Comment by hanibrel
17 hours ago
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.
How can they learn hard things if they have an infinite number of easy things to do? This is a middlebrow version of doomscrolling disease.
Most people have trouble not peeking at the answers. Look at Stack Exchange's long success.
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 ..
How well do you think someone will understand fractions or trigonometry if they always punch their math homework into Wolfram alpha?
The increasing pervasiveness of technology in US education has not produced more capable graduates.
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?
Who cares about them? I want Tao to stop proving all the interesting problems I was planning to work on.
Gauss and Euler, and also Ramanujan (results without proofs, which is a bit like unreadable Lean) did that for their lifetimes.
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.
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.
[0] https://news.ycombinator.com/item?id=49010345
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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.
OpenAI is doing problems because they know they can't do higher theory yet.
I asusme they're doing problems because its an easy way to turn $40m of someone else's money into a catchy news headline.