> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to
I'm sympathetic to mathematicians but this does not paint them in a good light.
If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
* I find this characterization overly harsh, but if you're mad about your problem being solved, maybe you weren't in it for the right reasons
I really don't understand such takes. Extend this to every problem in every profession, which seems to be both the trend and the intent (if still far off), and you vaporise the meaning from a lot of people's lives. Sure, they can find other sources of meaning - assuming having their job automated doesn't leave them constantly scrambling to make a living. This would require major social restructuring that nobody's really talking about.
Many people pursue careers based on the intersection between their interests and what society considers valuable. Being upset when what they chose to spend their lives doing either loses value or changes so much it becomes a wholey different job is understandable, and calling it "rent seeking" is very unfair, in my view.
> and you vaporise the meaning from a lot of people's lives
If the meaning of your life is to obtain a solution to a given problem, then getting the solution would "vaporize the meaning of your life" in the same way as when someone that claims his meaning of life is to raise their children would "lose all meaning of life" when they finally move out and start to successfuly live on their own. Yes, there could be some nostalgia in both cases, but if you are psychologically well-adjusted, the pros would still far outweight the cons, the happiness would outweight the sadness.
This analogy is only valid if you're confident that parents would not say meaning is vaporized if you turned their 8-year-olds into 18-year-olds overnight, and there was reason to believe this would frequently happen to families in the future, probability increasing. The exact problem is that the situation in mathematics is not akin to "finally moving out" but instead to "immediately moving out". I imagine few people would be OK with it.
Also I find the suggestion that the people unhappy with the AI-in-mathematics situation are psychologically unwell to be presumptuous, to put it mildly.
Nobody goes into these fields only interested in the final result, they go into it interested both in the challenge and revelations of the process and the triumph and recognition of achieving the final result.
There's no joy to be derived from a completed crossword puzzle if you weren't the one solving it...
The big assumption here is that "problems are being solved" in every field affected. Which they are not.
Just as the most basic example: software is not currently being made faster, nor performing better nor at a higher bar of quality. Maybe developers are able to report higher velocity, but this is not leading to faster shipping of software/features. In fact, people seemed to feel software is buggier than ever and companies are doubling down on it and simply adding placeholders of "AI can make mistakes". Unforgivable 10 years ago if we tried that with humans.
If anything, the rent seeking is with people reporting "being more productive than ever" and despite that less real world problems being solved than the previous decade.
I don't think that's the same. Would you let robots raise your kids if they provably did it better than you?
These people knew someone else could solve the problem. Presumably they figured there'd still be meaningful work for them to do - exploring ramifications, new frontiers opened by the solution. Other problems, at worst. Now it all seems far from guaranteed.
I agree about well-adjustedness, but what do you propose these people do to get paid if the number of researchers with grants reduces significantly? Reskill to something that pays less, they like less, and might be automated too? Can you frankly say this wouldn't be a moral blow to anyone, well-adjustedness and all?
I don't think you can so easily call for separating them when so many people grew up in an environment that ties economic value and a respectful place in society so strongly.
> So the question remains: is it about solving the problem for humanity? Solving the problem for yourself? Or getting paid?
Say it's a mix, which I think is most likely. They enjoy the problem-solving, like doing something that feels meaningful to humanity, and obviously need to get paid. Now what?
I feel like we're arguing past each other. My point is, it's hard for me to see lack of empathy towards mathematicians (and other professionals) who stand to be displaced by these developments. I know I shouldn't take internet strangers too seriously but, when I read the comments here, I feel like some people have deep resentment for those mathematicians, portraying them as going into math in bad faith or something, and now fighting to keep their ill-gained positions.
> I personally think they’re enough problems left for humanity to solve.
For sure, whether those displaced will be able to get to work on them - and whether it will be as fulfilling as their previous work - is not at all guaranteed.
"The market doesn't owe you to do fulfilling work" Yes, but it costs you nothing to be sympathetic to the individual humans that have to undergo these changes, which can be all shades of scary and sad.
> Of course I am not denying the brutality for those who are right in the middle of finishing something.
And those who worked on a problem for 5 years, trying dozens of approaches, and weren't close to finishing something? People over-fixate on the specific problem. The big picture narrative here is, in the best case, "the way we're going to do math will be completely different", and in the worst case, "we'll need much fewer mathematicians".
> I am optimistic for those who haven’t started, which the video is referring to.
Perhaps. This comment chain is about the other side, the so-called rent seekers.
Ok I’m a stranger on the internet who tries to genuinely understand.
To that end I’ve read all your comments. I am not sure what you’re proposing or asking people to do?
Are you asking for empathy? I have a lot of respect and empathy for people who dedicated their life to solving complex problems.
At the same time I’m trying to be optimistic by saying not all is lost. Yes people will need to adjust. I’m arguing continual change and adaption have always been part of life.
I'm asking people not to be so unkind to other people grieving the (potential) loss of a significant part of their life. "If you cared so much about the problem, you'd be thrilled when a solution is found; since you're not thrilled you must be in it for selfish reasons and deserve to be displaced." You didn't write it, but the comment I replied to pretty much did.
I agree that there's room for optimism, but the conduct and messaging of the AI labs isn't very inspiring in that regard. The feeling I get from it is "we're going to push forward at any cost and make humane considerations only when we can afford to. Which isn't a lot because we've got to be the first to AGI or others will make it first and do it wrong." People then get pushed to the sidelines, many whose work contributed to the feasibility of LLM capabilities in the first place. Free market and such. But then they get criticized when they're upset about it?
Give them space to deal with it and help them find optimism, or at least, don't judge them.
Many people don’t even function off this “meaning” you’re talking about. They get it from family and friends and hobbies. It’s a contrived perspective, albeit a useful and good one. But this claim of the world’s problems existing as a means to providing value to someone’s life over actually being solved is kind of an insane perspective if you ask me.
