alt Hacker NewsI Know Why the Mathematicians Weep
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> “Google Translate is amazing, but it has taught us essentially nothing about linguistics,” Strogatz said. “We don’t understand why it works. It just works. That’s the Twilight Zone. It is knowledge without understanding.”
This is not true, and it is the crux of an enormous debate we're now having across many, many fields.
Classical Chomskyan syntax (which models sentences as parse trees) has been enormously, astonishingly predictive of the rich structure in real-world human language. But we are quick to forget that we invented concepts like "words" and "noun phrases" specifically to help us analyze and predict things about human language. What LLMs and modern MT shows, definitively, is that there is another, totally separate way to describe these phenomena, which is both vastly less descriptive, and also vastly more predictive.
That these appear to trade-off is unfortunate, but it is NOT the case that we "don't understand why it works." We absolutely understand why it works, if we didn't understand we would not be able to improve these systems. What we do not have is a clean, descriptive theory that boils this down to something that is formally specifiable and analyzable. But those are different things, and this is the root of the disconnect between many communities working in and around these spaces (linguists vs computational linguists; mathematicians vs computational mathematicians; mech interp people vs empiricists).
I can kind of relate but I feel like I am mourning something different: the loss of the desire to seek truth in tech, math etc.
Nothing is validated or tested anymore. It’s all about the shape or believability or even how loud it is.
They dropped 100+ papers no one read. I am sure mathematicians are reading them now but even this forum has concluded that these problems are solved, without reading or validating.
It’s like everyone forgot “don’t believe everything you read on the Internet.” And it makes for a very boring discussion when everyone is just spewing unvalidated claims, layering them with strong beliefs founded on similarly unvalidated claims. It’s dull, without substance and just pure noise.
This piece circles, without naming it, around the concept of “deontic scorekeeping” central to the work of Robert Brandom on semantics. The idea that our ability to create and sustain conceptual systems depends on the give and take of reasons within a social setting. Brandom has been front of mind for me lately because elements of his theory both explain why LLMs should work in principle, and where they are bound to be radically deficient. An LLM encodes the normative regularities of our linguistic/conceptual games into its weights, but it cannot be a real participant in our games because it is incapable of staking durable commitments or changing its dispositions over time.
Worth reading: Robert Brandom, “Making It Explicit: Reasoning, Representing, and Discursive Commitment”
I think Thompson has no understanding of endeavors like pure math or the theoretical sciences. In the words of Einstein, "I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know his thoughts; the rest [is] just details."
I think mathematicians aren't bemoaning their lost sunk costs. They're now aware that they may never again have the joy of being the first to pull up the edge of the tarp of ignorance and see the raw truth beneath _for the first time_. Their voyages of discovery, which give life meaning, may never leave dry dock again.
To me it seems the ultimate question is why would we expect humans to have an advantage at anything in the near future. A few years ago that would have sounded insane, but intellectually I don't doubt frontier models are superior to the average person. Even in the arts and humanities, give your preferred frontier model an interface and a way to "see" its work and it'll make the average person's work look like toddler scribbles. Humans still have some advantages, some places more than others, sure. Working with a designer recently I realized how bad, or maybe average, frontier models were at design. But I highly doubt the vast majority of people will be economically viable. Maybe this is one of the great filters, a society driving itself mad when freed from necessity of economic utility and without the big philosophical questions having answers.
It's got to be alarming. Without a doubt, being not only on the frontier of yoyr profession, but in THE profession that is undoubtedly the most intellectually rigorous and well renowned and respected... It's got to feel pretty awful
I still think mathematicians are going to be as important as ever. The LLMs are only finding what was technically possible given our current breadth of knowledge after brute force solving problems. Eventually it will run out of things that it can do with its training and the only way to get it to do more will be training it on new human found knowledge.
Finding that new knowledge may be exponentially more difficult, but it will be much more valuable.
There was a time, not too far in memory, when the value of being human wasn't about our intellectual prowess[^1]. We were creative with the human worth thing: being there in the time of need, faith, nobility or being a well-dreaded, literally-bloody viking full of beads in your beard.
Yes, I fear we will stop being the top of the food chain[^2]. But by god weren't we getting bored? Maybe getting off our high horses and going into the weeds won't be such a bad thing.
[^1] And even today, if you go to parties and keep bouncing into people that have no trouble picking up intellectually stimulating topics, you are in a lucky minority.
