This is copium. Humans worked on it, but they didn't come close to actually solving it. Even if you do the whole "the AI looked at material in its training data" thing, modern AI can make their own math data to train on with RLVF. This new model is legitimately on a different plane of existence from modern mathematicians.
My point is, the AI could not have done what it did without the skilled mathemetician prompting it. It was just a tool in the hands of the human that did it. And that was a very skilled human. Unless you're a professional mathematician, you cannot get the same result even if you use the same AI model. That's the proof that it's the human's work, not the AI.
Why don't you try getting a Millennium Prize then? If you think it was the AI that did it, you have access to the exact same ChatGPT.
We don't know what the prompts were though. Terence Tao showed of some of his, and they are indeed huge, with lots of context, things that might work, things he knows don't etc. What we do know about this, is that 10k agents worked together on this. The initial prompt, while probably still very relevant, would get diluted over time. We simply don't know the level of inolvement of humans in reaching this proof.
I don't have access to the exact agent OpenAI used, and I certainly don't have access to the enormous amount of tokens that were used. That being said, I doubt there was some advanced prompting technique going on here. We've seen AI proofs with the prompts attached, and it's pretty basic stuff like "don't give up".
This is undeniably epochal, but I can't help but notice that this is yet another example of AI disproving rather than proving something. Is this just a coincidence, or does AI slightly struggle with proving theorems?[0]
[0] Struggle relative to its ability to disprove, not struggle relative to people's ability to prove theorems.
A bit of a hair-splitting, but isn't explicit construction the only way formal theorem provers can work? Of course you can still prove stuff with them, but certain axioms that more "human" proofs use may not be available, like law of excluded middle (every proposition is either true or false)
(Okay, they can be made available in a way similar to `unsafe` in rust)
I guess I don't understand the issue you're raising. If you want to formalize a non-constructive proof, it remains non-constructive, even if you have a computer check the proof vs a human.
As a trivial example, in lean you can work with probability theory/measure theory. This has oodles of non-constructive parts, but we can ignore that for now. As part of this, you can use the probabilistic method. For example, if you want to prove that codes with optimal parameters exist, for many noise models it is known that sampling a code randomly from an appropriate (and often naive) distribution will yield a code with optimal parameters.
You should be able to prove this in lean (or any other theorem prover). But you cannot construct these codes. While you can sample a code randomly, verifying a code has good parameters is typically NP-hard (e.g. it is an instance of the minimum distance problem). So, you cannot (efficiently) "construct" a good code in lean4, despite being able to prove one exists.
This seems analogous to me that you could validate that a non-constructive proof is correct in lean4. Sure, it would be nice if the proof was constructive. But it isn't, and encoding it into a computer shouldn't give you that (non-trivial) property for free.
I predict the opposite. With AI, labour costs will go down, creating an abundance of goods. Unemployment may be an issue, but the workforce is already declining because of the fertility crisis, so I think we'll manage having a certain percentage of jobs automated away.
You are either very confused about timescales, or very dismissive of "just" a generation of suffering while unemployment and birthrates somewhat maybe compensate for eachother.
This feels a bit like saying "global warming is bad and particulate pollution is bad, but the latter will cancel out some warming effect, so no worries!" Please make an effort before spouting theories like this.
But the EU was never meant to be a loose forum of nations. From the very beginning, the Single European Act made it clear that the intention was to integrate the member states into a single union, "speaking ever increasingly with one voice".[0]
>The concern is that autism as a rigorous category may be useless, but that doesn't mean that autistic people are suddenly neurotypical
IDK. I'm diagnosed as autistic, but I've become a bit less attached to that label in recent years. Like, I do struggle with eye contact, excessive noise, and social situations. I'm not going to say that I'm just a normal guy, but I do think that there's a wide spectrum here that encompasses everybody. I don't buy the idea that autism is some special category of people that are totally unlike neurotypicals. Instead, it's just one side of the spectrum, with neurotypicals on the other end, and an ambiguous group in the middle[0]. I think that once society becomes more accepting of neurodiversity, we're going to stop getting so hung up on labels like "autistic" and "neurotypical" and accept that there's a lot of nuance in the human condition.
[0] In reality, this spectrum would be multi-dimensional, but I'm choosing to describe it as a 1D line for illustrative purposes.
When I first considered my condition, I was looking around and was trying to mentally label people as neurotypical/neurodivergent.
After a few years, I started labeling more and more people as neurodivergent, because I could notice more subtle hints. Now, I instead just try to figure out how far on the spectrum everyone is, to know how the relationship dynamic will be like.
Something that gets ignored is that we're already facing a serious decline in the workforce as a result of the fertility crisis. If we can automate some jobs at the same time as people leave the workforce en masse, we can avoid a catasrophe.
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