Identity and Purpose Crisis

Recognition that mathematicians' sense of value and purpose is threatened when their rare skills become commodified, similar to artists facing AI-generated content

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The rise of generative AI has triggered a profound identity crisis within high-level mathematics, forcing researchers to grapple with the commodification of skills once considered the pinnacle of human intellectual rarity. While some see this shift as a liberating transition that returns math to its origins as a recreational pursuit of pure curiosity, others fear a catastrophic loss of purpose as years of hard-earned expertise are reduced to automated "slop." This tension highlights a divide between those who believe AI will democratize knowledge by amplifying individual intuition and those who view the automation of abstract reasoning as an existential threat to the "human touch." Ultimately, the discourse suggests that if machines can outpace humans in optimization and proof-finding, mathematicians must decide if their value lies in the results they produce or in the intrinsic, "sport-like" joy of the struggle itself.

41 comments tagged with this topic

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The foundations of a great our mathematics came from landed gentry who enjoyed the work and were not paid for it. Today we prosper in our technologies and algorithms (not talking about recsystems) because of them. If math should once again become the pusuit of the curious and free but with even greater "skills", that does not seem to be an issue for math, or for those of us who benefit from math. An issue for people as a concept and for mathemeticians, yes. But that's a separate topic, like the anguish of not getting into the Premier league.
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Sure, the world is a better place with fewer serfs in it, but what exactly is of "higher value" than being a research mathematician? It's already a profession that consists essentially of exercising our highest and most distinctly human capacities: creativity, abstract reasoning, and passing the results of those on through a distinctive language and culture. I don't think the comparison with serfs is useful. I'm sure most research mathematicians would like more freedom from some of the drudgery of their work (grading, admin, etc.), just like the rest of us. But we should be aiming for a world that allows more people to become mathematicians, not fewer.
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Sure, recreational mathematicians. Just like people that like to ride horses for fun.
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Constant recreation may be the ultimate purpose of humanity.
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We argued that AI would free us to explore the arts. Instead it first came for written language and images. So what's left when it can write all the programs, drive all the cars, and AI sensors on farms can monitor and distribute nutrients. I remember watching TED Talks about how AI weapons need to be carefully studied, and instead we see them autonomously picking targets. I'm not seeing any higher values, instead I'm seeing how we're on a path to assured destruction.
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I see that point of view but there's another that I've recently been thinking about. Many of the fields that were traditionally considered for "smart" people (STEM etc.) are the ones that are being really hammered by AI. Whereas, things which people considered lightweight often involving social relationships and interpersonal skills are still beyond the scope of AI (much of it even theoretically beyond the scope although perhaps robots might have an effect there). There used to be a sysad T-shirt from the BOFH days "Go away or I'll replace you with a very small shell script" which pushed the idea that whatever could be replaced by a computer was something trivial. Now we find that the things which we thought were only for "smart people" are the very things being replaced by computer programs which is telling. Perhaps what we considered tough and smart really wasn't.
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>>Similarly, the output of programming is not only a program, but also a programmer. It is you. This can be said about pretty much any job on earth. By that definition nothing should ever be automated. Everything thinks they are special, actually no one is. You become special by being rare. Find something that can be done by no one or only a scant few.
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> Everything thinks they are special, actually no one is. That sounds very nice, but isn't true. Most of the people I know, myself included, don't consider themselves special broadly. They're special in their own community, but not globally.
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Yes, but we've already painted ourselves into a corner by almost a century of moving all that work onto computers. Why would we want to sever this last thread of human control? What is there to gain from it? I don't think I have to convince anyone how much there is to lose. The situation being created with an overdependence on AI is looking much more like the burning of Alexandria, and less like a utopian dream or even the oft-warned-about authoritarian hellscape. The AI hype is over and revealed to be delusional and politically motivated.
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Anyone else draw similarities with this and the artists and authors who complained when gen ai first came out. I think a lot of people don't realise the disruption ai will cause to many industries, until its directly impacting them, basically personal fable at scale ( https://en.wikipedia.org/wiki/Personal_fable ).
