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.

While you are right in a way, I think you miss the point. In the past "computer" was a job description and mechanical power came from serfs. They surely developed skills we are lacking today but I'd argue that overall the world is a better place with digital computers and electrical motors. It frees up these people to do something else, something of higher value.

Sure, recreational mathematicians. Just like people that like to ride horses for fun.

Put another way, wage slavery is not the ultimate purpose of humanity.

The cancer of p50 users having comfy housing, 2 cars and a life. Almost all of the efficiency gains move to the 1%.

I don't think that "root[ing] for mathematicians to go away" is the problem. The problem (if there is one) is that the process by which that occurs is economically determined. No amount of complaining will stop AI from being useful in mathematics or erase the incentives to make it better. It's automatic process, like photography sidelining painting or shoe factories sidelining cobblers. We go through this with every technological advance and the outcomes are pretty much determined. No cheerleaders are needed.

For many of those automations, we're worse off for them. Like not being able to get some actual human when you call support, and talking to some fucking automatic system. This includes many of the " 1990s through the 2000s" ones, and earlier ones too. Sometimes what was lost was an added layer of attention and quality that was previously required, but it was sacrificed away for efficiency.

That really depends on who is the one that benefits from automation. Companies automate support systems in order to keep their support staff small, because apparently for many of them it is more profitable to frustrate their customers with crappy support than to pay more support staff to do a better job. In addition to your last paragraph: lots of things that we used to do the less efficient way had side-benefits that were not immediately obvious, probably because they compounded over time. Now that we're not doing them anymore, we notice all kinds of widespread societal problems (in particular among young people) that come up that were never there before.

Yep, and if history is any guide the only way to play it is to take part and get rich while you can, or play the super long game and be positioned for the collapse. Businesses will not adapt until they are incentivized to do so, and very few businesses have a multi-decade outlook. Even before AI, the senior 10x employee who retired and took all his domain knowledge with him because there was never any funding to train his replacement was a problem.

The existing models "top out" not because they don't get better, but because it is uneconomical. What we do know is that a model "tops out" wrt training data - that is, for a model of a given size, there's only so much training data you can squeeze into the set before you stop seeing gains. But conversely it means that if you already have a model of say 1 Ttok that is "trained to capacity", then a model of 2 TTok needs roughly twice as much training data to fully utilize all those weights. Which means that the cost of training it is not 2x but 4x (twice as many params x twice as many tokens). And then of course serving it is 2x more expensive, but even with optimal training the gains aren't 2x. So it very quickly becomes uneconomical. A good example of that kind of model is (was) GPT-4.5. The prices and the consequent lack of demand show why companies don't really do that sort of thing anymore. But no, there's no evidence of a plateau as such. I'm not sure what "evidence that we have not reached a plateau" would even look like.

> Now if I know anything about math for the sake of math, and academics, these are the same people that lament the idea of intelligent people going to the finance sector or any other trade they just happen not to respect as much IME a vastly more common sentiment among mathematicians regarding mathematical talent leaving the nest to apply their skills in other fields is that those other fields are lucky to get them!

I think you've slightly straw manned the lamentation there. Not that I agree with the lamentation, but using your talent to make the rich richer (which is what quants do, they are paid a fixed amount to provide a larger value up the chain), as opposed to advancing human knowledge, is the reason for the lament, not some sort of respectability issue.

Quants benefit from substantial bonus structure as part of their compensation.

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.

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.

> 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?

Sorry but I couldn't agree less. Deep esoteric research and trivial looking boring research can be as useful as state of the art trending areas. "Jobs for nerds" as has been stated, has given surprising and unexpected advances, or leveraged incredible advancements. An standard and boring bacteria in a specific Spanish biome, gave us CRISPR-Cas. There ar hundreds of examples. True knowledge is, and will be, a human endeavor, deiven by human curiosity. Promoting curiosity is the sign of a developed society.

Culturally, mathematics is a jobs program for nerds. The field very explicitly takes pride in working on problems that have no obvious applications, and most practitioners are funded publicly or supported by private endowments, with zero pressure to deliver specific results. Of course, this produces useful results every now and then, but it's not like we pursued ruthless efficiency / maximum rate of knowledge advancement before. We just let them do their thing, essentially treating them as artists and letting them pursue the craft for its own sake. If we weren't interested in maximum throughput before, why is that an objective now?

> It's not like we treat math as a charity project for eccentrics who like blackboards. Love it! XD I agree, and I think, as with physics, mathematical research produces building blocks whose utility won't be realised until later.

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.

Probably one of the funniest things to read on a site like this, when you consider that eg. Boolean algebra was entirely abstract and had little practical purpose for almost 100 years until Shannon picked it up for use in circuits

Boole was trying to improve logic for humans, "The Laws of Thought". So it has a connection to human problems, and eventually to practical matters. He could instead have been working on something much more abstract and much less useful. By which I'm trying to make an abstract point about the inevitability of staying somewhat down to earth. I mean "pure" curiosity is great, except it isn't ever really pure, and abstract mathematics isn't ever totally abstract, it's just sort of meta in relation to practical things that humans care about.

