271–280 of 617 posts
As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…
Earlier quoted context omitted.
Yeah. My other favorite example are books. Why do nonfiction books exist? There are some pathologies and corner cases, but fundamentally: to develop and share new ideas. Downstream from that, if it reads well and if you're lucky, you make some money. But now, LLMs can generate hundreds of books per hour. They make up 80-90% of new arrivals in many nonfiction categories on Amazon. They short-circuit the system, allowi…
I would argue that creating an llm book that sells also requires human labour, just a different kind of one.
I have sympathy for any jobs that might be affected (much as my own job has become more tenuous in software engineering). And if the field is disrupted by chaos that makes the research process unproductive, that's bad too and should of course be handled by applying better organization within the institutions that tend to perform mathematical research.
But to a large degree, the notion that "sloppy AI proofs are bad for mathematics research" seems like a total failure of the imagination to me. Attempting to find shorter proofs or more elegant proofs can be turned back in on itself via proof theory. There are proofs in Presburger arithmetic that are doubly exponential in the length of the sentence. Yet a more powerful theory like PA makes quick work of such theorems. The explainability or "subjective beauty" of a proof can be quantified and optimized against. Optimization itself can be optimized against. I really don't understand how this magical ability to know the truth of more theorems much more quickly—even via an "ugly" route—is anything but a net positive.
This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It…
Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a paint…
In a parallel thread omnicognate correctly pointed out that for AI companies it's a direct commercial loss to pour all this money into bruteforcing the solutions to these problems, and that a lot of times the solutions by themselves are not directly commercially valuable. They are doing it for stock price, trying to lure in private capital in preparation for IPOs.
Their models are good, but they are not the moat because Chinese models are good too, so what they are doing, in my opinion, is more harm than good. Mathematics is a science by humans for humans.
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I don't think it really attacks human understanding though. You can still read and understand an AI written proof. If another person comes up with a solution to a problem, you can read their methods and understand it. It doesn't matter if a human came up with that or not. It's really only attacking the "generating new ideas" part.
That's precisely the problem though. You cannot still read and understand an AI written proof at the current skill level of the AI being applied, because they're orders of magnitude longer than human written proofs even when they don't need to be, and spend most of that length on the parts that aren't important. This has been really thoroughly documented by expert mathematicians who are engaging with AI in public lik…
To be honest, I feel like the difficulty of reading AI proofs is due to the fact that we are on the verge of being beyond human comprehension. This is a demonstrable fact as no human has figured this out despite the problem being open for almost 100 years.
As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…
The maths community is now in the antithesis phase, synthesis will take a while ;) Lee Sedol said in an interview that "losing to AI, in a sense, meant my entire world was collapsing. ... I could no longer enjoy the game. So I retired", and I think there will be folks in the mathematical community who would feel the same when the solutions pages to hard problems are suddenly available. But on the other hand, people l…
Carlsen is bored by studying engine lines.
The popularity is boosted by YouTubers because chess is very suitable for somewhat higher class content.
I'm not sure we'd want that world for math. Positions will be cut just like archaeologist positions are cut now.
Earlier quoted context omitted.
I don't think it really attacks human understanding though. You can still read and understand an AI written proof. If another person comes up with a solution to a problem, you can read their methods and understand it. It doesn't matter if a human came up with that or not. It's really only attacking the "generating new ideas" part.
>You can still read and understand an AI written proof. No you can't lol, they're multi million lines of Lean, which is already an obscure language to understand. It's an assault on your senses.
https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...
To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…
Is it not an option to make academia more like a normal job, where people focus on collectively achieved outcomes rather than credit, priority etc.?
As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…
It's not just the isolated dumping, it's the fast, isolated, possibly untraceable dumping, without long term support. It'll basically become slop fatigue if OpenAI starts dumping out proofs faster than the community can keep up, and some turn out to be wrong, never formalize it, don't stay to support it, etc.
(Well that's my hopeful, optimistic take, anyway.)