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Also worth noting these are reactions to what is essentially equity in access to skills and knowledge. I personally do wonder (worry) about where all of this pans out and what society looks like post generative llms. But at the same time there is a particular flavor of amusement that I can't help feeling watching folks simultaneously balance, "llms produce nothing of value" and "llms are so harmful and dangerous to our culture that we need to start policing use within our community" Where that harm essentially stems from devaluing hard earned skills within the community. And while I do not take joy in the displacement of labor, never in my wildest dreams could I have anticipated how harsh and irrational of a reaction to the equity of these skills could be. Which, I would like to point out, though hard earned were earned under the tremendous privilege to pursue these goals in the first place. Llms are an amplifier of an individuals intuition and taste. That these supposed pillars of the community are not bravely exploring how to push and wrangle these bounds, and instead are retracting into conservative stances under the guise of human centric morality is (IMHO) demonstrative of lack of confidence and creativity within these fields more generally. I believe that this lack of creativity and imagination is how we find ourselves in the personal fable you're noting: the experts are so myopic that they can't even imagine how they're field can be disrupted until it's disrupted outside of their control, and feel the need to control rather than explore.
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> If you think 'most people are completely put off by AI slop', you're living in a blessed bubble I think most knowledge workers don’t like AI because most of them are aware that AI was created to replace them. Just about every CEO that has given a speech about AI at universities have gotten booed by the students which isn’t surprising as those CEOs are effectively promoting technology that will take their future from them.
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> do writers and authors still really care about AI it is demographics.. there is no single answer, you are talking about millions of people with varying amounts of this JOB description > most people are completely put off by AI slop this is almost pathological.. most people consume media not produce it. Those in the business of media have been eliminating people for thirty years, and this AI tooling has multiplied that effect > the value of XXXX writing or image generation generation is basically zero yes - bingo.. the average capable person now can expect to be paid ZERO for their ability to personally produce writing or image generation.. and, if you don't start somewhere, you will never get to ascend the ladder of success in those fields, by definition > I suspect that the cloud will pass on math too consistent with the other statements here, this is 180 degrees false.. substantiation? the content of the letter signed by world class mathematicians, who are visibly quite concerned
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The artists will be fine and AI will liberate them. It's the engineers and mathematicians who are walking into the blade. They built their entire sense of self on being the best optimizers in the room and optimization is the first thing the machines take. Their whole identity was a number going up. Now watch it go to zero.
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Depends entirely on whether "the market" ends up valuing what humans add to various artistic processes. Same for human engineers, who are still very much needed at least for the time being. Certainly the scenario where a human touch isn't valued by the market raises lots of very difficult philosophical and economic questions but that's a separate issue.
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> Depends entirely on whether "the market" ends up valuing what humans add to various artistic processes. No, it does not, at least for arts. There is a chance, that AI will free art from it's utility or the necessary to create value. Maybe graphic designers and illustrators will lose their jobs due automatization, but most paid art (concept work, corporate design) was instrumental compromise anyway. Take away the commercial floor and what's left is the part they cared about most. Engineers on the other hand identify mostly by being optimizators and creating value. They may keep their jobs, but at what cost?
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Sure, but the compiler didn't promote the assembly programmer, it basically ended assembly programming. So which side of that is the engineer on? You're assuming we're the dev who got the compiler. But if the premise is that AI does the actual problem-solving, then we're the assembly and AI is the compiler. > Engineers like to build finished products, not wallow in minutia This only works if what you loved was having built the thing. If what you loved was the building itself, the solving, then "here's a way bigger system, the AI figured it out" isn't a win. It's just a promotion from maker to manager. And a lot of engineers specifically tried to avoid this promotion in their career.
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My impression is that most developers are motivated to create a finished product for a variety of reasons. If what someone enjoys is the craft purely for its own sake then isn't the resulting situation exactly the same as for artists assuming a hypothetical future where the core activities of both are largely automated? Such people can still engage in the craft purely for their own enjoyment just as anyone who wants to is free to write assembly by hand today.
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I cant speak for engineers, but as a mathematician I wholeheartedly disagree with everything you claim in your comment. Almost none of the mathematicians that I know care about the optimization aspect of mathematics: the pursuit of optemizing constants in theorems and providing minor technical improvements is mostly seen as pointless unless there are significant new mathematical insights that fuel the improvement. I think most mathematicians rather build their identity around providing actual understanding of problems using mathematics and improving society's understanding of mathematical problems. Of course AI threatens this too, but the threat is of a much lesser degree. One could even argue that AI is helpful here with getting mathematicians to the 'frontier of knowledge' as AI is usually good in combining ideas from different fields.
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So that is kind of the point of studying maths right? Why something in unsolvable or undecidable can be as important as the output of a theorem. Questions like these, fields medal level problems or Karp’s 21 NP-complete problem are problems working mathematicians are interested in. Will LLMs help as an human assistant in the future? Probably. Will LLMs answer these questions themselves, provide insights and bounds to these new mathematics and teach other mathematicians why this new math they create is true? Will these models have phds and take candidates teaching them how to apply and think about the maths problems they are interested in?
