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.
Okay guys, I rolled my character. His name is Traveliezer Interdimensky and he has 18 INT (19 on skill checks, see my sheet.) He's a breeding stud who can handle twenty women at once despite having only 10 STR and CON. I was thinking that we'd start with Interdimensky trapped in Hell where he's forced to breed with all these beautiful women and get them pregnant, and the rest of the party is like outside or whatever, they don't have to go rescue me, I mean rescue him. Anyway I wanted to numerically quantify how much Hell wants me, I mean him, to stay and breed all these beautiful women, because that's something they'd totally do.
The orange site has a thread. Best sneer so far is this post:
So you know when you're playing rocket ship in the living room but then your mom calls out "dinner time" and the rocket ship becomes an Amazon cardboard box again? Well this guy is an adult, and he's playing rocket ship with chatGPT. The only difference is he doesn't know it and there's no mommy calling him for dinner time to help him snap out of it.
Somebody pointed out that HN's management is partially to blame for the situation in general, on HN. Copying their comment here because it's the sort of thing Dan might blank:
but I don't want to get hellbanned by dang.
Who gives a fuck about HN. Consider the notion that dang is, in fact, partially to blame for this entire fiasco. He runs an easy-to-propagandize platform due how much control of information is exerted by upvotes/downvotes and unchecked flagging. It's caused a very noticeable shift over the past decade among tech/SV/hacker voices -- the dogmatic following of anything that Musk or Thiel shit out or say, this community laps it up without hesitation. Users on HN learn what sentiment on a given topic is rewarded and repeat it in exchange for upvotes.
I look forward to all of it burning down so we can, collectively, learn our lessons and realize that building platforms where discourse itself is gamified (hn, twitter, facebook, and reddit) is exactly what led us down this path today.
Meanwhile, actual Pastafarians (hi!) know that the Russian Federation openly persecutes the Church of the Flying Spaghetti Monster for failing to help the government in its authoritarian activities, and also that we're called to be anti-authoritarian. The Fifth Rather:
I'd really rather you didn't challenge the bigoted, misogynist, hateful ideas of others on an empty stomach. Eat, then go after the bastards.
May you never run out of breadsticks, travelers.
He's talking like it's 2010. He really must feel like he deserves attention, and it's not likely fun for him to learn that the actual practitioners have advanced past the need for his philosophical musings. He wanted to be the foundation, but he was scaffolding, and now he's lining the floors of hamster cages.
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.