The distinction here is that they are in that situation getting information about what the market is doing slightly faster, or sending an order slightly faster. But here the information is information that is not publicly available. So yes, the distinction here is clear. This is insider trading. (That the other stuff should also be illegal but isn't is a secondary issue here.)

Yes, you and I have disagreed on these matters before here. That you might want to listen even a little bit to subject matter experts should maybe occur to you. But if you don't want to listen to me, then there are other options. Alvaro Lozano-Robledo did a great interview with Francesco Fournier-Facio about it the sofic group problem and why we care https://www.youtube.com/watch?... . Fournier-Facio has done a lot of recent good work in infinite group theory. If you want to learn more about the sphere packing problem and why we care, you can look at Conway and Sloane's book "Sphere Packings, Lattices and Groups." For the Ramsey problem, you can check out Ron Graham's book on Ramsey theory, although it is a bit old at this point. A more up to date book is Soifer's "Ramsey Theory: Yesterday, Today, and Tomorrow" but I haven't personally read it. But the upshot is that other than which of these problems I've personally worked unsuccessfully on, there's nothing here that you cannot verify yourself, so you don't really need to rely on me and your own opinion that I have no clue is only a little relevant.

Mathematician here. None of the ten problems under discussion here are remotely problems that "nobody really looked for a long time because the problem was not interesting enough." All ten of these were major problems in their subfields; I was familiar with 8/10 before this, and I've talked with people in the other subfields who have confirmed that the other 2 were also major enough. The sphere packing problem has been a problem which people have been thinking about variants of for literally over a hundred years, and is one that I thought about (and made no progress on) when I was doing my PhD. The Ramsey problem is one of the most famous open problems in Ramsey theory, and one I've also thought about, as my own research areas have moved somewhat into graph theory the last few years. Of the remaining other 6, I've never seriously thought about, but are still well known problems.

Your point about there being many open problems, and they've only solved a small fraction has more validity. But that's also just as true for how human mathematicians function. I've probably thought about hundreds of problems, and solved only maybe 5% of those, and nothing I've solved has been remotely of the level of any of these ten problems in fame or amount of prior attention. That these systems are only solving a fraction of the problems is true but is only the smallest hit on how impressive these results are. And these systems continue to improve. We'll likely see even more impressive results in a month or two.

The person you are referring to is not an AI hater, they are as they say astonished. I'm not sure which example they are referring to, but there have been multiple examples at this point with GPT 5.4 or higher or Fable where the primary thing the human has done is just told it to keep trying and continue every so often.

While we do not know precisely what system OpenAI was using, the proofs they generated in this case did not come with automatic Lean or other verification. And many of the successful uses of AI in math now, such as Erdos 1196, the Unit Distance Conjecture have been done using just the regular LLM without Lean, or any other system.

Well, that's true also for human mathematicians. I'm a mathematician, and I'd guess I end up solving about 5% or fewer of the problems I end up trying to work on.

Anthropic made a profit second quarter this year https://aitoolsrecap.com/Blog/anthropic-first-profit-2026-revenue-breakdown. We'll see if they make a profit in Q3, but at least right now, that statement doesn't look accurate. Now, there's reasonable concern about how real this profit is, given the weird amount of self-dealing and entanglement between the different companies. I also wouldn't be surprised if none of the major data center companies are taking chip depreciation into account to the extent they should. But at least on paper, right now, the statement isn't true.

People spend far more than $2000 on things like the Large Hadron Collider or the James Web Telescope. We care about these questions in part because they are questions about the nature of the universe. In that sense, they are far beyond just mere counting grains of sand. Note also that while none of these have direct applications, a lot of them are related to ideas which do have direct applications. Sphere packing is connected to making error correcting codes. the quantum parallel problem is part of a broader program to understand analogs between classical and quantum contexts, which is relevant for both physics and possibly for quantum computers, and the closest vector problem is important in understanding the robustness of certain cryptographic systems. That said, it is true that some of them like the sofic group problem and the Ramsey problem are just really good math problems, with no obvious connection to anything applied.

The answer here is that these systems are not "half-random-BS-generators" but have gotten very good at careful reasoning. Even the frontier models still make mistakes in mathematical reasoning, but the mistakes are often at the subtle level that a professional mathematician would make. LLM AI intelligence right now is very "spiky" very good at some tasks, and still failing badly at others. But you should reevaluate what your understanding is of what they are capable of.