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it can operate at the level of a mere mathematics professor, who everyone knows are barely conscious, basically automatons. wake me up when it's Einstein
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In general, most researchers already incorporate LLM into their workflows, as it is quite good at context search. However, the relevant training data is based on the collective works of the field of experts. Collecting current data on that work is what makes the LLM sound relevant, and any improvement of the LLM model requires frequent new data from both researchers and the chat bot users themselves. LLM are not real "AI", and anyone that says otherwise is selling people something. To phrase this differently, LLM companies conduct unauthorized targeted intelligence gathering on peoples work, codify that act of plagiarism or theft as MoE documentation, and sell unaccountable token output to other users. There is a reason output becomes more nonsensical as "AI" companies try to use dynamic weight granularity and conceptual compaction. It is not necessarily "AI" hallucinations, but rather people fooling themselves into believing smart people are no longer needed if they willingly become a hapless exploited data source caste. This simply isn't true, as people will leave the field for awhile. The LLM business model regularly requires copyright theft and plagiarism to persist. It will not magically become sentient/AGI/less-stupid, as these algorithms have been operating for over 40 years. What has changed is the scale of the deployment, data pool size, and the energy consumed. Scientists are still necessary, as they create the world models LLM try to guess at by statistical inference. Hype and FUD ahead of an IPO for a highly dubious revenue company is expected. We look forward to the low cost liquidated GPU hardware in the near future. =3
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The Ouroboros in western mythology is a cautionary tale about the uselessness of the first perfect immortal being, and why humans should suffer our imperfections with insightful grace. The concept also made a great Red Dwarf episode. LLM are more like the Mechanical Turk trick, but the persons inside the machine running the con is unaware of how their actions affect the confounded observers. Have a wonderful day =3
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> Have you ever been exposed to concepts that are so complex that you feel like you could devote your entire lifetime to trying to understand it and still fall short? It’s a very humbling experience, especially if you have classmates who pick it up effortlessly. I do have a PhD so I kind of know how that feels. I watched my entire field (PL) get eaten up by AI though, the problems that I thought were huge 10 years ago are just silly footnotes now. > Without a human holding the reins, consider an LLM a rudderless superboat speeding erratically towards the horizon, finding and proving meaningless theorems that not even your most talented classmate could ever begin to understand. I don't disagree with that. LLMs are a tool, a super fast pattern matcher, research, token predictor. I don't expect it to go out and define its own esoteric (or useful) problems to pursue without human interaction. That's for the humans to do. I don't understand what that has to do with my original comment though. I wasn't addressing what problems the LLMs were answering, just how to review and dissect the answers that they would come up with.
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The value of human understanding just cratered because we have machines to understand for us now.
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Wonder what Frank Herbert would have to say about letting machines do the thinking for us.
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Except, it was true before and it is still true today that the best "artists" whether graphic or mathematic, are the ones that do somehow manage to cross the chasm of pure research and providing a tangible benefit to their benefactors. That aspect of understanding your customer is not changed by the presence of AI.
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Spoken like someone that has no idea why mathematicians are important.
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what's wrong with artists having jobs via a program? whats wrong with struggling alcoholics having jobs via a program? athletes? politicians? there is no inherent virtue in the struggle and effort associated with great mathematical achievement. It may be satisfying and worthwhile for the solver, but not for society at large, any more than any other pleasurable activity. No, as it is, the sole reason for it is in the result itself. In increased understanding, as it flows down into the sciences, and engineering. There are other benefits, recreation and joy as experienced by others, from access to beautiful proofs, though these are never explicit goals of such programs because they are both impossible to quantify and rarely ever remotely relevant compared to the value brought by the practical value brought by maths. Of course, there may be some valid arguments that everyone should have a jobs program in the form of ubi or something similar. But I feel thats very different to arguing for mathematicians specifically
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People need many things, there are all kind of theories ready to assess and assimilate if deemed worth it out there. A job is not part of any I’m aware of, though it can encompass some human needs in some cases, or go straight against them in some other case.
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Every human needs a vocation, better if it's of their choosing.
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People talk about research mathematics being a science or an art, but it's also a sport. AI will kill the sport aspect of it. The art will survive. The science will thrive.