[^2]: More about my fears, which are unhealthy and you don't have to read but I feel compelled to include citations: https://w.ouzu.im/aweb/unhinged
As a software engineer it is hard for me to feel sorry for these mathematicians. Software engineers are getting laid off because of advancements made by AI. Math researchers are employed at universities, and universities aren't laying off mathematicians now that OpenAI has solved some of their puzzles. Mathematicians can still feed their families, software engineers displaced by AI can't. Yet I see far more of these blogs about the plight of mathematicians, not enough about the plight of software engineers.
I think there is totally justified distress knowing your source of livelihood may be in danger.
That said, I don't think the reactions have been entirely circumspect.
1. Is the role of math academics really going to go away? Is there concrete evidence of this? Faculty still have very important roles to play, training students, training engineers, determining the direction of research. The breadth of math is absurdly, perhaps infinitely, wide, especially if including applied math.
2. You need to be a bit crazy to go into pure math academia in the first place. If you value the pursuit of knowledge for its own sake, shouldn't the emergence of such powerful tools to that end be a good thing?
> I am not one of those AI people who believes that hundreds of millions of jobs will be wiped clean from existence in the next five years
"Wiped clean" is the wrong phrasing, and 5 years is a short timeframe given the ability of some sectors of the economy to resist change. But yes, hundreds of millions of white collar professionals will need to rethink their careers and their business models within the foreseeable future.
Just today there was an HN article about how shady the dental industry is. In the future, you will go to a special dental imaging facility where a modestly-compensated technician images your whole mouth and feeds the results into an AI system, and when you get home you can look at the assessment and chat with the AI about it. Then you can potentially go visit a dentist, oral surgeon, etc, if you actually need work. This system will produce far better dental health outcomes at far lower cost: the diagnoses will be more accurate, and there will be no bias towards additional, unnecessary procedures.
In chats with models like deepseek the LLM makes many wrong claims, for example it doesn't know that the inverse image of a closed set by a continuous function is a closed set. Maybe more advanced models can in special circumstances, guided by the work of humans and Lean, prove theorems. But just like in RL, the brute force approach of failing a million times may not be enough when the reward is far.
In math the reward is finding the decomposition that reduces the problem to simpler cases, and in many cases that reward is very far. Furthermore, the LLM may process the many cases fast, but the decomposition often comes from a human, and the model takes the credit for the proof.
I happen to be (re)reading Strogatz' book "Nonlinear Dynamics and Chaos" right now. It's beautiful thing, and nothing in the "age of AI" threatens to equal it or in any way diminish my enjoyment of it.
Hacker News is so depressing these days. One doomer post per day to keep the valuations up.
Nothing has changed in math. Math is not solved nor has the human been kicked out of the loop. Same with programming.
*I said nothing really changed because LLMs becoming superhuman at deduction was priced in with o3 and neither the peer review, training nor publishing methods will get a revamp beyond what could already be done with SQLite and a website.
>Yes, some are crying about bruised egos, the feeling of wasted years, a creeping sense of status obliteration, the frustration of an unfair competitor, the indignation of feeling cheated and mistreated, and uncertainty about the future. But they are also mourning...
This nails it, however IMHO its almost all bruised egos and feeling of wasted time. I don't know the ratio of A:B but I also don't know anyone that is in the latter category of feeling doom and mourning that their craft is about to regress.
Even if this was overly long and mostly things I've seen before, I'm just very thankful that it wasn't yet another claude piece.
I guess I'm lucky that I've always hated my job, because that prevented me from tying my self-worth to it.
I need to do some more research on this. Because I've always been told that AI, more specifically LLMs, are "glorified autocompletes". Yes they have huge data sets but ultimately they can only provide answers based on data that they were trained on.
So how can they possibly solve problems that humans have worked for decades or centuries on without being able to solve? How did they find something new? Is it that they were able to deduce the solution by examining all current data sets? Or simply brute force it until the produced solution passed all necessary tests?
I'm convinced the people who do not see what Mathematicians see simply have not considered that their jobs are just as vulnerable. The day when OpenAI replaces their own AI researchers with GPT will be upon us, and the response from the Mathematicians will be "First time?"
As usual the author is ending on a completely unrealistic positive note: "humans may come to value more highly our capacity to relate and care for one another".
Does relating to someone pay my bills? People will use the informational tools to improve their social status and resource accumulation, there is no doubt about this.
I am not quite saying "if you can't beat 'em, join 'em", but I know more math now than in any point in my life because I want to understand how LLMs work.
I understand there are many types of math and the mathematicians don't all want to sit around and do KV cache and gradient descent things, but surely a percentage are as interested as I am and can contribute to this new emerging field? I would wager that Xl+1=Bl Xl+Cl ℱl (Al Xl) makes much more sense in their mind than mine.
