I think you are missing the point of the main criticism. It is not about not wanting results in terms of proofs.
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.
"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."
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.
Because keeping all the easy things coordinated and understanding the big picture is still a hard task yet unsolved by LLM's?
But yeah, who knows what happens once that change. I assume even after the singularity, it still makes sense, that we train some people to know what is going on ..
If a modern Gauss, Von Neumann, and Ramanujan appeared and started dropping proofs from the sky, would people be saying the same things? And if they could live forever, so they wouldn't need to train their replacements?
Not exactly, because we would have cool people to inspire us and hang out with us.
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.
Gauss was generally quite secretive and Ramanujan would famously tell people answers that he had received from divine inspiration, often with no ability to articulate how he knew. Von Neumann did just go into random fields and revolutionize them. If the three of them did come back from the dead and form a little powerhouse group that barely collaborated with the outside and just started publishing results for everyone else to try to keep up with, they'd no doubt still be considered geniuses.
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.
It's been doing all of the actual coding part of my job for the better part of a year, and you're commenting on a post about how it just released another round of math breakthroughs, besting a bunch of top humans. It can search the web and analyze documents it finds for me. It can do reverse engineering. It can analyze and create images.
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?
Isn't it curious that while LLMs are apparently on the precipice of "AGI" and possessing superhuman capabilities for knowledge work, the frontier labs are still hiring armies of humans as "Account Associates", "Account Directors", "AI Support Engineers", and "Applied AI Engineers" (https://openai.com/careers/search/). Since those roles are much more pedestrian than top math problems, one might expect the frontier labs to be at the forefront of automating those jobs using their world-beating models. Wouldn't that be a more direct flex of their economic value?
Not sure I follow: if it weren't incredibly useful, my salary wouldn't depend on it since it wouldn't be doing my work for me, innit? So if I am dependent on it, that's just agreeing that it's now replaced programming per se as a professional activity. That quote applies to the people selling the tool (not me), not the people who it will replace (me), and in the meantime who are buying/using it.
I think the point is that people (software engineers included), will be biased to believe AI won’t replace them because believing otherwise would cost them their job (and therefore salary).
I’m not taking a side on that debate, just clarifying the relevancy of that quote.
Yes, and they are revered as geniuses, which makes it clear that this is all sour grapes. And surely if people died, went to heaven, and were able to talk with God whenever they wanted, they wouldn't be upset that now they could know the answer to any mystery whenever they'd like; they'd appreciate that now they have someone to guide them! Or were they similarly upset when lecturers handed them already completed theory in school? There's already enough developed theory that people don't have the time to learn it all as it is.
The only thing potentially stopping these models from also outputting new theories along the way is the goal they were given.
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.
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.