That occurred very early on with some highly obscure Erdos problems. That stopped being the situation a while ago when Erdos 1196 was solved by an AI. This was a well known enough problem that that was highly unlikely to have some obscure paper out there solving it. Similarly, then the Unit Distance Conjecture and the Jacobian Conjecture got solved. And all ten of these are pretty major in their subfields. That means that obscure papers that do the same thing and no one realize the question had already been asked or solved are extremely unlikely.

Why? Many of these books are books which would get pulped or destroyed anyways, or in the best case will sit on a shelf for decades until they fall apart and then get thrown out? Moreover, prior to AI, most book digitization involved destroying the copy of the book one is digitizing. One can digitize a book without destroying it, but it is much slower, and cheaper. Is it only a problem when AI does it? Finally, there is the issue of legal incentives. Under the Bartz decision, the AI companies are engaging in transformative work when they digitize a book and destroy the original. This is consistent with a variety of prior precedents. So, if there's a problem here, it is with the legal framework.

They pay me in honeycomb!

It is plausible we're in a bubble. And there's some evidence for it. That companies can just add the words "AI" to something to get investment is a serious sign. But the revenue situation, while weird, is not by itself definitive. Anthropic even made a profit in Q2 this year https://aitoolsrecap.com/Blog/anthropic-first-profit-2026-revenue-breakdown . Now, there's enough weird accounting going on, and circularity within the various companies, that interpreting that as a definite, genuine profit is something I'd be hesitant to do, but from all the public information it does look genuine.

There are two, related issues. First, if a "bubble" keeps going on for long enough, it stops being a bubble because society just reorganizes around it. For example, there's a decent argument that the industry was in a bubble since the 1930s (or even earlier) but that we reorganized cities and infrastructure to support it. And then when there was finally, almost a hundred years later, a danger that that bubble was going to pop, as it really had deserved to decades before, we had the auto-bailtouts (which were not just in the US, but also included the UK, Russia, France, Germany, Italy and others). https://en.wikipedia.org/wiki/2008%E2%80%932010_automotive_industry_crisis. There's a related saying which generally comes up in the context of people thinking of short-selling: "Markets can be irrational longer than you can be solvent." Second, even when a bubble does burst, the tech itself may still grow or be highly useful. When the train bubble burst in 1873, it was devastating, but by most major metrics of the industry (amount of track laid down, number of stations, estimated number of people-miles traveled per year) numbers barely dipped or kept going up. Similarly, when the dot-com bubble burst some specific things did get really damaged (with some early fiber optic being just abandoned) but by and large, the internet continued to grow to the point where it ended up more ubiquitous than even boosters in the late 1990s would have predicted. So a bubble bursting doesn't mean that LLM based AI is goes away.

n general, when there's an optimization process involved where one is minimizing stress or something else, hexagons often show up. In fact, hexagons are more often in nature than square patterns. One nice example is Giant's Causeway which has large hexagonal basalt columns https://en.wikipedia.org/wiki/Giant's_Causeway (although a few columns have seven or eight sides). But neat to see another example, on another world no less. (We have on big hexagon on Saturn already.)

This seems like essentially a variant of the Waluigi effect hypothesized here https://www.lesswrong.com/posts/D7PumeYTDPfBTp3i7/the-waluigi-effect-mega-post which had the advantage of a pretty fun name for the situation, and is worth reading. . There's also some related prior work by Ball, Gluch, Goldwasser, Kreuter, Reingold, and Rothblum https://arxiv.org/abs/2507.07341 which suggested that fundamental information issues or computational complexity issues meant that making an LLM AI "safe" from jailbreaks by having a less computationally powerful/less intelligent AI system look over its input would always fail, since one could construct inputs that would be complicated tasks or essentially hidden puzzles that the less powerful AI would fail at but would expand out by the more powerful AI into instructions/jailbreaks. Ball et. al's work is also discussed in detail in this Quanta piece https://www.quantamagazine.org/cryptographers-show-that-ai-protections-will-always-have-holes-20251210/ There's also some similar work by Rao, Choudhury, and Aditya https://arxiv.org/abs/2406.12702 which I haven't read in detail but seems also thematically very similar.