And yes, fun counts. Nobody said this had to be only a hardship.
I'm well aware that if at some point AI is good enough to replace me as a software engineer then I won't have a job. I don't expect a company to continue to pay me simply because I enjoy it if there are cheaper options out there.
Math is no different.
Total compensation includes fun.
Perhaps that won't matter if we enter an era where AI participants are the main participants who matter for discovery-level mathematics. But it would likely be what economists would see as a market failure if only a small oligopoly of AI participants, closely held behind closed doors, is able to fill that intellectual role.
New theories and insights are typically created while working out proofs. If proofs now suddenly fall out of the sky (cause LLMs create them) then that work is not done which means the substrate on which new theories and questions and conjectures used to be grown disappears. It's in that sense that the math community (and thereby society as a whole) will lose something.
It's similar to how software engineering will need to find a solution to train their next generation. Current generations have all been through manual steps of designing things from scratch and writing them by hand. That's what allows your 10x engineers to understand whether what their LLM tools are doing is good and how to massage those tools to do the right thing. A junior engineer who has only ever used LLMs to write code and create architectures does not just not have that experience but also won't acquire it. You can't just say "we don't pay them to have fun and learn, we pay them to produce results". In the short term that is the case, but in the long term you as a company and we as a community will lose out.
I'm not saying don't use AI tooling. I'm saying that this is a hard problem which we yet to have to find solutions and approaches to. As a software community as well as as society in general.
My ego tends to agree, that how can they be ever competent, if they have not endured the same hardships as I had crunching trough problems and getting allmost lost in the details.
But I rather suspect, they will turn out fine. I know LLMs are great for me to learn and I think the young generation will learn what they need to learn to get the job done.
Most people have trouble not peeking at the answers. Look at Stack Exchange's long success.
The increasing pervasiveness of technology in US education has not produced more capable graduates.
But your argument is nonsensical because even if Gauss and von Neumann appeared, they wouldn't go into random fields and just prove things mechanically. They'd have to attend seminars, teach others, collaborate with others, and generally inspire others with their brilliance. It's the precise lack of this activity that makes AI in math so reprehensible.
Your argument encapsulates a contradiction because human mathematicians wouldn't be dropping proofs arbitrarily like AI is doing. They would do something completely different. Even the best of them.
Give it six months and models might be able to explain things better than any human. They can already collaborate perfectly well if you ask them to. e.g. there was a post here a couple months ago where Tao shared his ChatGPT logs[0].
If you're not inspired by the ability to talk to a superintelligent machine, and can't find what you'd want to know, that's a you problem.
Ah, the "six months till AGI" meme, but unironically :)
Also, before citing Terence Tao on LLMs maybe you should read what he has to say about it...
Not sure what your definition of AGI is, but it clearly has superhuman performance on most knowledge work already. Do you think after already having demonstrated that it can solve top problems, that the final frontier it won't be able to cross is explaining its solutions to the experts that were researching those problems, and eventually to e.g. grad student or postdoc level practitioners as a lecture course/set of notes?
I have to assume OpenAI is only prompting to solve problems, presumably they could also prompt to not interesting new theories or paths of research found along the way as well.
Largely I thought that this is what you do once you're established in math (or any field) anyway. You have some ideas, but the details are kind of too tedious for you to work out, so you give it to grad students/postdocs. Senior engineers have some ideas, but the details are tedious to work out, so you give them to junior engineers.
Now, obviously in the meantime, there's the question of how do we train the next generation? Or do we need to train the next generation? And maybe while we work that out the answer becomes more shadowing/apprenticeship instead of farming out easy tasks.
Yours is more likely in my opinion though, mainly because universal high income is completely infeasible and shaky even at the level of definition.