I'm curious to know if the withdrawal was due to an actual mathematician looking at the papers and noticing the errors, or they ran a model on these to proofread, which would not be the first time, presumably, since they would have surely done that before publishing. Both options have interesting implications.

Well, let them have these. They'll play around with open problems which generate media hype and then they might run out and move on to something else, because "AI came up with a problem and solved it in 3 days" won't have the same effects as "AI solved a problem in 3 days that humans couldn't solve in 100 years".

Regardless of that, what happens long-term if AI gets good enough to solve all the hard open problems?

Millenium problems may give AI companies some temporary hype, but advancing research in some narrow directions to find new problems is probably not worth it to them. In addition, current problems have clear, human-defined acceptance criteria. Problems that are both found and solved by AI will be opaque enough not to generate interest in anyone unless they are found to have immediate applications. Mathematicians will somewhat distrust 1M+ LOC Lean formalizations as well as any original AI output in the form of creating a bunch of new concepts. There will surely be heated discussions around that.

Afterwards, mathematicians take some time to catch up with the solutions to existing problems, use AI to understand them and map out further directions. Problem solving by AI companies slows down since there are no cool problems left. They move on, mathematicians get back to whatever they were doing before, now with the help of AI.

With every mathematician having a strong mathematical AI model, a new problem arises. At any point of the current mathematical frontier, a mathematician can use AI to explore a new direction at a high speed. If all mathematicians do that, each will have their very advanced understanding of their direction until they fail to catch up the AI, and nobody knows whose direction is the one that others should check up with. Many possible connections with other branches and explored directions will be lost, unless there's a unified map of all these explorations. It will be hard to create this map, because while exploring one direction may have a moderate cost for a mathematician, having an AI do an overview of all other explorations to find some commonalities and synthesize the findings into a unified theory will take serious amounts of resources only available to AI companies, which they might be reluctant to spend.

Individual mathematicians' explorations will slow down to human level, too, with their unique findings being hard to publish because nobody will care and the mathematical community wants to do things that other mathematicians can appreciate.

In the end, the mathematicians' work does not change that drastically, unless AI gets good enough to one-shot some new crazy branch of mathematics that reveals something with high real-world impact. But that's a discussion for another time.

I really don't get the hate for mathematical notation here, do you have specific examples? Notation is a necessary tool to express complex ideas compactly so that others can understand them. It allows you to carry out technical proofs that confirm things that are "obvious". Then it uses previously introduced concepts to build new concepts on top of them. This keeps mathematics interconnected, there's value in explaining a concept in terms of already known things rather than just vibing it.

> makes itself intentionally hard

It doesn't make itself intentionally hard, it is just hard. You can simplify some expositions and make concepts easier to understand intuitively but it won't necessarily give you the skills to actually work with them in mathematical practice (which is the point of mathematics as a discipline).

I find it curious that you've protested against that joke but not against the statement that "it seems likely that there's a finite number of interesting math problems". It doesn't seem likely to me personally and I haven't seen proof of that, even in a joke form. There's a finite number of problems at any given time, obviously, because mathematicians are finite, but it would require a very good understanding of the whole of our mathematical knowledge to declare that if we keep expanding it we'll hit some kind of wall, of "interestingness" or whatever else.

> And the control column confirms the resonance-necessity conjecture empirically: break the skeleton alignment and the joint kernel dies at the constrained window, exactly as the transversality heuristic predicted.

> The den has air in it.

> Drift fuel exists.

Sometimes one can be convinced that their mathematics will be useful, too. I've just recalled a rather motivating (though his life story is rather sad) quote by Grassmann, the inventor of modern linear algebra, whose mathematical work was not appreciated during his lifetime.

"I remain completely confident that the labour I have expended on the science presented here and which has demanded a significant part of my life as well as the most strenuous application of my powers, will not be lost. It is true that I am aware that the form which I have given the science is imperfect and must be imperfect. But I know and feel obliged to state (though I run the risk of seeming arrogant) that even if this work should again remain unused for another seventeen years or even longer, without entering into the actual development of science, still that time will come when it will be brought forth from the dust of oblivion and when ideas now dormant will bring forth fruit. I know that if I also fail to gather around me (as I have until now desired in vain) a circle of scholars, whom I could fructify with these ideas, and whom I could stimulate to develop and enrich them further, yet there will come a time when these ideas, perhaps in a new form, will arise anew and will enter into a living communication with contemporary developments. For truth is eternal and divine."

Either way it seems like nobody is in a position to say "this branch of math will surely stay arcane abstract nonsense forever", so the argument for continuing specialized math research comes down to "we might lose out on some cool stuff if we stop", even if most of it will indeed remain useless for a long time.

Do you believe it is possible or have any recent examples? I feel like most of the stuff that could be applied to something like this has probably already been developed 100 years ago. This hope for some miracle math that cures cancer sounds like the thing they tell the government to keep the funding going. Most of modern pure mathematics doesn't look like it has any chance of being that. It's getting more specialized every day with more and more papers on obscure topics being published that 2 people in the world read.

I'd love to be corrected as I quite enjoy mathematics myself, though not professionally.