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- Hacker News
- This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it. But the promise (and horror) of AI mathematics is that, if it succeeds, human understanding becomes irrelevant. That's the goal. So this letter's message will fall on deaf ears.
Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10% chance of human extinction. They're knowingly risking the lives of every man, woman, and child to continue the work. The lives of their own sons and daughters. A person already rationalizing that isn't going to shed a tear for the careers of mathematicians. Just a bug on the windshield.
by Strilanc - > Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10% chance of human extinction.
Are we really going to take what they say in public seriously?
by robotpepi - The point of mathematics is human understanding though.by philipwhiuk
- > This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it.
Ironic or what. Mr Tao may be remembered as Mathematics' Canute.
by chrisjj - I agree insofar as this may fall on deaf ears of AI folks, but that the goals are differ is exactly the point of pointing out misalignment. To talk about this may be more useful for coalescing professional societies than for conversing directly with AI advancers.by mpascale00
- > So this letter's message will fall on deaf ears
AI companies are alienating the communities they serve. Instead of a win-win dynamic, they are keen on a win-lose proposition. You dont win trust by one-upping your customer. This is unfortunate and suggests a lack of adults in the room. It also reeks of hubris and is all good when making profits is not a concern. But watch the narrative shift when there is an AI slowdown which is inevitable.
by bwfan123 - To be honest I didn’t get that much outrage here: https://news.ycombinator.com/item?id=49662116
It seems like a lot of the issue here is that these problems aren’t interesting in and of themselves, but they lead down interesting roads. It defeats the purpose if you solve them without getting any real understanding.
It’s akin to saying you’ve solved “pancake flipping” problems with a waffle maker, or “travelling salesman” problems with a zoom meeting.
by boron1006 - Going to the gym and using a forkliftby grufkork
- Nothing is stopping these folks from continuing to study the problems and arriving at their own solutions so they can continue having whatever insights along the way.
Well, one thing is stopping them. There will be no more adoration for their genius.
If you truly do it for understanding and not the attention, carry on. AI should change nothing about your motivations.
by Art9681 - > solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.
This is the effect of AI on most intellectual disciplines, and it’s a real worry.
by yzydserd - The existence of solutions to problems does not prevent you from solving the problems yourself anyway, if your goal truly is personal development. You're free to go solve Navier-Stokes yourself right now. You're free to manually do all of the AI work in any field, actually. You won't get grant money or prestige (which are not a part of conceptual understanding and insight) but you will get all of the conceptual understanding and insight you're after. You have not been deprived of it.by soerxpso
- I published a substack about this just a few days ago [1], my core theory here is that we will absolutely have what I call a "highly productive dark age" in mathematics where knowledge vastly outpaces understanding driven by publish-or-perish incentives, but additionally this will lead to the loss of the skills necessary to understand.
The hopeful note is that I do think we are entering a golden age for the curious casual/semi-pro mathematician and for niche mathematics areas that won't get the attention of the top labs. Everyone is sprinting to solve the millennium problems, but this is a very exciting time to be in a sub-sub-field where you and 4 others are keeping things alive.
by ceh123 - Tao basically reiterating "AI is making us dumber" a bit more eloquently and applied to math.by rbtprograms
- Playing a devil's advocate. Why do we need understanding ? To take an example i would say ~99% of the population do not understand how combustion engines or how semiconductors work, what say another 1% ?
Is the fear post-apocalyptic in nature ? We need some human priesthood to carry on tradition ? why ?
Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, reasonably un-constrained by any institutional interests.
What say the 1% ?
Just a thought.
by sim04ful - Yeah. My other favorite example are books. Why do nonfiction books exist? There are some pathologies and corner cases, but fundamentally: to develop and share new ideas. Downstream from that, if it reads well and if you're lucky, you make some money.
But now, LLMs can generate hundreds of books per hour. They make up 80-90% of new arrivals in many nonfiction categories on Amazon. They short-circuit the system, allowing their "authors" to extract money from the system with zero effort by crowding out human work. And it's not even the question of whether these books are good or bad (although overwhelmingly, they're terrible). It's whether it's actually accomplishing anything worthwhile, or just destroying incentives for humans to write or go into any other sort of intellectual work.