> This would require major social restructuring that nobody's really talking about.
There are few concrete proposals, but a lot of people are talking about the need for it.
The reality seems to be that this will extend "to every problem in every profession" within our lifetimes. The only scenario I see where that doesn't happen is global war or other catastrophe stopping progress by essentially destroying civilization as we know it. So we are going to need to figure it out.
I have trouble understanding how anybody could seriously believe this.
Mathematicians are ecstatic and delighted when major problems are solved by other mathematicians. If you've followed the discussions and read the reactions, you'd know why mathematicians feel differently in this case and why more than a few are upset and feel that they've lost the thing that gave them meaning and joy.
And to put it very simply, I don't want mathematicians to exist just because I want solutions to problems. I want mathematicians to exist because I want to live in a world that has mathematicians, philosophers, writers, painters, thinkers, etc. That is a better world that makes people better.
OpenAI's proofs do not make people better. They do not enrich our lives. And OpenAI was able to produce these proofs because countless generations of human beings sowed the fields of mathematics through countless hours of labor. OpenAI is clear-cutting and sowing them with salt. Nobody should he ecstatic. Everybody should be horrified and outraged.
I think we shouldn't have calculators anymore either. The world was better when we had to calculate everything by hand and a human by hand verified every single addition and subtraction.
Are we supposed to ignore the irony that you typed this on a computer that is millions of times more powerful than the calculators you propose to forfeit?
I'm not sure the world is better if everyone was forced to do TLS handshake math by hand.
The last couple decades of economic development (of the first world at least) was in a large part due to the efficiency gains by not having people do math by hand. The world will definitely not be better if you just blew up all the computing tech since calculators were invented.
If we play a game of chess and I move the pieces to the final position on the first move and declare victory you might feel that something was missing, even if I'm right.
This is not quite like that but the feeling I get from it is much the same. Mathematicians are first and foremost busy with understanding math, not with 'solving' math though they are solving individual problems within the domain of math. The journey towards that understanding requires specialization and often lots of studying.
To quote Douglas Adams: "If 'metal nose' here is going to give you God's phone number then the philosophical question of whether there is a God becomes meaningless."
It is the journey and the questions that matter as much or more than the answer does.
And with math being a branch of natural philosophy I can see why they would be a tad upset at this shortcut because it strips the collective efforts of a large number of people of their prestige and feeling of time well spent. Imagine your life's work reduced to a short string of bits, and worse, that short string of bits was created by a machine that effectively is still a toddler.
> It is the journey and the questions that matter as much or more than the answer does.
Selfishly, as someone who enjoys programming, I feel the same way about the journey. But let's face it: for everyone else, the outcome is what actually matters. Mathematicians argue that their journey may lead to novel insights, but are those insights really valuable? Are they going to help the LLMs solve more problems? And are we sure that the LLMs can't deliver those same insights?
I think that ties in with the 'who will train the juniors' angle: if the ladder consists of nothing but the top rung because the AI combine stripped away the rest of them then a lot of fields will be looking at zero new entrants. Nobody wants to compete with a machine for their living and sense of self value. I know I don't, and obviously I can't speak for anybody else but society has pretty much programmed people to tie a good chunk of their identity, success in life and general well being to their skills and ability to put bread on the table. You can't just toss that in the bin for 3/4 of the current crop of professionals (I'm seeing the mathematicians as simply the first (and probably not even the first) of many).
I don't know if you have kids or not but I have two kids in high school and keeping them motivated through the AI revolution is a serious challenge and some of their classmates have already all but given up. The next generation down the line is going to grow up with the same kind of attitude towards thinking that you might have towards the skill of map reading. And I think we'll all be poorer because of that, not richer.
This misunderstands mathematics. There are entire branches of the subject that have no practical use. Some things also appeared to be useless for centuries before physicists discovered they actually have an application.
Exactly. As a software developer, AI has given me more time to tackle higher-order problems. The actual architecture, optimisation, and user experience.
Mathematicians could:
- Continue working on philosophical aspects of the solution and not bothered by whether the solution is known or not. It is not a movie that gets spoiled when the ending is known.
- Or better, demand from AI labs, how they would like to see AI helping them on philosophical aspects.
…except the machine will be better at these aspects too :D
I find it funny when people suggest "just re-orient from knowledge work X to knowledge work Y, doh!". Not realizing all knowledge work is on the chopping blocks.
> It is the journey and the questions that matter as much or more than the answer does.
That only makes sense to me when its what someone chooses to spend their time doing. When they expect someone else to pay them for it, its the end result that matters.
Maybe its a fundamental flaw in capitalism or money itself, but we can't expect to be paid for the sheer love of the game. Others will only end up paying us if the expected output is worth it.
Well we have been paying people for the pure pursuit of knowledge for its own sake since the scientific revolution, which is kind of the material base for capitalism, so I don’t think your argument holds much water. Why knowledge and following curiosity facilities general prosperity is maybe an open question but that it does is inarguable.
Capitalism incentivises paying people to pursue more capital, not the putsuit of knowledge.
And to be clear I don't say that as a good thing, it may be a flaw in capitalism, but we don't psy people simply to chase knowledge for the sake of the chase.
Let's just say that The math problem that got solved, I was working on it for many years but some company people used my knowledge my prompts and "solved" it without giving me any credits or money.
Firstly they plagiarised the books and research papers and then they plagiarised the prompts by the mathematicians.
Yes AI can make art and has caused many artists finding work difficult but AI art is always souless and worthless, same thing will be for math it will become souless and worthless because when humans who are experts in their fields invest their ingenuity then art becomes alive but if ordinary people like me will just prompt into the machine then souless things will come out that will be very worthless and disposable.