> So it has a connection to human problems, and eventually to practical matters. But in relation to parent post I was replying to, it did not provide an answer or solution to anything. It has much closer relation to philosophy than anything. Focusing on only ‘solutions’ in any field is shortsighted because you can’t know how the dots will connect. Someone’s seemingly pointless curiosity or experiment can unlock something unexpected, just like Boole

Depends on the solution. If the solution is that P≠NP, the concept of NP-completeness remains the bigger contribution, unless the proof techniques are particularly interesting and lead to other major results. The same applies if P=NP but the proof does not ultimately lead to a practical algorithm. If we get a practical algorithm, the answer is more valuable than the question.

Maths pretty much is a jobs program for nerds though. It occasionally produces results that are practically useful for society but there's absolutely no way the vast majority of today's maths research falls into that category. There are definitely exceptions, like crypto. I still think it would be pretty silly to stop maths research anyway. And anyway part of the job of maths researchers is to teach maths to undergrads and that's obviously enormously useful to society. But on the scale of "how useful is this research to society" it's dead last after engineering, chemistry, biology, and physics. Well maybe computer science would be last actually!

for mathematicians, they do a form of fundamental research that is 1. (generally) incredibly cheap to fund, and 2. (occasionally) has extremely out-sized commercial impacts. This is to say that jobs programs for math (and more generally fundamental research) have lead to extremely positive ROI for society, which is the typical justification given for funding them.

> “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University As a former physicist and current data scientist/engineer, I know for a fact that commercial utility drives math research and researchers. Math is a tool to solve problems. Some mathematicians might only love the process of using the tool, but commercial logic absolutely drives mathematician attention to develop commercially useful tools.

Is there a useful abstraction that doesn't help solve a problem someone has?

You're right, but what I'm saying is that solving the problem isn't necessarily the primary goal and these new abstractions can be valuable in their own right.

>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.

>and the pursuit of knowledge for its own sake Except when someone hands you a magic button that just gives you knowledge?[at least in the framing of this "warning"] Then it's about peoples' livelihoods, about "culture", etc? "Computer" used to be a job. Did science on the whole lose or gain by making these clerks obsolete?

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.

This feels like a troll comment, but I'll bite. Mathematics requires substantial creativity at every level. There is problem selection, conjecture formation, proof strategies, definitions, models, and explanations. Yes, it's constrained and guided by logic and rigor but having logic won't give you creativity. > Music is a human endeavor and musical recordings hurt musicians, bands, orchestras, etc. Especially those starting out. The medium it is recorded on has no bearing on what composed the music. If people don't get rewarded for composing they won't. Same with mathematics. If people don't get paid for being creative they just won't be creative. I am not saying I agree with everything in the article. OP of this thread just made a low effort comment that was addressed in lengths during the article.

The choice only remains if using it isn’t a huge multiplier. If it is a huge multiplier/accelerator, then for a while it will be ambiguous and the choice will remain. But as time goes on, the gains of using it will be so apparent and the advantage of the people who use it so great (in publication numbers, hiring, etc) that it will force others to. I don’t say that with any particular relish. But I am skeptical of the choice angle past a certain point.

I don't think all universities or research agencies are particularly pressed on this. I mean my daughter is a notable researcher in a scientific field and they have absolutely no pressure to use AI to pump out papers or deliver value quickly.

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.

Well I rather like to be paid more than a mathematician so left academia rather quickly. In my case corporate modelling mostly involves making prediction models based on shitty data and metrics to make poorly contrived business decisions that lose millions of dollars.

lol.... but they are still data driven decisions, everyone loves those, especially when you lose millions of dollars and need to justify it.

Does it matter if the Leiden Declaration is correct? To the humans, maybe but not in the bigger picture. At scale, correctness and reward are becoming increasingly disconnected. Example: capital continues to compound regardless of whether it reflects underlying human welfare, just as information can spread regardless of whether it is true. Reality still matters, of course. If you want airplanes to stay in the air, somebody eventually has to be correct. The problem is that our economic and social systems are becoming less effective at distinguishing between what is true and what is merely rewarded.

""" However, the declaration argues math is more than a machine for producing correct answers. The discipline, its authors believe, is a deeply human endeavor built on creativity, understanding, collaboration, and the pursuit of knowledge for its own sake. Those values often clash with the incentives driving AI development. “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University told The New York Times. """ I mean, what field doesn't? Everyone works to make money. Slightly unrelated, but, their website " https://leidendeclaration.ai/ " itself gives an eerie feeling of being built by Sonnet. That color scheme and the layout is what Sonnet chooses by default most of the times.