>> 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. This assumption may well turn out to be correct, but it is not self-evident. Nearly everyone who has ever got interested in mathematics got discouraged at some point and they left the field. Mathematics is very hard. Those very few that remained certainly have talent, but they also have characteristics that are necessary for success in a competitive field, which are perhaps less valuable per se. Such characteristics as may be over-represented in males for instance. This is not a point about gender differences, but about the intrinsic merit of different success factors. It seems equally possible that the above assumption will turn out to be diametrically incorrect. People that would have been discouraged before LLMs will now retain their curiosity longer. Democratisation is surely a possible outcome. Arguably, chess has never been as popular and accessible. And that discipline fell to AI three decades ago.

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.

An issue I see is who controls the information. The next generation may not recieve the knowledge, it may be gatekept by industry who *will* own the gate. The future may not have access unless we fight to ensure they do. This is how I read the article.

Do AIs produce answers whose work is incomprehensible to humans? It seems like you could just have the AI elaborate multiple times until you were satisfied with the explanation and documentation of what went into figuring out the answer. It’s not like the AI is one shotting the answer in a single opaque query anyways.

I don't get it. LLMs don't have ego, they don't have the ability to say "no, this should be obvious, I'm not going to explain further", they are just token predictors, and given context, they can generate more tokens. If you don't understand how the answer was derived? You just ask more questions and it isn't going to get bored or annoyed, it will just try to answer the questions. Is that what is offending you so much?

Esoterism is mostly a social tool to keep those not initiated excluded from the private club. Most of the time mathematics becomes tricky less due to unfathomable intrinsic complexity, and more due to the way it’s communicated. LLMs don’t give a shit about social side effects, leave alone on unconscious level, because they are void of any intention. At most they are tuned on their thin edge layer to lean toward this or that kind of output, but that’s it. Now the landscape shift as it’s sold (I guess) is that anyone can take a postdoc gibberish infused with the hard gained academic winks and subtle references and turn it into a ELI5 "does it have any applicability for my concrete issue at stake, prove it through Lean, good let’s deploy".

One of the reasons why over a decade ago, I dived deeply into the OSS world instead of mathematics was that it was so much more accessible: there were docs for everything, and I got direct feedback when something worked vs when something didn't work. Most of my questions had answers on stack overflow, and once I joined Rust (which back then in 2015 didn't have a big stackoverflow presence) I had a community who answered them for me (and in maths I didn't have that). 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. Of course, one can't trust it blindly, but fundamentally it's amazing. I think that's a good thing, but of course this means that a lot has to change in culture and behaviors, also in the research world. The software engineering world is more or less in the same situation, it's also changing. But for now I think it still holds true that someone who knows maths plus an LLM is better than someone who doesn't know maths plus LLM. At least in software it does.

Agreed. As someone who was always curious but had difficulties learning math the way it's taught at the university, AI teaching me the way no professor ever could is a blessing. I fail to see the point of the memo besides: we got here first and we decide what math is because we can. I'm really optimistic about AI and the value it brings in education. Gatekeepers will complain, but ultimately, will either adapt or be left behind.

Yeah, among other factors, that "figure it out" mentality put me off in the end. Especially because often you need to show the same mentality unless you want to overkill proofs and spend more time on them than assigned to you. I sometimes miscalibrated and pointed out some details that didn't need pointing out in my proofs while in other proofs, I skipped over too many details for the TA. Of course I agree that if the student just asks LLM to do their homework, they have not learned anything. But it's sad if one can't ask questions about a proof or such. Having the LLM around to review the homework submission is also useful, to make sure that the arguments are solid.

You will have to learn to voluntarily figure things out for yourself without being pushed towards that. In a sense it's analogous to the presence of cheap calorie dense foods. In order to not be overweight you have to be mindful of and regulate your food intake in various ways. Alternatively, perhaps universities will provide access to fine tuned models that are mindful of such things.

You can ask the LLM for a hint as well.

I think it's going to reduce the friction of exploring new areas in math, and that we're going to see a golden age of math unlike anything seen before.

Right, most professional mathematicians know almost nothing about their neighboring branches of mathematics. An algebraic geometry researcher would be hard pressed to understand a new result from category theory or even something closer like commutative algebra.

> “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” I briefly studied at a pure math department. We were learning linear algebra and I found the symbol heavy, proof oriented approach very difficult and unintuitive. But when I squinted at the diagrams I realized, oh wait, this actually has dozens of practical applications! Across dozens of different fields! How fantastic! And the textbook, for some reason, chose to mention precisely none of them. Which I found quite disappointing, because it made the whole thing seem quite abstract (which it actually wasn't), and made it harder to understand. I mentioned this to my colleagues, who became extremely upset, and informed me that I was in the wrong department.

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."