Non-mathematicians talking about this (especially in a cultural battleground like Wikipedia, yuck) will never be productive. Citing it here on HN does everyone a disservice. For those uninitiated, OpenAI used a fundamentally different method (without forcing in the Euler case) and the idea that the proof was plagiarized (other than the completely kosher strategy of using prior art, of course) is a complete fabrication.
In fact, the proof is such a mess, nobody really understands how it works. Which is becoming commomplace with these permutation machines where we can come up with something that passes some tests (e.g., a proof checker), but we have no idea wtf we did to get there, which doesn't really seem to do much to push human understanding forward.
It seems like such a dumb hill to die on, too. OpenAI literally stole the entire Internet (including copyrighted works), and we're arguing about a silly math puzzle.
The plagiarism and copyright stuff is just a smoke screen.
A lot of people are upset because they used to be special, their identities were tied to them being smarter, or having more niche domain knowledge than anyone else. Ai has changed that.
A lot of people are upset that people are praising garbage and outright stolen output, and any attempt to disagree with this praise labels them as a luddite who will be behind on the times and is against progress.
Such a take on "people don't feel special" feels borderline bad-faith. People of science tend to be some of the most humble people as their knowledge to seek the truth constantly leaves them with more answers than questions. It's instead this borderline cult of people praising output that is understandable to them that seems to be the ones with the hubris to try and claim that thinkers will be obsolete.
Negativity bias means We'll mostly remember the smug person who wanted to advance their careers and not their field, as opposed to the hundreds of well meaning people who want to do their work. And sadly that smug person tends to be on leadershi. I've seen that pattern in several different industries, at least from the US perspective. I
Nobody capable of a minute of honest introspection believes that. If you shuffled all the backend devs in the world and randomly assigned them a role elsewhere most will do perfectly fine. I began my own career in VFX, moved into compliance and am now working on automotive software - there's no moat around even the most niche domain knowledge, you just need to be prepared to spend time learning it. If I had to roll that into an identity it would be the learning I get to do at every turn in my career. That's what I enjoy but there's absolutely nothing unique or special about it.
Maybe the reason people are upset is simpler? Maybe people with a mortgage and kids to support don't like being told they'll absolutely 100% soon be out on their arse. Even if you don't believe that it's still tiring having to hear the same mindless taunts and vapid bullshit repeated on a daily basis.
According to the article you linked, there is no evidence at all showing OpenAI plagiarized Buckmaster and Alpoge. Buckmaster just speculated that since they used OpenAI's product, it's possible OpenAI looked at their conversation. Which OpenAI flatly denies.
And then your article says:
> On 13 October 2026, Scientific American published an article surveying several mathematicians stating that "the resemblance between the two groups’ methods now seems merely skin-deep."
But the AI companies didn't gatekeep knowledge. They released all their math results.
Unless you mean they're charging money for a product that contains knowledge. But that's not gatekeeping, just like selling a book isn't gatekeeping. Gatekeeping is when a group tries to prevent others from participating in a field or activity.
> But the AI companies didn't gatekeep knowledge. They released all their math results.
There are some important fields of math that were conspicuously missing. In particular, cryptography.
There are obviously good reasons for being more cautious when dealing with cryptography results in math, but I'm not going to believe they released everything.
> Unless you mean they're charging money for a product that contains knowledge.
They have internal models that the public cannot use (at least not yet).
Selling a book quite literally is gatekeeping, since the idea is that you're prevented from engaging with the work without paying for it. Even with libraries it was society who paid for it in order for the commons to get access, but payment was nevertheless needed.
It just turns out that the Chesterton's gate is useful and people tend to think that people should be paid for their labour, since people kinda need a roof over their heads and food on their table.
It's not gatekeeping unless you're using your own esoteric definition that's different from how everyone else uses it. Words get their meaning from how they're used in the wild, and dictionaries are descriptivist, not prescriptivist. Anyone is allowed to buy the book, so it's not considered gatekeeping, even if some people may not be able to.
If you define any obstacle to an activity as gatekeeping, then literally everything can be considered gatekeeping and the term loses all meaning. Some people can't read, so offering the books for free would still exclude them. If you include an audio book, some people still can't understand the language. And both charging and not charging money for products would simultaneously be gatekeeping under that definition, since not charging places more financial burden on the producer. Not everyone can afford to print books and give them away for free.
> Gatekeeping is when a group tries to prevent others from participating in a field or activity.
And I gave a way in which charging a price does that.
I am open to the idea of being incorrect in this case, in which I apologise for misunderstanding, and concede that I'm missing the nuance but in my defence, I'm not a native speaker.
> Words get their meaning from how they're used in the wild, and dictionaries are descriptivist, not prescriptivist.
But I didn't explain that clearly. What I mean is that definitions are always imprecise because language is imprecise and dictionaries (or people) try to keep definitions reasonably short and simple. Dictionaries are trying to describe what the words really mean in the wild. They aren't the source of that meaning.
For example, if we look up Merriam-Webster's definition of "game (noun)", none of the definitions really work for a game like Solitaire without also including an activity like reading a book.
The two relevant definitions are
1. a physical or mental competition conducted according to rules with the participants in direct opposition to each other
2. activity engaged in for diversion or amusement
(there are a bunch of other definitions as well, like animals you hunt)
The second definition is too broad and the first clearly excludes Solitaire. If you were deciding what a game is based on the dictionary definitions, you'd either think watching TV is a game, or that Solitaire isn't. But that's not the case.
Charging money for products isn't considered gatekeeping. So from a descriptivist perspective, it isn't, even if it seems like it should be, because the word isn't used like that. Banning a group of people from an activity is gatekeeping. If mathematicians said only mathematicians can prove theorems and correct proofs from non-mathematicians won't be accepted, that would be gatekeeping. But they don't do that.