>Newton famously compared his achievements to “standing on the shoulders of giants”
Newton was possibly just taking a dig at his small-statured rival, Hooke. Newton was brilliant, but a shit.
As a programmer I’ve been ‘weeping’ for a few years now.
As a mathematician, I will never understand how my colleagues had never foreseen this. Okay, maybe you can believe in a plateau but at least accept as a possibility that there won't be one. This applies to every other human endeavour.
I am also sad, but my sadness is, in a way, priced in.
The author mixes "Science" and "Mathematics". Mathematics is not a science. There is nothing empirical about it. By mixing the two concepts, a reader might think that AI is on the verge of solving all of science. Until AI gets good at digging large circular holes in the in the ground, I think Experimental Physics is safe.
Article refers to Hugo Duminil-Copin, who also did a podcast with Brady Haran [1] about this subject, for him it isn't case of bruised ego, or gatekeeping. He realized that the way things were done were going to change, and it made him emotional, he is not pessimistic or against AI.
When anyone can push a button on a machine and out comes a math result, it still doesn't become theirs or anyone else's until they can internalize it and make it part of their thinking.
I remember the same doom cycle during my PhD when GPT 4 came out [1,2]. It seemed like everyone in NLP was freaking out except me. A few years later and new CS PhDs are still graduating and joining academia and industry. Much ado about nothing.
Considering I currently live in Ithaca and have a friend doing a Math PhD, so I've heard from him some of the discussions in the department. I think the biggest shock for people is that individuals spent significant portions of their time on some of the problems that OpenAI supposedly solved (I say supposedly because all of the proofs have yet to be independently vetted). I understand that it's a shock, but I'm confident that in time it will be no more of a blip than it was for NLP.
[1]: https://xxcancel.com/mayhewsw/status/1636476184098643968
[2]: https://xxcancel.com/andriy_mulyar/status/163613925780582809...
I object to a few of the assertions made by maths folk in the article- 1st being that Google Translate taught us nothing about linguistics. If you use google translate you learn less about linguistics than if you had to experience learning the languages first hand, maybe, but you can learn form just that output if you are determined to, ad, more importantly, the folks who built it and are still building it are still learning a huge amount about linguistics.
What are the relationships between many languages that become apparent, including code as a language that were not obvious before llms? Translation is fairly solved. The study of how and why languages, not at all.
My friend, who is a math professor, told me that they weep because they are about to become just like us developers: prompt writers and AI output reviewers.
OpenAI didn't have to mass publish these solutions. They did it to make themselves look good. They are ostensibly making a tool for people, to better humanity. Instead, they chose hubris and self-interest.
Letting mathemeticians use these tools to reach the same conclusions would have been far less destructive, and potentially, even exciting. Shame on OpenAI.
Mathematicians are grieving the birth of something that is, in a very real sense, the crowning achievement of mathematical ingenuity.
I never appreciated hard math much because my brain just can't get there. I thought so much of math was much ado about nothing, but now I see the art in math...not in the inscrutable formulas, but in the creation of AI.
Well done, mathematicians. You can now rest from your labors.
I love that we have new ways to solve problems. And it's been hard to accept that my own unique intelligence—which I've spent decades cultivating—just isn't as important as it used to be. I am developing new ways of thinking to better adapt to an AI-enhanced world, but I'm not done with the mourning process. We're all finding our way through this.
A hypothetical... suppose AI "solves" (for your preferred definition of "solve") your field and what you used to do becomes useless or near-useless. But you still enjoy doing it and you also get UBI that provides for comfortable lifestyle regardless of what you choose to do.
Questions: (1) Do you still weep for what has transpired? (2) Do you continue to do what you used to do (with optional AI assistance)?
For me: (1) no, (2) yes and I think the same would be true for most people. So I can't help but believe that most of the anguish about AI is far more about a direct economic hit to people's livelihoods than it is about the impact to their respective fields. Which is more than reasonable. But then why not frame the conversation that way instead of beating around the bush?
One of the driving forces of math achievement is an internal award (yes, friggin business speak).
The vanity, fame, self-improvement, it's very selfish as everyone does.
Now the fame coming from proving things like Riemann Hypothesis is taken away. Self-improvement? relying on AIs make you stupid. It will be lost. Vanity? Who else don't know how to use AIs? It cannot fill your void.
Now also the most important thing is the communication.
There will be less communications amongst mathematicians at least in person. On paper? maybe but mostly via AIs.
