about criticizing AI. He very often emphasizes the usefulness of it.
This is tiresome. People should be able to flat-out criticize AI without the implied need to justify themselves all the time or "be careful". Its almost like AI has a trillion-dollar agenda backing it, to the point that you have to add a careful "its really great! But there's this little issue..." for any criticism.
Even those who are very pro AI should have the intellectual honesty of admitting that there are very valid reasons to criticize AI.
Based on the amount of low-effort criticisms out there, clearly nobody is afraid of "big AI". Tao seems careful about his critiques of AI because low-effort off-the-cuff criticism can lead to all sorts of future problems/hypocracy.
That's not really addressing the same issue though. I'm saying that there is a pressure to preamble any (good or weak) criticism of AI with an Apostle's Creed of AI positiveness, reassuring the reader that what follows isn't blasphemy against AI (to borrow Huang's terms).
I see where you are coming from. I imagine LLMs will follow the same feedback lifecycle as other groundbreaking tech. Most legitimate iPhone 1 complaints came paired with a few positive messages to the devs and engineers. Years later, after countless improvements to the hardware and UI based on user feedback, now it's just complaints.
Both of Baudelaire’s criticisms were reasonable, and the same thing happened again when AI image generation showed up. You think the opponents look ridiculous because you’re viewing the history from the winner’s side.
As for “the public,” people had a real demand for photography as a way to record things, which is also why it won. There is no comparable public demand for proving Fermat’s Last Theorem.
> There is no comparable public demand for proving Fermat’s Last Theorem.
It's a capability demo, not the main point. There is plenty of demand for intelligence on tap. These flashy results are necessary though, otherwise people keep claiming AI is just hype, it can't do anything etc. So they need something to point at. And it seems to be working because the anti-AI narrative has changed from the previous stance that it's just the new NFT that will simply go away to how it will replace human intellectual work and will be bad for artists and desk workers.
I think there's a difference between "photography will change art--we need to be ready" and "photography will change art, therefore stop photography."
There is no doubt that AI has changed the practice of mathematics, just as it has changed the practice of software engineering (and will soon change almost every intellectual job).
Trying to deal with change by saying, "please stop the change" is foolish, IMHO. Mathematicians need to redesign the discipline with AI in mind. But I get that it's easy for me to say that and hard to actually do.
> I think there's a difference between "photography will change art--we need to be ready" and "photography will change art, therefore stop photography."
That wasn't the critique. The statements then were that photographs weren't actually art at all. They were the results of specialists with skills but not 'art'. Yet the photograph as a product was displacing real art in the marketplace.
Genuine Art versus Mechanism, from 1901, (https://www.jstor.org/stable/25505621) is another article that I read a few years ago that other people might find interesting.
Tao doesn't go as far as Baudelaire, but there are some similarities. In particular, Tao has criticized that AI is not being used to create new interesting conjectures, and that the rush to prove old conjectures is not giving human mathematicians enough time to carefully analyze and understand the proofs and the methods used in those proofs.
My answer to both is the same: nothing stops mathematicians from doing both of those things, with or without the help of AI. And we all understand that it will take time to do that. But complaining about the dawn of a new era of advancements seems counterproductive.
But the point is your original analogy with Baudelaire now just boils down to "both of them were critical" which is quite shallow indeed.
It's especially annoying given that many people are making repeat Baudelaire's critique of photography (or Socrates critique of writing) in the context of AI and the declaration is interest because it's not that.
There are no similarities whatsoever, other than them having opinions on a new tech that affects their field.
> nothing stops mathematicians from doing both of those things
Actually yes, and they explain that pretty clearly in the letter. These problems have been used as "goals" not because the solutions are necessarily worth it, but because they set a clear direction whose process would probably yield very useful theories, and also more conjectures and problems. If the goals get solved by AI models that do not generate comprehension, then the direction gets less clear, it's harder to collaborate and get funding (think what would be easier, to get funding to try and solve Navier-Stokes or to try and understand an already proven Navier-Stokes?), and we get less open problems to work on.
It all comes down to this. Yes, they will need to give a good and convincing argument to the taxpayer. And at the end of the day, if the circumstances change, and you're unsuccessful in making your case in your plead, the taxpayer and their representatives may not want to keep the same level of funding and instead put that money to use elsewhere. So make a good argument why your job is still worth that cash under the new circumstances. The argument can appeal to aesthetics and art and philosophy and a kind of feeling of religious elegance and so on, it's fine. I can't say how well that will work, but it's worth a try. Taxes also fund theology and other pursuits with no tie to cold hard engineering etc. But that level of funding is not the same as for math currently. That gap may shrink.