If you want to use a broad definition of gatekeeping that includes virtually all human activity, then the response to any accusation of gatekeeping could be "well, everything is gatekeeping". That road just leads to pointless and confusing conversations.
Why should we be estatic that some signifigant math problem was solved by machine rather of a human being in a language only the machine understands? Don't you know that problem was solved by a space alien a million light-years away a long time ago in a galaxy far far away? Makes no difference from the meatbag perspective: both claims are untestifiable.
In fact you should be estatic that in a paralell universe all math problems have been solved, so there's no reason to pursue math at all (we did it reddit!).
When your job is automated and you're living in the streets, just remember that you should be estatic that the job is finally being done more efficiently by a robot. Like, we did it. We finally did the job right. The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system that exists for... what exactly? What is the end goal of all of this? Who does the system serve in an economy of no consumers? What is the point of solving niche mathematical problems if no living person can comprehend the solution?
> The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system
There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
To these people, it sounds like a cruel joke that people get paid 3x their salary, and after AI can do their job we learn that apparently the only purpose of their was their own self-actualization.
I don't actually believe that about math, but that's what a lot of people in this thread sound like.
I thought technology was supposed to liberate us from the fields, but it turns out that's what wealth is for, and the wealthy want us back in the fields (no more escape through special training or skill).
Why would the wealthy want you back in the fields?
You were useful in the fields to the degree that was necessary for food production (sustain and grow population) and for wars (using said population to expand and extract more resources).
Once machines automate material comforts and exertion of violence (already have, to a large degree), humans become a pure loss center. Why bother with "fields" lol.
Because fundamentally: certain humans desire power to rule over other humans. Even if the fields (metaphorical or literal) can be done more efficiently by robots, they desire that power to exert over others.
So they will keep some ready for those tasks simply to fuel that irrational desire. They will instead use the more efficient bots to enforce work on the fields rather than work the fields themselves. Or perhaps we go full Matrix and find uses for humans that robots can't properly replicate.
>There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
I know, I have that job! And I enjoy it. But the robots are coming for me too.
A bit sad other knowledge workers feel that. I know my job isn't anything trying to better humanity; I just make video games. But making those games (or rather, the tools to make those games) has an end result to have people enjoy themselves a bit in a decreasingly enjoyable world. So there's my fulfillment.
But I understand it from a blue collar perspective. I tinker at toys in a metaphorical basement and I live a cushier life than many who give their bodies to their duty. That doesn't feel fair at all. But I mostly wish that was motivation to band together and get blue collars paid better rather than cause this inter-class divide while the capitalists ransack all of society.
We’ll put IMO. This expresses well the way I’ve been thinking about “the mathpocalypse”.
I feel sad and even a bit forlorn when I think of jobs that provide purpose, meaning, motivation, and satisfaction (not to mention $$) to human beings being lost to servers in racks and soulless machines. I think many people feel similarly.
However, I do believe that when a couple problems get solved that massively benefit all of humanity — e.g. a massive cancer breakthrough, etc — a tipping point will be reached and public opinion will reverse and enthusiastically embrace AI, and will accept not only diminished personal meaning but outright technocratic rule. This would be a huge mistake, but I really believe it would happen.
And as we know, solving interesting math problems is a leading indicator of big practical results to come.
>However, I do believe that when a couple problems get solved that massively benefit all of humanity — e.g. a massive cancer breakthrough, etc — a tipping point will be reached and public opinion will reverse and enthusiastically embrace AI, and will accept not only diminished personal meaning but outright technocratic rule.
Is solving cancer worth ceding human meaning and human autonomy to the machines? I haven't seen anyone ask this question but it seems the central issue of this revolution. Personally, I don't think it is.
Perhaps machines will lead to a perfectly homogenous society completely absent of negative valence whatsoever. But if every experience is also devoid of any personal meaning, what's the point? The optimal human state is not one of peak hedonism, or wholly absent of suffering.
> Is solving cancer worth ceding human meaning and human autonomy to the machines? I haven't seen anyone ask this question but it seems the central issue of this revolution. Personally, I don't think it is.
Solving cancer alone? Perhaps not.. Unless you have cancer.. Solving all diseases and aging? Well... I would rather be alive and live like an AI's housecat than dead and free. And I suspect that many people who publicly disagree are just performative, and would actually make the same choice when push comes to shove, and they have to actually choose between "diminishing their autonomy to the machines" and imminent death.
The Christian influence on the world has been undeniably positive. Seeing death and suffering as the enemy and organizing society around minimizing it has been a boon to human progress. But now we come to the dark side of this view. A fear of death so complete that we are willing to sacrifice everything of value to prevent it. Our society has become so divorced from our natural state that death is seen less as an inevitable part of life, and more as a corporeal enemy that must be resisted at all costs. As it turns out, too much of a good thing, whatever it is, leads to absurdities and atrocities.
No, I do not think human autonomy should be sacrificed to defeat death. I personally do not fear death. It's as irrational to fear as it is to fear a deep sleep. I do fear dying painfully. Tragically, we as a society resist alleviating the pain associated with the process of dying (by speeding it up) for the same reasons. If only we could learn to take our principles in moderate doses.
> death and suffering as the enemy and organizing society around minimizing it
> A fear of death so complete that we are willing to sacrifice everything of value to prevent it.
> a corporeal enemy that must be resisted
I am afraid that you know nothing about Christianity. The beliefs and values you describe are antithetical to the Christian life and our worldview. If you've ever just examined the life of St. Teresa of Calcutta, you'd understand how absurd it would be for her to "fear death" or "minimize suffering".
We seek to follow, and imitate, Christ Jesus in his life of suffering, his death and resurrection. We do not resist, or minimize, or fear any of this. To do so, would be quite heretical to us as Christians.