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>My job is uniquely creative and human, other jobs can be automated away but mine is just so special. If you love mathematics so much, and it's not the prestige and accolades that drive you, then what stops you from just solving problems on your free time even if they are already solved by AI? Why does your field have to remain economically viable for you , why does this not apply to textile manufacturing or something? Someone's positions in society is owed to textile manufacturing too, and it has a culture that some people would lament the loss of and so on.(See guild system, craftsmanship in Europe). I can't predict whether this will be a good thing in the long run, but this is literally the same complaint that every industry affected by automation ever had, and many who are now complaining would dismiss it if it were about something they personally do not care about or isn't sufficiently "noble" or intellectual. I know it hurts, but the core complaint is just economic displacement, many have had to deal with that before. Most people who have something they love have to do that on their free time because it's not economically viable as a job, tough luck.
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Is it possible they feel threatened their jobs are at stake?
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Human mathematicians are being exposed the same way the "artists" are. It was always about the money and to look clever, superior to other humans. Whether its robotically spending millions of hours drawing until they can put something together at the level of a chatgpt 3 or the rote memorization of formulas and rules. They like people to think it all came naturally and that its genetic and that they are special snowflakes.
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This is false on so many levels. Is it ragebait? Both mathematics and art are comprised of two phases, the first, technical one, where the novice grinds the skill and the second, the creative one which can only be achieved if you have the means (skill) to express yourself. What you described is the technical phase, not the creative one. There is intrinsic value to it that has nothing to do with money or cleverness, something that if you ever experienced it yourself even once, wouldn't need to be explained to you. Only people who never reach phase two have your stance. Artists and mathematicians who pick academia didn't exactly have great commercial prospects before AI was a thing, yet they still chose those paths because that's what having a real passion looks like. >They like people to think it all came naturally and that its genetic and that they are special snowflakes. No, they don't. Most of them are the humble people that know the value of cultivating a skill and when they do pride themselves it's precisely because they know the staggering amount of hard work and commitment they invested. Most of them are worried for unemployment and don't want all their work to be reduced to training data and on top of that not be given well-deserved credit for it. The only thing being exposed here, is how much AI in its current form was being underestimated and constantly labeled as "not real/good enough intelligence". This was and still is a shared sentiment even among tech people. Can't really blame them for going through a bargaining or acceptance stage. And since you also sound like the kind of person who thinks prompting can replace the "robotically spending millions of hours" of practice, I've got news for you: it cannot. You are about to learn the hard way the value of skill and human understanding because as much as capitalism rewards "impact" and "results", the market never values easy things.
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I highly doubt there is any overt pressure in academia right now to use AI. It’s a relatively conservative institution. But there’s certainly pressure to publish (publish or perish being a common phrase for decades), and competition for jobs in academia is fierce. That’s what I meant in referring to long term pressure.
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This is all contingent on AI forays into mathematics being slop and low quality. However it's clear that recent AI models are capable of genuine mathematical achievements which surpass the frontier of what humans are able to accomplish (wrt the unit distance Erdos problem). The issue is, how is a group of intellectuals, whose identity derives from their ability to do something rare, useful, and requires many years to get good at, react when a machine can produce all of their useful output nearly automatically, can verify its own outputs, and is getting better exponentially? It is the complete annihilation of one's sense of value and purpose when the binding element to your culture is commodified. I think there will be a lot of arguments trying to claim that the point of mathematics is curiosity, or that there is always some ineffable human element that AI can't replicate, but I fail to see how somehow these wishy-washy human centered values somehow mean anything compared to the amoral pursuit of mathematical truth, which has nothing to do with humans. It's just that we humans happened to be the only beings in the universe good at math until ~2025. Now there is another species which can do many of the things we do, and it is not bound by the size of the human brain, our short term memories, or the architectural limits of biological computation. To imagine that humans would retain supremacy in this very un-human like discipline seems like wishful thinking.
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> This is all contingent on AI forays into mathematics being slop and low quality It's literally a set of recommendations for researchers on how to use AI to advance the field and prevent slop from overwhelming the people who might do anything with the research produced. For people who are so eager to declare that everyone else is just having an existential crisis because "your culture is commodified", AI people are getting awfully defensive about this document.
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I will argue that AI and flood of low quality slop makes genuine human work more valuable, not less. The ability to clearly outmatch trillion dollar machines is a very unique satisfaction. I even write ordinary internet comments with an intention to make them clearly better and more fun to read than boring Claude output.
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You will never be able to match insanity of human mind embodied in a walking sack of meat that was shot out of another.