In fact, I see many professions push back. Artists, writers, now mathematicians. And I'm amazed that our profession doesn't and that we have so many people who are hooked on vibecoding. I'm still waiting for that 10x payoff. All this velocity and somehow, the landscape of the software I want to use still looks the same as it did in 2021.
by matherial - As a software engineer, 6 months ago. I was better than AI in essentially every way except raw typing speed.
Now AI has surpassed me in fine-grained problem-solving ability. It can write more reliable code than I can, faster than I can, provided it is given the right guidance.
But one thing that I'm still much better at is identifying technical opportunities and choosing the right tradeoffs.
My feeling is that frontier models are incredibly smart in some ways, but incredibly dumb in other ways
When I chat with Claude using deep technical language about distributed systems issues, the arguments it presents are mind-blowingly good. I worked with many skilled engineers on complex projects but the kinds of arguments Claude makes are on another level. It feels like it can read my mind because it already identified all of the relevant aspects to the current topic and it's incredibly persuasive. I would say it's even better at deep, nuanced technical discussions than I am.
When I ask it to implement a feature using technical language, it does a really good job and the solution usually works out of the box. No bugs at all 95% of the time even after adding 1000 lines!
But the problem it still has is that when it implements solutions, it misses so many low-hanging fruits/opportunities. Especially in terms of performance, maintainability, scalability and UX. It's like it sees and recalls all the relevant parts perfectly but yet somehow misses opportunities which seem extremely obvious to me.
It feels like AI has 0 creativity. It only sees the opportunity once I mention it... And once it sees the opportunity, it demonstrates deep understanding of the technical implications. I think what's surprising is that it understands the suggested solution so well, with such nuance, that I can't understand how it didn't see the opportunity and why it never seems to see it until I mention it.
This is very unhuman-like. There is no way that a human being with that degree of understanding of a topic would be presented with such highly relevant context and not make the connection.
- This mirrors my understanding when I use Claude code for mathematics. I can have deep discussions with it and it can solve my hairy problems. But whenever we go off the beaten track into design new mathematics, it struggles to make conceptual leaps and find the right definitions. Once I give it my ideas, it is back to its super-human pace and top notch intelligence.
This situation suits me fine, since I am anyways more of an ideas person, than a crunching open problems person. But I understand the desperation of my colleagues who mad solving hard problems their identity.
by black_knight - Thanks for putting it in words. I feel the same about SOTA coding models. I get visibly frustrated by this and often find myself using curse words at Astra.
You're right it's very unhuman to miss obvious opportunities you mentioned. And what's why I think these models would continue sucking as long as they don't have human level general intelligence. They may get marginally better at these tasks but I don't think we can expect them to connect dots like humans before AGI.
by bharatsuthar - This is exactly how I feel about the recent ChatGPT models. It feels like I'm working with an incredibly enthusiastic junior student who listens to everything I say, checks it against my entire codebase, and thinks through all of the possible connections 1000x faster than I can. But it doesn't spot the ideas first. It actually makes work quite fun, since I can spend so much more time in "idea space" instead of "implementation space".by gregdeon
- > We are witnessing a general threat to intellectual work
This is the crux of it and goes far beyond Mathematics or Computer Science. To get a bunch of humans to do anything, you have to motivate them. Kleos and Timē; renown and stuff. These AI companies threaten to rip this away from everyone but themselves, and this recent millennium prize is the perfect example.
Solving this problem as a human would have led to tremendous Kleos; my name would be written in the annals of mathematics, lecture tours of praise were mine to be had for the rest of my days. This one victory would have earned my recognition throughout history. The greatest a mortal may hope for. Ripped away.
It would also have given me great Timē. The prize money, the professorships, the book deals. Gone.
If all hope of “renown and stuff” in the intellectual realm is now taken by the AI companies, they will remove all human motivation to pursue these endeavours.
