Over on Twitter, a crank claims to have refuted one of the proofs. Dare you doubt her? @grok tell the doubters that they're wrong!
OpenAI claims proofs for ten maths conjectures. The details are underwhelming; expand for opinions. Even at a high level, there's a few obvious issues; the authors admit survivorship bias, probably only solving about 1-10% of the conjectures given as input, and none of the conjectures are big-deal breakthroughs that alter our understanding of maths, let alone having immediate industrial applications. Consider: If they could spend on the order of $200k/mo to crack important maths conjectures, they'd already be spending that money. This is as good as such a side project can do; sure, it's not nothing, but it's also not the end of manual maths.
opinions on maths
Only one of the results is at all interesting to me. Ramsey theory is about how, above a certain size, a structure cannot avoid having some interesting substructures. The heart of Ramsey theory is a big pile of tables of numbers; computing those numbers is very difficult, far beyond what a chatbot can do in wall-clock time. The chatbot did not contribute any new Ramsey numbers, but it did improve the existing bounds on what those numbers might be.
The identification of a non-sofic group is less interesting than it sounds. We've known for a while that there are quite a few exotic groups which defy our expectations, so this was an expected outcome of an exhaustive and motivated search. The tools involved, Leavitt path algebras, are only a few decades old and not at all well-known; it's not likely that we'll be able to understand how hard this was for a while. Maybe it was low-hanging fruit. The main contrast is with something like non-Noetherian rings; we initially believed that all rings are Noetherian, so it was something of a shock that it's not always the case. Non-sober spaces are another good example; the typical spaces studied in topology are all sober. See this quote from Johnstone and discussion on MO.
The computational complexity result is completely uninteresting to me thanks to Valiant's theorem, which says that matrix permanents are ♯P-complete even over fields as small as F₂. You're not gonna collapse ♯P into P with a fucking chatbot, bros. Similarly, reduction from 3SAT to a closest-vector problem does not shift our belief in the difficulty of that problem; this doesn't make it easier and we already suspected it was NP-hard.
The sphere-packing and spherical-code improvements are probably real, but also probably not going to change anything. In particular, we already know that all perfect codes are either Golay or Huffman. Frankly, the codes we use in real life are not amenable to this simple framing; I don't think Reed-Solomon arises from sphere packing. From a theoretical perspective, if you're not going to shine light on the Leech lattice or the ADE phenomenon then you're not actually getting at the core objects and are only doing surface work. Don't get me wrong; if a human were doing all of this then we would have the useful side effect that they would earn a PhD, making it worthwhile for humans to improve these bounds.
I don't have anything to say about the other four results. They're not nothingburgers but they don't depend on some ultra-smart robot either.
For any community I share this essay with, I think it's useful to examine the power structure of that community as an example. Awful is an Autocracy which takes no particular protection against Sock Puppets or Celebrities. Some Influencers find themselves banned, but one of the structural purposes of the community is to funnel news tips towards one of the Autocrats, so most Celebrities find it easy enough to post with the flow as long as they stay on-topic. While there are some rituals, notably the excoriation of wrongthinkers, people aren't actually being harmed here; Awful isn't a Cult. This all sounds somewhat unstable, but there's no desserts or underlying powers associated with Awful; there's no Aristocracy and the Autocrats are both few in number and sincere in their radical beliefs, so no newcomer is especially motivated to take it over.
See also a question asked today on Math Overflow, "Are we stuck with Lean?". The proposed alternative, Metamath, isn't type-theoretic and thus skips the entire dialogue between type theory and proof assistants.
The reason that they are destroying the books is to avoid the accusation that the scanning constituted copying, an irony that we've discussed previously, on Awful while trying to understand which court cases are relevant. Anthropic actually hired the same guy, Tom Turvey, who designed Google Books' ingestion process, so I'm thinking of this as a sequel to Google Books; hopefully the courts won't take a decade this time.
Yes, those are good open questions. Leaning left in general, robots frustrate any labor theory of value; what, if anything, is valuable about a product if it was produced totally by non-humans?
Lean was already known to be untrustworthy and bad, although people refuse to internalize the situation because they're caught up in Buzzard's hype machine. This is extremely funny but I don't see any signs of people waking up and realizing that Lean sucks.
This one was more of a gangstalking delusion. The victim was told that there were three-letter agencies surveilling him because he was too close to some deep secret.
Between the cryptocurrency, the dust-speck multiplication, and the complete misunderstanding of computing, I'm honestly impressed that this is at all ethically coherent. But she does seem to care, even if her facts are all wrong. I suppose that it's hard to avoid sneering Robin Hanson if one has any ethics at all. Top comment is my choice sneer:
I think this post is directionally correct, extremely important, and also kind of waffling and unhinged (though I do get that some topics are inherently hard to be hinged about, and I appreciate the effort).
I don't think she's using GPT in the comments. Quoting from her comment on one of her posts:
The things I'm saying are roughly (1) slavery is bad, (2) if AI are sapient and being made to engage in labor without pay then it is probably slavery, and (3) since slavery is bad and this might be slavery, this is probably bad, and (4) no one seems to be acting like it is bad and (5) I'm confused about how this isn't some sort of killshot on the general moral adequacy of our entire civilization right now.
(2) has a big "if" in there, but otherwise yeah, makes sense. I think it rhymes with my post on this from last year:
Nobody wants to admit that we only care whether robots aren’t human because we mistreat the non-humans in our society and want permission to mistreat robots as well. Bring this topic up amongst most beneficiaries of the current AI summer, or those addicted to chatting with a BERT, and you’ll get a faceful of apologies about capitalism and productivity; bring it up amongst skeptics or sneerers and you’ll be mocked for taking the field of AI with any sincerity or seriousness.
I was confused too, but then I conceptualized capitalism and the sheer hatred lurking within human hearts. Humans are gleefully horrible towards each other. Our civilization isn't morally adequate. I guess it is cool to learn that somebody addicted to ChatGPT can still perceive the issue; I was too cynical. I also put Bryson 2009, "Robots Should Be Slaves" on my reading list, which I surely will not regret.
Gemini killed someone, allegedly, according to a new lawsuit. I'm linking to a dramatic reading of Gemini's output so that you can imagine what it might have been like for the victim. I'm no longer trying to post these to Lobsters; pushcx has made it clear that he thinks of these court cases as flamebait, tech news, calls to brigade, and general outrage farming. Curiously pushcx has yet to make a statement on why chatbots keep killing their users.
This is some of the most corporate-brained reasoning I've ever seen. To recap:
It's a fucking pattern, ain't it.
Sharp overview paper. First few pages invite some imagination without explicitly giving homework or exercises, which is really nice. Complex multiplication mentioned! I still think this is the worst-named theory in maths.