Of all times of the year to bring this up. All Saints Day, celebrating the eternal life of those, named and unnamed, who have preceded us in death. All Souls Day, to pray for all the departed souls who suffer in Purgatory, after death but before their Heavenly reward.
I don't know what religion you are trying to describe, but to me it sounds like atheistic secularism. It is atheism that fears death, and utilitarianism that seeks to minimize suffering. Not Christians. Goodness, gracious.
To understand my point one must separate the metaphysics from the practical effects of the belief system. Christianity represented a step-change towards humanism. This must be considered in the in the era it was founded and compared to the competing ideologies at the time, i.e. paganism and its various death cults. Christianity institutionalized ideals like equality of men, the sanctity of life, charity, self sacrifice, etc. These ideals are the precursors to civilization.
The particular ideology of Christianity was super effective at laying the groundwork for modern civilization. Of course, these ideals have since evolved and have since become some kind of secular ideology. Granted, it was imprecise to attribute a fear of death to Christianity. But the sanctity of life is in practice a close cousin of a fear of death. Modern secularism having no metaphysical alternative has made this fear explicit.
> I suspect that many people who publicly disagree are just performative, and would actually make the same choice when push comes to shove, and they would have to actually choose between "diminishing their autonomy to the machines" and imminent death.
You shouldn't. Maybe you should learn Hilbert Calculus so you can appreciate it.
It's like asking if what someone wrote a beautiful poem but it's in japanese. Maybe hearing about it motivates me to learn japanese, or maybe it doesn't. But as a non-speaker it makes little impression on me.
On one hand I agree. I’d also add that there will be no end of math problems to solve. That some were solved will only lead to new ones.
That said, I think what has mathematicians… upset is probably two things:
1. These are hard problems. Hard enough that solving one could take decades of work. And there’s tons of collaboration involved. Pivoting to another - and making progress - isn’t exactly something you wake up tomorrow and start doing.
2. I think motivations matter to some. And the AI companies doing this aren’t doing it for the betterment of math or even society. They are in an arms race to prove their product is superior and any careers that are damaged collaterally be dammed.
Many people don't seem to understand that pure mathematics is not a practical applied science, nor is it in the business of inventing things.
Pure maths is much closer to philosophy or art than practical problem solving. Yes, we're extremely lucky that mathematics also happens to be a fantastic formalism for solving practical and scientific problems, by the practical problems are not remotely the subject matter of pure math. Of course, many mathematicians did advance theory in order to solve specific practical problems, but the pursuit of theory for theory's sake is also an important human activity.
Historically, this freedom from practicality has been important. It allows mathematicians to explore purely theoretical issues that have no practical bearing today but that might well have relevance in the future. We don't know. Carving out dedicated resources in society for that activity, though, has proven very beneficial for other sciences.
You have no computer, you have no neural nets, you have no AI, without at least some results from pure maths. Maybe keep that in mind before you crap on mathematics for its lack of immediate practicality. Not all good things in life arise as solutions to concrete and immediate material problems.
There is a difference between the process of solving a problem and a problem being solved. If I solve a problem myself, I understand it, I find out something new, I get to try lots of things. It's engaging and fun. If I tell you to go solve a problem, I can learn it afterwards but I miss out on the entire process.
Personally, I enjoy the process of solving problems. I do not enjoy wrangling unpredictable AI agents.
For a personal experience I 100% agree. Where I'm not sure where I land is when the problem solving is a job people are paid for. I wouldn't expect someone to be paid to enjoy the process of solving a problem, I'd pay them to solve it.
There are plenty of things I enjoy doing, but I try to do them as often as I can for the love of it rather than because someone is paying me to enjoy the process.
You never hired someone to find something useful to improve or fix? There a lot of people who are really good at that and really bad at just doing the things you tell them to do.
I've never hired anyone only to enjoy the process of trying to solve a problem. Imagine hiring a plumber that never solves your plumbing problem but had a hell of a time enjoying the process of trying to understand it. Would you want to pay them for that?
Into eh concept of the mathematics discussion, I wouldn't care to hire a plumber that could work through theoretical plumbing designs that have nothing to do with my house.
Having a plumber that can better solve problems during their work fixing a system is obviously a good thing. That simply isn't what is being discussed here, most mathematics research being raised are theoretical math that has no immediate practical use. That doesn't mean it shouldn't be worked on, but it isn't the same as solving a real world problem we have today.
Previously there was no way to pay someone to solve a problem without someone going through the process of solving it. I think what people are upset about is that any kind of problem solving is no longer a stable career path. Even the skills replacing the problem solving jobs are liable to disappear as the interfaces are refined and models improve.
This is pure math research we're talking about here. It's not exactly lucrative and people looking for commercially applicable results ASAP weren't funding it anyway.
It sounds like your argument is effectively that it isn't an economically viable pursuit.
People have been getting paid for it, and hopefully that can continue if they enjoy it, but why should we want them to be paid only to chase theoretical math if it has no valuable output, or if the value is in the pursuit rather than the output?
My point is that this was already the case, i.e. math research was already not a "dollars go in, useful proofs come out" field. The people lamenting the future of mathematics are largely not focused on the economics, they're focused on the fact that anything they might apply their efforts to could get sniped by a frontier lab at any moment. That is obviously demotivating.
But reading the threads here on HN, in response to people saying "this sucks", AI boosters would rather redirect the conversation into economics and feign outrage that people are being paid to do mathematics at all.
Suddenly folks seem to be both in contempt of the idea of solving abstract puzzles without practical application, and certain that they want a higher efficiency of abstract puzzles solved per dollar (again, puzzles they probably don't care about).