I don’t get the argument you are making. If you want to reduce funding for mathematics research, argue for that. But wanting to make getting funding and coordination and collaboration harder in exchange for nothing other than PR for AI labs does not make sense
Is it just PR? Okay then the useful math can be done by AI and we can leave aesthetic math to human academics who will ascetically refrain from using AI and if anyone of them submits a paper and it turns out they used computers they will be treated like WADA treats Olympians on steroids or chess players with a vibrator up their ass telling them what move to take. But again the taxpayer may not foot the bill for this endeavor as much as they did while thinking it may be useful for technology, science and engineering innovation.
But did you read the letter, or are you familiar with the people signing it? Several things tell me you didn’t:
- The useful part of math is the tools, the understanding and the theories. Knowing whether the result is true or not is usually not useful. Imagine an AI that just says “cancer can be cured” but doesn’t say how: that’s what the letter is criticizing.
- Terry Tao is one of the biggest proponents of AI use in math. He’s been for quite some time and he shares a lot on his blog.
Seriously, it seems like you’re arguing about some idea you have in your head and you’re not making the effort to actually understand anything about this letter.
AI won't just say cancer can be cured without saying how. Not sure where you got this from. AI will be superhuman at writing the executive summary at any prerequisite knowledge level.
These people are concerned about internal community dynamics like tenure, chairs, PhDs, grad students, the whole ecosystem, papers, hiring, conferences, journals etc. But the wider population doesn't care about this and academics don't understand that nobody cares about this outside their bubble.
As Feynman said, "mathematicians can research what they please. If you want something else, you work it out yourself" (not verbatim). Indeed, now people can do this with AI and it makes mathematicians salty that they will have less prestige.
> AI won't just say cancer can be cured without saying how.
It was an example, an analogy to argue that answering a question might not be as important as how it arrives to that question. Hence the “imagine”.
> These people are concerned about internal community dynamics like tenure, chairs, PhDs, grad students, the whole ecosystem, papers, hiring, conferences, journals etc.
You just described most of the parts of the mathematical community.
> But the wider population doesn't care about this and academics don't understand that nobody cares about this outside their bubble.
I don’t care about the logistic system and yet I want my food to be in the market. If the population at large wants to use mathematics they will have to find a way to support a mathematical community. Now, if you don’t want mathematics, again, go argue about that.
> Indeed, now people can do this with AI and it makes mathematicians salty that they will have less prestige.
Except that they can’t. I do not know how many more times we need to explain that “answering questions” is not what mathematics is about. That if that path is followed, then mathematics will suffer as a result and the pace of mathematical development will slow down.
Honestly, I think it would be better for you to really stop attributing the arguments of mathematicians that are by no means anti AI to saltiness or other childish feelings. Try to be more humble and try to find what kind of ideas they might hold for them to argue this letter. Of course, that requires reading the letter and trying to understand it.
> You just described most of the parts of the mathematical community
Just as science (as in the scientific method) isn't the same as Science, the community social practice and logistics and tenure rules and committee compositions and journal page limits etc, mathematics is not the same as the academic mathematics community. They are not the sole producers of mathematics and not the sole users. The funding is largely in the hopes of the usefulness of the resulting math. Not all. Some funding is like art and culture funding, for propagating a cultural legacy, like folk dance also gets funding and experimental performance theater also gets some tax funding. But that's not the bulk currently in math.
I have read the letter. It's all about stuff of holding back because they don't want the answer key because prestige reasons, and how will grad students train their brain if we have too many answers. This doesn't consider that many people, like engineers, use math as a tool. They don't want to hold math back. It's fine to think that applications are too dirty. Again, they want funding, they have to explain why exactly they should get it. And it better be an explanation that still holds water with AI available. They can do the aesthetic math as an art side project like an accountant can paint or sing off the clock. But generally you also don't pay everyone for their hobbies even if those hobbies are nice culturally rich endeavors.
> they don't want the answer key because prestige reasons
No, that’s not the reason. They don’t want the answer key because the answer key is useless.
> This doesn't consider that many people, like engineers, use math as a tool
Of course it considers it. Many people, like engineers, could not care less about the answers to most problems mathematicians work on. They do care about the tools they develop in the process. I’ve already shown examples of this but I’ll do it again: Galois theory was developed when trying to answer whether there are formulas to solve roots of polynomials of degree 5. Fourier analysis was developed when trying to find an analytical solution to the heat equation. Riemann developed his geometry to explore which Euclidean axioms were actually important. None of the direct answers were as important as how they got to them.
