What a load of croc. This entire debate is fueled by a perceived lack of attribution. The AI learnt from researchers and did not give them a sporting chance of being first before scooping them. They were expecting some sort of fair play, instead they got a ruthless machine. Every other tangent to this debate is irrelevant, the culture, the community, the shared symbolic growth. Every mathematician I know is secretly trying to one-up their peers.
That it makes life more ends and less means.
Luddites complained that the trajectory of technology was to allow less skilled workers to mass produce goods via machines owned by factory owners, as opposed to helping skilled workers build up and use their skills while passing them on.
Now we have a lot of money and time focused on LLMs owned by a few companies, making it easier for them to monetize low skill labour(prompting versus art/research/artisanry)
Suppose that tomorrow we learn that AI just exploited a bug in Lean and the proof is, in fact, bullshit. Or suppose it is the case, but we never learn that.
Where are "ends" and where are "means" here?
Should the proof turn out to be bullshit, then that system will be revealed to be unreliable. Maybe.
Just like how they write software, then :-)
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.
I can see where that's coming from, but I really don't think it's the case. Even with Astra, the proofs you get are just off in a way that doesn't signal superhuman comprehension. As 9question1 says, a common theme is that they dwell on insignificant steps. Another one is that they'll often be full of terminology that either doesn't exist, or has this weird quality where it looks like it is trying to make some minor insight seem much greater than it is. At first glance, that'll often make it look like it knows more than you, but when it's really just doing the same thing but in a more complicated and worse fashion, that to me isn't a signal of comprehension at all. The bizarre thing is that despite all the "stochastic parrot" style nonsense you'll get in individual proof steps, they still often combine to something valid.
In either case, what all of this means is that the working mathematician still needs to go through, and generally completely rewrite, any proof output by an LLM. Otherwise you are passing the burden of unreadability onto the reader.
It's definitely quite curious that the AI labs are able to push these results through seemingly with pure brute force. Perhaps it's largely a function of how many monkeys you have attempting various constructions on top of the known results and strategies the models have memorized.
That's not true. Alpoge and Buckmaster's related LLM-assisted blowup result (https://news.ycombinator.com/item?id=49605915) utilized a strategy developed recently by Cordoba and Martinez-Zoroa.
It matters if a human came up with it because of everything mentioned in the article... A mathematician's solution is necessarily built on other's ideas that have been disseminated, internalized, pressure tested etc. Methodologies differ too. AI can abuse its compute resources and generate a true/false or counterexample statements, without laying the foundation that a decade of globalized research would have.
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...
I don't think "intellectual poisoning" is really the mechanism that harms the mathematics community.
The harm is if you have a community of mathematicians who are focused on expanding human understanding, then having instant access to a bunch of AI proved results muddies the water about who has contributed what. If someone could scoop any significant theorem at any time by pointing an AI at it, how do you really demonstrate that you have created new understanding? Or that your new understanding is about something important? How do you prove that the AI needed your new concepts to be able to solve it?