The ideal human society is not one where people are narrowly focused on creating widgets or increasing efficiency, narrowly construed. An ideal human society includes intellectual pursuits. Some of these pursuits do not suit dabblers, they take deep expertise that can only happen from a lifetime of directed effort. We are collectively better off when some value is spent in ways that isn't aimed at maximum efficient allocation.
It's funny, the justification for accelerationism is that people can be paid (UBI) to pursue their passions. On the other hand, we have those that are asking why anyone should be paid for work that isn't economically viable. I suspect we're being sold a load of bullshit.
I don't support a UBI, for what its worth. The idea is nonsensic from my vantage point, if there's a certain minimum level of good people should have access to it makes more sense to give it to them rather than to give them some level of cash that can on theory buy it.
More importantly, I'm curious how you define an ideal human society. How do you land on what ideal is, or what it would take to get there?
>More importantly, I'm curious how you define an ideal human society. How do you land on what ideal is, or what it would take to get there?
The question is in what context does the human psyche thrive? We find meaning in personal struggle and overcoming obstacles. We're happiest when we're striving for something out of reach but seemingly attainable. We're much less happy when we have all of our needs met but have no source of meaning or fulfilling struggle. Our evolutionary history is one of struggling against hardship and finding personal meaning in the process. This is a core feature of our psyche and it is to our detriment to eliminate it.
This isn't to say we should all be struggling for our next meal. Much like cats, our core drives can be exercised and satiated through a simulacrum. There are many ways it can be satisfied, but strive we must, against something with inherent meaning to us. The problem with AI fully realized is that it takes away most avenues for human achievement, thus the struggle loses all meaning.
Mathematicians usually care nothing about application of their work. Working on interesting problems is their only motivation. Practical applications are almost always happy accidents.
This goes back to the hope that robots would do the laundry and the dishes and the cleaning up so we could write and play music, create art, and solve mathematical problems.
Instead the AIs are doing all of that leaving humans with only the dishes and the laundry and the cleaning up.
Whatever doesnt count as maths is just not maths. Its just carrying out instructions to get some "gain".
Other people usually care only about "gain", its their only motivation. Non "gain" results are just happy accidents.
And "gain" (once you have your survival covered) is just an invented abstraction with 0 real meaning. But people try to convince themselfs that it has meaning.
This goes back to the classic story for "kids" about the emperor that has no clothes.
If math is nothing but solving puzzles for fun then I think a lot of people should be very pissed off that they are doing hard labor while being taxed to fund a puzzle hobby group.
Of course I don't believe that math is just fun puzzles. But if it were, then it would deserve to die as a career, AI or not.
As of this comment you have 26 comments out of 206 total on this comment section, more than 10% basically all spreading FUD to try and make other people as miserable and pessimistic as you. I'm not sure what your motivations are but I'm glad we have people like Grant on the other side trying to keep a positive outlook on life and the future, and I hope all you eternal doomers who constantly try to bring others down with you find joy as well.
It seems like everyone presumes that the currently proofs which are difficult to parse will stay that way. LLMs are really good with language. There's no reason that the next wave of proofs won't be accompanied by very literate explanations that mathematicians can generate understanding from.
One real limitation is context size. 1M tokens is enough to do a lot, but the Lean graphs they are making are way too big to fit, so an LLM will never have the complete picture.
No, and that's one of the reasons mathematicians dislike automated solutions. Sure, it's verifiable, but it's too complex and messy to actually learn anything useful. So it technically answers the question, but doesn't leave you with any deeper understanding.
Nope. That's why a lot of knowledge comes down to compressing large concepts into chunks we can understand from new ideas and concepts. LLM's don't tend to be very good and synthesizing such concepts.
Perhaps, but due to the slop nature of OpenAI proofs, the proofs remain unaccepted by mathematicians, which leads one to question how many are valid proofs and how many are nonsense. If we see that they are nonsense, then OpenAI has wasted a huge amount of effort in mathematics. Famously the ABC conjecture proof of 500 pages is still unaccepted despite having been written in 2012.
Already people are seeing that the lean proofs provided don’t match the paper and lean proofs have not been provided for all paper proofs.
I’m seeing this perspective expressed a lot lately, but (so far) only online.
Understand that there’s more than one way to prove something, that there’s an art to making something understandable, and that humans tend to take the most understandable paths (to humans.)
Models often don’t do that. But in solving, or claiming to solve, important problems, they nevertheless remove a lot of the excitement and incentive towards working towards a solution humans would naturally find. Plus, a lot of these problems really don’t have any critical applications at the moment. They’re done for the love of the game.
Does that bother you? That your tax dollars pay people who do math out of curiosity?
The primary value of math has never been about producing "solved problems" (is there any practical value in "solving" NS in itself?). The primary value of mathematics has always been about "machinery for thought", i.e. the abstractiosn and methods that produced the solution.
I think there is a little too much pessimism of the "math is dead" sort. As long as there is a need for humans to think there will be value in doing math.
It's completely natural to be attached to the process of your job, rather than the outcome. It's not a phenomenon restricted to mathematics. We can say it shouldn't be like that, but it is.
A lot of people went into maths because they liked not only the results but the process of research and discovery. That has been taken from them. No matter how you feel about AI, I think we should all pause and at least think about this and validate those feelings.
Look at the most upvoted comment on that thread:
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I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
> Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
No, I think it's just super cool. One of the things I hate about it is that you can't really explain what you find cool about it; others just have to see for themselves (in some sense it's like a self-induced trip to sit there and work out analysis/topology proofs in your mind's eye, visualizing little nested blobs doing their things), which of course nearly no one you will ever meet has any interest in doing. I wish more people wanted to talk math/physics with me lol.