> Again, they want funding, they have to explain why exactly they should get it. And it better be an explanation that still holds water with AI available.
The explanation will be exactly the same. Only it will not be just hard to explain why the problem is important, but also it will be harder to explain that no, just the answer by itself is not useful without the understanding. Just like I am here having a really hard time explaining to someone who doesn’t understand how mathematical research works why “just getting the answer” is not a useful output.
This hangs on the strange assumption that the AI will "just give the final answer" and will be unable to give a human-preferred explanation. I find this assumption strange. If it holds, then mathematicians will still have a job digesting these proofs. If the AI can digest it better, then academic mathematicians will become humanities professors funded similarly to theology, philosophy and dance professors etc. for the sake of preserving a cultural practice, like traditional handmade broom makers etc.
Why is it strange? Are you familiar with how unsupervised proofs are made? It’s basically iterating on Lean code, even if it were able to explain the code to humans it doesn’t mean it can extract actual understanding and structure from it. The papers being outputted by these approaches are nowhere close to being understandable, much less useful.
> If the AI can digest it better, then academic mathematicians will become humanities professors
Cool, then once that happens we can discuss what to do. In the meantime, AI does not digest proofs properly, does not explain them and does not generate any understanding, and it doesn’t look like that’s going to change. Hence the letter and the criticism made to the approach taken by AI labs. It is not that hard to understand.
I find these discussions pointless. It's like complaining that diffusion models make hands with the wrong finger counts. Yes there was a year or a few months when that was a legit complaint. The phase where AI proves Millennium Prize level problems but can't write up a human-like paper explaining the proof strategy may be similarly brief. It feels pointless to build a grand theory of what AI can fundamentally do in the space of math proofs based on a few months of existence of such strength models.
I find it interesting how many people are incapable of imagining that the tech capability will not be frozen at today's level and where we were e.g. a year ago and that a similar change may happen until next year. Instead they make sweeping assumptions that the current limitations will be with us for our lifetimes. You need a much stronger way to adapt to the new reality.
> The phase where AI proves Millennium Prize level problems but can't write up a human-like paper explaining the proof strategy may be similarly brief
It's absurd to assume that because LLMs are improving in certain aspects they will improve in everything, specially when the part they are lacking in is not precisely something that would be a strength of their architecture. I mean, models have improved a lot but they are still not good at strictly following instructions consistently (there's a reason why AI labs are worried about safety alignment). They are still mediocre to bad at software design, even the latest models (haven't tested Astra seriously yet). And it's the same reason they are bad at creating mathematical theories: they do not have mental models like we do, it's not even useful for them. Their comprehension is limited to textual context that they need to refresh and reprocess continuously. That's just how LLMs work.
> I find it interesting how many people are incapable of imagining that the tech capability will not be frozen
I find it interesting that after taking this long to, I assume, finally understanding the point the letter was making, you automatically switch to "oh well AI will do that too".
> But complaining about the dawn of a new era of advancements seems counterproductive.
you completely misunderstood the critics. your analogy is awful. this is much closer to the industrial revolution in the uk: it brought a lot of progress, but also extreme inequality and concentration of power.
It's not about whether the conjectures themselves are interesting or not, or whether people simply have enough time. It's that a bare proof made by a machine doesn't actually do much for us. There is not some set of problems that, once finished, will amount to some kind of final, correct system and we can call it a day and, like, utilize it. "Mathematics" is the people doing it (the "mathematical community" Tao references below). This other stuff is kinda just.. expensive exercises to render a result. They are only actually beneficial to us insofar as they exist in a context of research among peers.
You have expressed a few different ideas, so I will address them separately.
> It's not about whether the conjectures themselves are interesting or not, or whether people simply have enough time.
Tao seems to think otherwise, if I am reading him correctly:
I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce [0]
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. [1]
> It's that a bare proof made by a machine doesn't actually do much for us.
I get it, and I think the same can be said about all sorts of human endeavors.
> There is not some set of problems that, once finished, will amount to some kind of final, correct system and we can call it a day and, like, utilize it.
Sure. Although there are certainly practical applications to be found along the way. E.g. proving P=NP would be potentially very significant in the real world. I think we agree.