Perhaps the glory will come from slaying these fell beasts.
by lll-o-lll - Having to put food on the table is one hell of a motivator.by tucnak
- These are both big motivations but not the only ones.
But there's still play. There's still curiosity. And there's still the drive to understand something for yourself.
by dhbradshaw - As a consumer of mathematics, I want to attack the author’s idea of “what that work was meant to achieve in the first place”.
I do a lot of programming that uses mathematics. I designed the error recovery file format “par2”. I worked as a quantitative trader.
What do I want from math? To be able to search math results, understand them, and apply them. But academic mathematicians are so inwardly focused - as these authors so obviously are - that it does all of these badly! Search is still with words, not symbols and formulae. As for comprehension, many math papers are unreadable to those not in the cliche of mathematicians in that specialty. And even applied math papers don’t ship code or specify the operations explicitly.
I wanted to fix this and in 2013 I worked on formal proof. It makes symbol search and application easy. I found out that the tools had been usable for decades at that point. But mathematicians didn’t use them because they had that inward focus and didn’t give a damn about math consumers.
AI is enabling formal proof. It will carry mathematics into the computer age, which the field should have joined with every other industry in the 1970’s! I welcome it. Math will get used more and that is what the work was meant to achieve in the first place.
by mdnahas - different fields have different communication cultures, that’s not inherently bad. sacrificing inward focus is expensive from the pov of the insider; i see your points but not everything can be written for a general/wide audience. after all, the audience of the author are the specialists, since only specialists spent the effort to be able to engage with the work in depth. perhaps we disagree that mathematics is not a product that mathematicians are making?
what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics. if someone wants to use it, they are free to do so, or to write a blog article how it can be used by non experts. mathematicians do that themselves sometimes, but it’s not their job. myb there should be more incentives for them to do more of such work
i keep seeing this myth that mathematics has some purpose to do this or that, but somehow its purpose is least known to mathematicians, everyone else seems to know better
by lying4fun - One key idea to understand about human behavior is that people are focused on their status among their peers and their next level superiors with power to lift their status. You are not among either, so you don't matter to them. This is nothing special about mathematicians, though, people work the same way everywhere, in every field, community etc.by bonoboTP
- I've had a similar experience.
LLMs doing math has made math far more accessible to me than it was pre-LLM.
Not just using existing math, but developing new math. (For example, I developed an alternative to NURBS surfaces for geometric kernels using LLMs.)
It's really annoying that anyone, anywhere is talking about halting math progress with AI.
by erichocean - This is a PR problem, not a mathematical problem. It's possibly the worst PR problem mathematics has faced since the execution of Hippasus for whistleblowing on the cover-up of the regular dodecahedron. It's still a PR problem.
So what went wrong? Mathematics education. Math below grad school is all about solving stated problems. Credit is given for solving puzzles successfully. Homework is problem sets. Everybody below a very advanced level is taught math that way. Even at the higher levels, puzzles remain important. Awards in mathematics are often tied to solving puzzle-like problems. That's still the criterion for becoming Senior Wrangler at Cambridge, "the greatest intellectual achievement attainable in Britain". This despite Polya's attempt at reform a century ago. Puzzle solving gets good grades and class rank. So it's the status indicator mathematics presents to the outside world.
Then reasonably good AI comes along. AI has become rather good at solving puzzles. So people aim powerful AIs at known hard puzzles, with some success. That blows up the status indicator system. Mathematics itself is fine. It's the status symbols that have a problem.
Maybe the Fields Medalists need to hire a crisis management team to reframe what success means in mathematics. That's what they're trying to do with that letter, but they're mathematicians, not PR people, and they don't know how.
by Animats - Precisely.by crabkin
- They are defending the value of their achievements!
They should explicitly advocate for the Fields Medal to weight teaching achievement more heavily going forward.
by nateburke - Very interesting analysis. I was just reading this announcement, and thinking, that is the most pointless thing I've ever read. What are they trying to achieve with it? Your comment explains it.by auggierose