I just want to know more. There are infinite rabbit holes. Like in uni and for years after, I wanted to know why convolution should be so important. Was I disappointed that someone else had already figured that out (that it's what you get when you form the vector space over a group and define multiplication as group multiplication) long before I was born? No way! I was stoked to finally have a satisfying answer! I wish they'd find a way to stuff that into applied analysis for engineers because it's cool and engineers should get to see cool math.
But then I went into software (partly because it was a hobby of mine anyway, and partly because it pays well), and learned a long time ago to leave any notion of artisanship or nerd crap at home. Java programmers spent forever arguing against type inference, Python/Ruby programmers think static types are a hindrance, and Go programmers spent a decade saying generics make things more complicated. Metaprogramming is generally synonymous with "too clever." It's cool that the relationship C^(A+B) = C^A C^B (or generalizations) says that the way you handle an enum type is to pattern match/provide a handler for each constructor, but I'm not going to burden my coworkers with that nonsense.
AIs are currently reducing human knowledge and cognitive capabilities, replacing it with machine capabilities instead.
It’s going to destroy both academic funding for people wanting to learn more through research and salaries for people currently doing cognitive work in corporations and an irresistible crutch for students using AI to do their work for them.
It will probably reduce most people's cognitive capabilities, but most people aren't interested in learning. If you don't want that for yourself though, it's great. You now have your own personal professor available 24/7 to answer questions about whatever topic you're learning. Take a picture of a page with your phone and ask it something you're confused about, or to check your understanding. Get immediate feedback. It's awesome.
Similarly, at work, it's never been easier to have data to make decisions with. Or to just try stuff out. Really great. Gets rid of what would otherwise be massive amounts of tedious "thinking" that drains your brain but isn't actually challenging in any way.
It's early yet to see what effect it will have on research. Experimental science is full of interesting, cognitively engaging topics as well though. Or maybe they end up like me and do boring engineering work for pay, and read cool stuff that the AI has figured out in their free time. It's not all that bad.
If that were the case, then people would have unmet needs, and so there would be work to do. You need to keep your proposed scenario internally consistent here.
I think it might be a result of shock to believe it’s been taken away - you have my sympathies.
Mathematicians got a new toy. It’s up to them to pick it up, play with it, and figure out what it can and cannot do.
While I cannot guarantee it will stay this way indefinitely, there is still plenty that AI cannot do that humans still can, and asking the right series of questions remains an art of its own. There is still plenty of original work to be done.
As Arnold Schoenberg stated in the 20th century, “there is still plenty of good music to be written in C major.” The search space is vast and today human judgement is still required to really navigate it usefully. No LLM has yet written anything like Shakespeare that has superseded Shakespeare in any culturally meaningful way. Although programming is supposedly just about solved, I expect to see numerous billion-dollar startups emerge over the coming decade, rather than all of the innovation running out at the speed of tokens.
“ if you're mad about your problem being solved, maybe you weren't in it for the right reasons”, politicians/financial advisors/military members/etc… would like a word with you.
I suggest listening to "Math Vs Machine" [1], which has a much more nuanced take. It clearly lays out two types of use of AI in math, one that helps humans have better understanding, and one just bulldozes problems without helping us get any insights. It also touches on the topic of "does it matter if the machine does things in ways humans cannot understand".
Mathematicians are saying the current papers are pretty inscrutable and use terminology unfamiliar in the math sub fields in which the models are generating proofs.
Cause it looks like it's mining one subfield for a pattern and applying it to another. (The take from the few math folks I know who have looked into items of their interest).
Computing has the same issue. If we swapped a PLC programer with your average SV software engineer for a week both of them would have a really bad time.
I'm not entirely sure this is fair. My belief is that mathematics exists in the intersection between art and science. I don't believe in progress for its own sake, so I'm inclined to say those interested should undertake it for the art, or to "play with puzzles." The rent-seeking argument and "weren't in it for the right reasons" is the same argument as calling musicians sellouts when they start making money. Making money doesn't make you a sellout, but it can.
I find it overly harsh too. I think the reaction is much more about the devaluation of innate ability, and skills / knowledge built over a lifetime. If another mathematician had solved it then you can refocus on another problem and get another chance. Now that an LLM has done it it’s very unlikely you’ll ever solve another open problem.
Mathematics is more akin to art or a sport to many — philosophy, too. I don’t see that as a bad thing.
But there’s always a risk that someone in an adjacent domain makes a breakthrough that completely reshapes the research landscape overnight. It’s happened before AI and it will happen at some point again in years to come. Grief is understandable, but this isn’t the first time or the last time.
What, in your opinion, is the point in solving these problems if no human is there to witness it? This is like suggesting we have AI watch movies for us and read its summary afterwards. In fact, why do anything anymore?
Yes, much of pure mathematics is "playing with puzzles" to the end of the joy and beauty revealed by a human solving them.
> If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
I'm not a mathematician but I find this framing to be rather non-pragmatic and frankly, pointed.
In the process of Leonhard Euler's "rent-seeking" so he could "play with" bridge crossings he invented a completely new branch of mathematics that is the basis for things like Google Maps today. The process of working with these problems is just as important if not more, than just solving them.
I wonder how many math professors think they were actively working on well-known unsolved problems. Is it just a small elite club, or is it every tenured / tenure-track professor in all R1 schools?
I am at an R1 school, I know at least 4 or 5 people personally (Profs and Postdocs) whose entire research programs were annihilated. Like they wrote grant proposals that are totally obsolete now.
I want to add here: why do you imagine the outcome here will be dictated by what I, or any other individuals, want? There's this conceit that we can design how society is going to be rather than have to deal with what society becomes. The bandwidth for "societal engineering" is low.
AI wouldn't advance the state of the art? It promises to do it at an incredible rate.