> "Mathematics" is the people doing it (the "mathematical community" Tao references below)
Sure. And the same can be said again about all sort of human endeavors. But I don't see how that is a reason to stop using AI in those fields, either. It doesn't subtract anything, in the same way that chess engines didn't destroy the love of the game for chess.
And just like in chess, these AIs can be used to gain a deeper understanding. Including, but not limited to, explaining to humans the proof they just came up with.
Are you trying to argue toward some final verdict with regard to LLMs and mathematics? I thought you were just trying to make a comparison to Baudelaire? I think maybe being clearer on this point would help. Even if you argued sufficiently for the latter (which is going to be tough already), it wouldn't really speak to the former. Or at least: that would have to be a separate argument I think.
Also, how, in your words, do you feel like the first quote justifies your point (presumably with regard to the question of "interesting" or not)? And why do you think the second one is more about time itself rather than attribution? Do these things actually contradict the letter above (or the comment on it) in your mind or not?
In general, do you disagree with something here specifically? Or is it kind of a yes/and thing? Does any of this help, in your mind, with the Baudelaire comparison you were at least at one point trying to argue for? Its a bit hard for me to see the argument here, if there is one, just with what you have written. But I am sure I am just not knowledgeable enough to grasp the argument!
My opinion is that the field will adapt. AI will not spell doom for mathematics. On the contrary, it is the beginning of a new era. Math is having its Deep Fritz moment, just as computer science is going through the same.
Some folks are struggling to adapt to this change. Tao actually sounds like he is doing alright compared to most, even if some of his arguments seem a bit weak, as I alluded to in other comments in this thread.
Hopefully it makes some sense. And if it doesn't, at least we had a nice chat.
Haha yes I imagine we all know your opinion is something like that! But isn't it much more fruitful and interesting to form an argument for it? If he is still in the context here: is there something about Baudelaire's critique you were discussing originally that has helped you arrive at this opinion? Do you think he is wrong? Or is he right, but providing the right kind of nuance that we need in order to cope with the revolutionary changes? Genuinely curious!
> But isn't it much more fruitful and interesting to form an argument for it? If he is still in the context here: is there something about Baudelaire's critique you were discussing originally that has helped you arrive at this opinion?
The historical record. That's why I am drawing some lose parallels with Badulaire. Incumbents being unhappy about a disruptive technology, lashing against the early adopters, and fearing that it signifies the end of their craft, when in reality it's just a period of change and adaptation. Without the advent of photography we would not have Impressionism nor all the movements through the 20th century. Photography forced painters to reinvent themselves, and LLMs will force mathematicians to do the same.
I thought the historical examples of photography and chess engines would be enough for people to connect the dots, but apparently not.
Sure, but then it's kinda less that you're making an argument here one way or another, and more of just an appeal, right? Like its just broad strokes? The inherent actual qualities of photography aren't supposed to parallel anything with the LLM case other than just the bare fact of being a new technology at one point?
I guess I am sorry for pushing, I felt like maybe there was going to be something more specific to the point.
I think one thing to keep in mind in the future is that for every Baudelaire, there is a Benjamin or Italian futurist saying the exact opposite! Its not like the fear of photography was a monolithic, shared thing, even at the time. Just, it's not so straightforward to have the "historical record" speak exactly one narrative, and unless you are a full-on technological determinist (is anyone these days?), you can't really conclude anything from the past like this.
> I thought the historical examples of photography and chess engines would be enough for people to connect the dots, but apparently not.
You're just an overconfident idiot who thinks that because there is an analogy along one dimension of a absurdly complex problem you've somehow arrived at a superior truth.
I repeat, this is an incredibly complex situation in which no one fully understands what's going on. The letter is simply asking for greater awareness of the implications of what AI companies are doing, they're not even saying that AI is bad!
I don't see any meaningful analogy with your cites of Baudelaire. First of all, Baudelaire discusses art, which is very different to science. Several new forms of art have emerged, and then slowly integrated, despite the strong opinions of some. Here, Tao's letter discusses mainly practical aspect of scientific research. It is not about what a "failed mathematician" would do, or if "LLM can only record what already existed"; in fact, it ackowledges that LLM could become a central tool. If you want me to be even more precise, what they're saying (without saying it out loud) is that tech companies have too much power and are being irrespondible with it because they don't even think about the externalities.
> It is not about what a "failed mathematician" would do, or if "LLM can only record what already existed"
This is what I was alluding to:
I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce [0]
Of course there's a meaningful analogy. The poster wants to make Tao sound unreasonable and against "progress" while ignoring the very real concerns Tao has.
