> Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them, often in the context of their own autonomously guided research. This expert knowledge is essential, both to effectively use mathematics, and to continue to articulate new and significant research questions. In a word, the job of the mathematics department is not only to produce mathematics, but mathematicians. Similarly, the output of programming is not only a program, but also a programmer. It is you. Outsourcing the work deprives you of who you become by writing it.

> This can be said about pretty much any job on earth. That isn't really true. After push button elevators with floor-logic relays eliminated the need for "elevator operator" to be a job, nobody needed to be an elevator operator anymore. The equipment could do 100% of the job and if the equipment was out of order then you call a repair technician or install a new elevator rather than needing to find an elevator operator to pull out of retirement, since knowing how to repair or install elevators was never part of their job to begin with. The trouble with AI-generated code is that it can't do 100% of the job, so you still need a programmer to do the parts that it can't, but then you need the programmer to understand how to do the parts that it can't, which in turn requires them to also understand how to do the parts that it can.

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.

To me, the most interesting feature of the OpenAI solution of the Unit Distance (Erdös) Problem is that the solution - using deep algebraic number theory as a source of extremal combinatorial/geometric constructions - is much more interesting than the problem’s elementary statement might lead one to expect. Writing off Erdös’s problems as random, useless, or meaningless dismisses his mathematical intuition, second-to-none, and strikes me as somewhat uncharitable. Finally, I agree that AI threatens mathematical training by rendering an entire class of acolyte-level research problems solvable by prompt. But the Unit Distance Problem is not of this class.

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.

Sounds like yet another example of how AI is kneecapping industries from the bottom by "removing the barrier to entry" but really just removing the training path by doing the work itself with no guidance for juniors.

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.

That's an interesting perspective and I wholly disagree with the conclusion You are saying that tough problems with no applicability are useful because people that you happen to respect got good by their curiosity and pursuit of trying to solve these kinds of problems and failing, but branching off into other cognitive areas as mathematicians 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 The similarity being that their exact criticism of why, something they don't respect and view as having little utility, is the exact reasoning presented here now that AI can solve their pointless problems What I'm seeing is that human mathematicians have a laundry list of problems they have failed to solve for decades, centuries, which is what they are funded and employed to do. "Computer" used to a human job title too. This leads me to being excited about AI one-shotting these problems, let move on to something else.

But this is missing the fact that the vast majority of starting jobs for artists/writers would be in the former category. Similar to how AI coding or automation hurts junior hiring more than it does senior. I found myself thinking about this issue when I was experimenting with an MCP server to handle tuning some precision parameters for scientific simulations. Claude did a much better job than I used to do when I was a fresh PhD student, yet being given tasks like that was how I learned, so it almost felt like pulling the ladder up after myself. In the sciences, I think this is less of a problem because the PhD to scientist pipeline is pretty normalized, labs are used to the idea of having to let younger people take longer on problems that experienced people could solve much faster. But this doesn't seem to be as normalized elsewhere.

> 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

Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI generates and verifies proofs without humans in the loop. Where the mathematics may be beyond human comprehension. In that future, does it matter that early career mathematicians are inhibited by these developments? Perhaps not. Programming faces the same issue. As AI crawls up the competence ladder, does it matter that fewer people have opportunities to develop the skillset of a senior engineer? Perhaps not.

On the other hand, it could stall out at: good enough to take the easy problems, not good enough to take over the field, but damaging enough to erode the quality of new entrants. (Which incidentally is the scenario I think plays out for software)

>AI makes the math world more accessible than before. If you have a question about a proof in the lecture, you can just ask it. I think that is great, really! but does anyone remember asking a TA or teacher or prof or parent and getting told you can work it out for yourself, or maybe just given a hint? What if that is an essential part of learning, having to work through things you don't understand, but that you have the tools, the foundation, to figure out. A calculator can't teach you math. A forklift can't build your strength. This is really a double edged sword, as far as education or accessibility goes. You have to constantly ask... what do I lose by not figuring it out myself?

I don't think current mathematician's jobs are at stake, as much as the field itself, if LLMs take all the "easy" problems that phd students would try to learn by solving on their own. Mathematics is susceptible to the same ladder-pulling situation that we see with junior programmers and LLMs.

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.

From the article: > 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. Generation X was the last generation that had 'general knowledge', as in an abundance of fairly useful information stored in 'grey matter' that could be recalled quickly. When search engines came along there really wasn't much need to know anything since most things could be looked up. However, you still had to think. With LLMs, thinking is kind-of optional. This really is an existential threat to our intelligence since 'use it or lose it applies'. I am glad these mathematicians are doing their duty as canary in the coal mine.

Are maths AI models now using "tools", aka formal solvers? I understand that the "language interface" of a "maths AI" could be some specialized trained LLM (Large Language Model) that to convey, with human language, "high level" mathematical mental contructs and intuition. But then, you would need some models which does the reasoning using formal mathematical solvers (and probably a ton of "scratch" memory, it would be interesting to see how those models end up storing "mathematical" lema data). I guess you can have ML (Machine Learning) for those models on 'general maths', but also we can think about more mathematically focused ML for a specific problem, area, etc. And in the end, ML for maths, would it be mostly permutations of truth statements fed to a neural net? When we were talking about "AI", one decade ago, that was what most had in mind (it may help a bit in physics, but it seems less likely, because reality/experiments are hard to teach to "AI"s). If that becomes a reality (aka easy hardware access, and some "working" models), mathematicians will have to be as good in maths than in maths ML. And this is were there is an issue: training honestely good mathematical human brains may become very hard with some broad availability of good general maths reasoning "AIs".