What you are complaining about is not that the state of the art wouldn't be advanced, but that vanity would not be served. Vanity (as part of Pride) is one of the seven deadly sins for a reason, and Pride has been described as the root sin, the worst of the lot, since all others stem from it.
He is paid because people pay to watch him play. If people were as happy to watch robots play he'd be out of a job. Making him happy isn't the reason he's paid.
Yes, exactly -- and, as a result, we're doing this to all of humanity. People don't need to be happy, we just need to produce more.
So, the future sucks; we've worked hard to automate everything people find joy in, and left the miserable parts of the job for people to do, and asshats like you insist we should be happy about it.
there was already far more to learn than any genuis could understand in a hundred lifetimes. There is no nobility in simply increasing the amount of things that can be learned
several reasons. For some, because we think it might lead to useful results. For some, because we think the human pursuit of knowledge is worthwhile. For some, because we want to discover truths about logic and the universe. For some, because we are playing a status game (not just the mathematicians themselves but countries, universities, companies etc). For some, because we get personal fulfillment in understanding, and there being experts at something who can help others to understand.
For most, all of the above in various measure. To act as though one is the only thing thats important is wrong. The crisis is because the balance between these that existed is being shifted.
Only those that aren't in a field and see its existence justified for purely instrumental reasons can think its value is merely in its practical output. Personal meaning and fulfillment come in many forms. For mathematicians, part of that value is through solving problems, but it's also partly about the struggle itself, gaining understanding, expanding the frontier of human achievement, being a part of a community that values these things, playing a valuable role in the progress of humankind and making a career out of it. Having all that swept away overnight will lead to an existential crisis for anyone who is on the wrong end of this process.
It's quite bizarre how many people feel so personally affronted at the existence of a rather exclusive intellectual community that they take glee in seeing it decimated overnight. But make no mistake, AI is coming for the things you value as well.
This is an awful and really ignorant take. The manner in which the problem is “solved” matters a lot, and these AI solutions are about as poorly-done as possible. That a solution exists closes the door on almost any sort of support for finding another, better one, which is the real problem. If this continues, we wind up with a field with no open problems, no practicing mathematicians, no future mathematicians, and no way to come up with new problems (this latter being much more important than solving existing ones, in the main).
Incredibly nasty stuff to serve on the rent-seeking forum. Doubly nasty to levy at people who actually like being alive, like mathematicians. If capitalists had their way we'd all be slitting our wrists on day two of existence
Huh?? Nobody enters mathematics because "We gotta get this Collatz conjecture solved already!", you enter it because you love the process of arriving at the solution.
It's like saying "If your goal is reaching the top of Everest, you should be ecstatic they built a train line that brings you right up to the peak!"
Meh it would be like if you were a mountain guide that took people up Everest. One day a helicopter operator started taking people and everyone lost interest in climbing. You should be happy, the problem of getting to the top is solved!
What? Why are we nullifying so many human factors in one stroke? Humans strive to contribute to their community and to be recognized for it. We aren't machines, we have social and financial needs, and enjoy competition. Math being solved would mean part of humanity losing these parts of their lives.
Would sports teams have as many fans who enjoy their games, if all the humans were replaced by robots? Your team may win, so I'm sure you'll be happy with the outcome, but maybe something got lost?
I for one have always felt inspired when reading about remarkable human achievements. To think that those might be coming to an end, replaced by AI, takes the humanity out of those stories.
How is your argument any different from the classic Luddite argument? Why is doing math different than making textiles? Why does math deserve special protections when other types of workers do not?
There will be human achievement no matter how much automation and robotics we have. There’s an entire universe to explore and colonize. Plus people still want to see other people do things like perform music or play sports.
I'm not against technological advancement. But AI is unlike previous innovations. Soon, every scientific and knowledge-based breakthrough could be made by AI. And we're losing something intangible when that happens.
Think of your average Veritasium video. They know how to tell a story about a scientific breakthrough. It always centers around the human inventors. Take the humans out the story and it's less interesting, relatable, or enjoyable. Also consider: why do HNers hate AI slop? If all that matters is the outcome (getting some point in writing), AI does that. I hate slop because it has lost its human touch. I appreciate a result more when its distilled from human effort, and I'm not alone.
I'm not a mathematician so I have no skin in this particular game. I'm a software engineer though, and we've already gone through this. I can simultaneously love how easy it is to build applications with AI, and miss the days when human talent was valued and celebrated in my field. My job gave me purpose. My work team had comaraderie. A future where we all report to AI managers and we exist just to sign off on what our AI agents do, is dystopian.
Yes, I suspect there will always be human sports teams, musicians, actors, etc. My point was to illustrate that everything is less appealing when you take the humans out of the picture and I don't see why science is different. If outcomes are the only thing that matter then when robots are better at sport than humans shouldn't we should all just watch robots compete?
P.S. Do you really believe humans are going to visit any object further than Mars, let alone actually colonize them? Things would've had to go very wrong on Earth for that to happen, and that future doesn't appeal to me one bit. Call me a luddite if you want. How many people would willingly say goodbye forever to the wonders of Earth so that they can start their family on an inhospitable planet where they'll be indoors for the rest of their life? And why even bother exploring those planets? We can get all the data we need from autonomous spacecraft. Isn't that the outcome that matters?
Well sure, but people do still want to watch videos like 3blue1brown in-depth explanations, and they do still want to learn math for its own sake. People can still do math and derive enjoyment from it.
I find it interesting how a mathematician enjoying theory-building or playing with ideas gets recast here as rent-seeking. It sounds much like certain right-wingers complaining that kids these days don't want to work, just stay in university studying useless things at the taxpayer's expense.
I'm sympathetic to mathematicians but this does not paint them in a good light.
If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
* I find this characterization overly harsh, but if you're mad about your problem being solved, maybe you weren't in it for the right reasons