Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questions on the wrong end of the spectrum: Erdos problems are exactly the sort of "useless" questions that people might answer purely for the love of the game. The sort of questions that a young person might cut their teeth on and gain confidence. Solving questions like these automatically, I think, is not good for the long-term health of research. At least for the foreseeable future you still would like people to become interested and develop skills in these fields. These developments, and especially how they are presented, directly discourage that.

I don't think Erdos problems are useless myself, I put "useless" in quotes to emphasize that they are the sort of research that doesn't have an immediate application, and so their automated resolution should be weighed against the sociological cost. As opposed to, say, drug discovery.

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.

> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.

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?

Hardy would agree with the viewpoint that you espouse but it would be pushed back against by Arnol'd, Poincare, Gauss, Von Neumann, and even Grothendiek: Arnol'd and Poincare were vituperatively against the division between "pure" and "applied" mathematics; they considered mathematics and physics interchangeable, and Arnol'd lamented that the field had lost a large amount of funding/prestige/relevance due to groups like the Bourbaki that took a purely aesthetic view; Gauss had a critical view of problems like Fermat's last theorem (he felt that you could construct infinitely many such problems, and felt that attempting to prove it was a generally useless endeavor), along with outright calling pure mathematics worthless; but while Von Neumann and Grothendiek were more moderate, both were critical of the field losing motivation/quality as it strayed away from empirical science into—quoting Von Neumann—"abstract inbreeding". Arnold's polemics are perhaps the most infamous and easily found online (see "On Teaching Mathematics"), but the written opinions of Poincare et seq. are also easy to find. Even today the vast majority of research funding for mathematics, at least in the United States, is dolled out for highly applied fields like partial differential equations. The field does not even close to unanimously (contemporarily or historically) "explicitly take pride" in working on problems that have no obvious application, or being a "jobs program for nerds": the notion of such "pure" or "nonapplied" mathematics is at the very least a highly fractious and controversial subject, with a number of big names taking opposing viewpoints (often vehemently). I think your picture of the field is over-represented on the internet, much like the fixation on certain niche fields: Category Theory, Homotopy Type Theory or, worst of all, outright dubious fields like Geometric Algebra; fields with a large number of online promoters, but with much less funding and relevance in the actual academic space. Of course there are reputable people with PHDs that feel this way,—but I can only imagine that there's a legion of tyros, pop math consumers, and undergraduate students who disproportionately promote this viewpoint.

> We just let them do their thing, essentially treating them as artists and letting them pursue the craft for its own sake. I think we generally did that because that seemed to be the best known process for maximizing the quantity of useful mathematics that they occasionally stumble upon. It's not like we treat math as a charity project for eccentrics who like blackboards. What we want is new mathematical discoveries that have a huge positive impact on other areas of the world. It's just that math and/or human brains are such that seemingly the best way to find those discoveries was to let mathematicians wander around randomly in mindspace. If a more guided structured process produced more results, we'd probably do that. But it doesn't seem to, so we don't. I don't think anyone knows yet what the best process for producing useful mathematics with humans + AIs looks like.

> 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.

> The authors warn the consequences are already becoming visible. AI-generated papers could overwhelm peer-review systems with low-quality work … It seems like a key problem here is that peer-review is expected but not explicitly funded/rewarded while it is probably one of the aspects where humans still add a lot of value. Academia’s incentives are hugely misaligned (… as usual unfortunately).

The wording in the declaration may be a bit romanticized. But the points are valid: Is an 80 year old unsolved problem maybe unsolved because it was never prioritized? Some problems stay unsolved because few people consider them worth working on. Who is going to validate the results? Or do we skip that, with the risk of flooding the literature and collective understanding with unverified proofs?

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!

People need jobs. What's wrong with nerds having jobs via a program?

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

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.

This is to say that jobs programs for math (and more generally fundamental research) have lead to extremely positive ROI for society Which makes it not a "jobs program" as the term is generally used.

it arguably still is. The primary unit of production of the jobs of mathematicians is itself not particularly useful for society. In this sense funding them is a jobs program. It is also true that they occasionally produce things of great value, and more frequently the things they produce can be leveraged by other researchers to directly produce things of value. But neither of these are what the job of a mathematician is (either in a day-to-day sense, or even for many mathematician's careers). To go back to the analogy of jobs programs for alcoholics, it is somewhat similar if there was a small chance every time an alcoholic defecated in public gold came out. This fact might be used to support a jobs program for alcoholics, on the basis of it being positive ROI to society. At the same time, the "job" any individual alcoholic is doing in this setup is not particularly useful to society, so one might still call it a jobs program.

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.

> But not because it's a jobs program for nerds. We’re becoming increasingly embarrassing as a society.

My vague prediction right now is that in five years LLMs will be heavily used by universities in grant-funded math research but nobody else will be able to afford it, much like supercomputer clusters 25 years ago.

Are they? The jobs of programmers are definitely at stake; at any given time there's some fixed amount of software that can be consumed. Mathematics research doesn't have an economic buyer. If you raise the complexity floor for discovery, you reduce the annual productivity of a researcher, but that might not matter to the field.

I've said it before, but there's a massive risk that we simply stop educating researchers. So much of a Ph.D revolves around the person learning how to do research. They learn how to read papers and literature rigorously. They get low-hanging fruits to practice on, which can take months. Their funding doesn't come from thin air either. So what happens when the group leaders would rather spend money on compute, and get models to solve the low-hanging fruit? Which the models could very well do in mere hours, compared to months. Nor does it help that publishing is the number 1 measure in academia. Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups. It is basically the "junior problem", but even more severe.

> Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups. That's not new - especially in the experimental sciences ( ie perhaps more than maths ) - where the ability to have access to the latest kit is often what determines success - a huge amount of science progress is driven by new experimental technology rather than smart people thinking beautiful thoughts.

Absolutely, but at least in the pure / less applied fields, access to computation hasn't really been that critical. The more towards the pure and theoretical, less so. But now you have people like Gowers and Tao, pure mathematicians, hyping up what the SOTA models can do - and I figure they both are getting access and tokens us mortals can't afford. So I guess the question is - will everything be as expensive as applied fields?

Hopefully not as expensive as CERN :-) Though having said that - the ~5 billion for the LHC now seems cheap ( even inflation adjusted ) in the context of Google investing 180 billion in infrastructure just this year!

Mathematics is not inherently a human endeavor and claims such as those are why the GOP voters are fine with cutting research funding so heavily. Even if you think it's true you probably shouldnt write think pieces that say so because it's bad politics.

And the goal of computer mathematics research is computer understanding of mathematics. I fail to see a reason provided as to why society should defund automated reasoning just so mathematicians can put off burger flipping for another year.

Eh. This isn't "AI" or language models masquerading as intelligence. I submit that this is actually the long tail of the internet and the decision to rest on the laurels of peer reviewed submissions rather than advancing the field to better disseminate knowledge. The barrier to entry just got lowered. This has happened many times before in history. We just end up with fewer of what David Graeber would call "bullshit jobs."