Mathematicians are smart enough to have figured out which way is up. You can debate the stuff outside someone's field not knowing the details but the insiders know what is happening. Ai may not be better than someone with very specific knowledge at this point but it is certainly better than the net. Once it gets optimized for every little super human knowledge, it can do better.
These guys know because they looked at it. Denying it is useless. But maybe some of these guys can figure something new using it and asking it to look for it.
We are seeing many fields being impacted. Makes me happy to see things like artcraft coming out that directly impacts the big tech companies themselves.
I'm wondering if mathematicians are sort of going through what programmers have been going through recently, really questioning whether their craft can continue. But now it feels like, in the software world, at least from my seat, people can handle much larger scope and work on much more complex problems. If anything, my job has gotten a lot _more_ interesting.
So I wonder if mathematics will go through that too? A period of chaos and doubt, but finding new and more effective ways of working.
Mathematicians should web search the arguments when artists were hit by the wave. Scientists in general and people that think humans know better.
This is probably the first time in history deep thinking is being replaced by a machine, but the overall arguments are the same in all cases. Graphical artists saw it first, then programmers, now mathematicians.
No, there is not stopping the wave. No, society won't probably be able to support the same number of mathematicians as before. But yes, there will still exist mathematicians after the wave break, just probably completely different than the old way.
And yes, some people will still try to do artisanal mathematics and say it's better, it probably is, if the artisanal mathematician in question is doing deep creative and out of the distribution work.
This is such an insidious propaganda targeted at the demoralization of entire professions. Strogatz is an AI booster who "wept". Totally representative!
How much do they pay you? Does OpenAI have bulk subscriptions to your Substack?
My take is that it is an exciting time to be a mathematician since the frontier for interesting math problems is about to explode, and without prior art or references, it's green field for both AI and human. Think of all the new discoveries we'll make.
> “They have annihilated my field of research.”
I think they might find comfort in knowing it's not just mathematicians - this is coming for all of us. Computers putting us out of work has been coming for a long long time.... and now it's here.
Those of us who loved programming have already been through this.
I hate programming these days - back in the day, the cubicle-hell nature of "popular" frameworks was at least offset by being able to think through and solve interesting problems.
These days most of us are stuck in the "endless-review" loop with LLMs. You can't afford to not use it given the inflated expectations. As with all of modernity, productivity doesn't yield leisure - it just proportionally increases your workload.
Hardly surprising that the other side of the Curry-Howard correspondence is now getting hit with this. Math was one of those depts. where slow/deep-thinking was possible (CS was already insane 10 years back - now it's just absurd) - now even this fortress will be broken. Tragic.
I mourn the loss of comfy, intellectual, thinking jobs like those of the mathematicians where people could spend time pondering without the immense pressure that would come from doing something like that in a corporate environment.
If understanding is so important and AI systems can only produce knowledge. Why can't mathematicians continue their work on better understanding?
The beginning of this article is decent, the end sounds like a tobacco lobbyist touting the health benefits of nicotine.
> If intelligence becomes less uniquely human, we may come to value more highly what remains uniquely human: our capacity to relate and to care for one another.
Lol. How does the author think relations between people work? (At least those outside the family). Relationships require something that fills them with meaning - a reason why you would want to have that relationship in the first place. Without meaning, no relationship.
I recommended reading this other post that was on HN earlier today: https://thetheorygirlie.substack.com/p/ai-was-great-until-it...
It describes in pretty grim words what happens to collaboration once you have nothing anymore to collaborate on.
> Mathematicians may still teach proofs, argue over what they mean, translate alien logic into human insight, and pass that understanding to students.
This would people to have time to understand and dissect those proofs - it doesn't work if there is a new breakthrough proof every week.
I think beyond the specific elements of any domain AI eclipses humans in, overall, the notion of the thing that grants you status, prestige, and a living wage being commodified would spark in anyone a profound sense of dread.
Beyond just making you redundant in your job, the whole architecture of your existence, the thousands of hours of struggle, the sacrifice of putting off social games or personal enjoyment are now rendered moot in hindsight. You are made one step closer to complete worthlessness, which will surely continue as AI becomes a more satisfying personal companion, a more worthwhile friend, lover, etc.
How is one to feel safe in the progress of the future when the only hints of the wonderful post-scarcity utopia we can quantify so far is the removal of all human leverage via their labor? All it tells us is we will be bargaining with superintelligence with nothing to stand on, only a trust that the 5000 lab executives and researchers solved the most important research problem of all time on the first try.