It's what fanatics do when they want to enforce their view on the world, they have to attack anyone with a reasonable viewpoint because they can't imagine a world where someone tells them they don't like what they're doing.
I do not want to make him sound unreasonable. He is a brilliant man. But I also think that he is a bit shell shocked, much like other luminaries in the past have been when confronted with rapid technological development, so I wanted to highlight some historical similarities, imperfect as they can only be.
As for the rest of your comment, I hope you have a great day.
He’s not shell-shocked. He’s had an extremely consistent narrative for years now. You are experiencing a bias where you project your own views onto others, probably because you are not very informed on this.
Tao is quite the opposite of what you describe. He's had an ongoing dialogue intellectually with the challenges created by ai for mathematicians for some time (years) now and his viewpoint is quite balanced. He is not alarmist but rather correctly addresses the real problems ai advances create for mathematicians traditional way of working.
> But I also think that he is a bit shell shocked, much like other luminaries in the past have been when confronted with rapid technological development
You're locked into that idea, but provide no real argument. The dangers they describe in the letter are real.
Portraits are not an artistic medium in the same sense, they’re something one creates with the tools of a particular medium. Painting is a medium, photography is a medium, both are capable of producing portraits.
An LLM can produce a portrait of you as well by generating a facsimile of you based on existing material (or functionally a “guess” if you describe yourself I guess).
People aren't ready to discuss AI assisted imagery as art yet. Most discussions lack the nuance that Baudelaire lacks in that critique, which deals with the nature of art and the importance of human intention and input.
We can’t look back with perfect hindsight because both the past and present have deeply ingrained blindspots. They don’t know what it is like to live in a world with perfect edges. We don’t know what it is like to live in a world with no edges. We can read about someone who proclaims that “something will be lost”. We will just think “but I have no need for any of that.” But we don’t even know what it is.
I don't think the analogy works because for the past few years Tao has been one of the most vocal advocates of AI in mathematics and has used it extensively in his own research. You can find several of his talks about this on YouTube. It's completely consistent to believe two things at once, that the tools are useful and that the companies are misbehaving.
Wasn’t the criticism of photography kind of correct though? I don’t think people think of photography as an art as much as painting is an art.
There aren’t a lot of photographs that a layman couldn’t in principle also take, but only a few people could replicate a good painting.
Keep in mind that his critique is very recent, and likely applying to a specific use of AI, as opposed to AI as a whole. If you've been following his Mastodon account, he's been happily using LLMs for math purposes for well over a year.
I'm really tired of these arguments (this and "it's just like calculators").
Photography decimated other forms of visual art, so the concern wasn't wrong. But AI threatens the entirety of human intellectual endeavors. I can make do without oil paintings in my home. I'm not sure I want to live in a future where we make do without brains.
Lots of people still make bad music that other people still manage to enjoy (a lot of it has gone multi-platinum!) even though they're not Mozart or Bach.
Of course it is, because our society is pretty much structured to place sociopaths on top. Why is it at all surprising that any technological advancement is going to be used by them in a way that doesn't benefit the rest of us?
But it's equally obvious that this has nothing to do with the tech itself.
If the tech enables certain behaviors then it can’t be casually divorced from a discussion of how people use it. “Tech” isn’t inherently neutral. It’s made by people with intent for a purpose and how else it can be used must also be considered.
This is like separating “the use case” of killing people from guns and still trying to have a coherent discussion about them. You simply can’t handwave it away with “well that’s not the tool’s fault.” It’s unproductive and sidesteps the conversation.
It did. While you're busy recording an "instagramable" moment, you are not entirely enjoying that moment. Your eyes are on the screen, not on the subject.
In a way, if photography is an ersatz for painting that eventually made imaging available for the masses, then AI could become an ersatz for thinking. But it feels like I'm paraphrasing TFA.
What will happen when AI companies have spent their advertising budget on math problems and whatever else gives the maximum wow effect for the bucks? Probably customers hooked on the vain satisfaction of spending token$ to impress friends.
Indeed. As Nassim Taleb says, "Something bad for the (existing) class of mathematicians as they lose their privilege, but not necessarily bad for mathematics & our body of knowledge?"
https://xcancel.com/nntaleb/status/2098498124419305639
Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a painting could.
He also criticized the public's craze for "rushing" into it, and complained that this technical "progress" was weakening the arts.
Do you see some parallels as well?
[0] https://fr.wikisource.org/wiki/Curiosit%C3%A9s_esth%C3%A9tiq...