That's why it is using it to look over drafts. You take the AI output and then go through its suggested edits or concerns. Essentially it functions as a very fast, half-way decent proof-reader. For example, my spouse looks over a lot of drafts of things I write, but if I give her a 15 page paper, there's good work on the first 8 or 9 pages, probably a joke on page 10 about my notation, one or two comments on the next page, and then a few comments on the bibliography. Claude is not as good a proof-reader as she is, but Claude doesn't poop out after a few pages. And Claude is much faster. So reliability goes up without having to rely on the AI being reliable itself.

And sometimes it catches subtle things. For example, not too long ago, I gave a paper draft to Claude, and it noted in the bibliography that the journal volume number seemed unlikely given the year; it turned out that the volume was correct, but I had actually written the wrong journal down in the entry. Another time, Claude noted that one entry in a bibliography was from a "borderline predatory" (its words but it wasn't wrong) journal, and since I wasn't using it for much other than as part of a list of "hey, here's prior literature" and the paper in question didn't prove anything interesting, I discussed just dropping it from the citation list. Claude then without me asking, pulled up preprint I already had on the arXiv and noted it saw that paper cited there and suggested we remove the paper there also. I didn't do so, but this is the sort of thing that it can suggest. One still has the human make the decisions, but the input itself is useful. And for the most part, verification by a human for most issues is much faster than finding the issues one self.

Not really. It turns out that specialized models do not do as well as large general models. This is essentially a variant of the Bitter Lesson https://en.wikipedia.org/wiki/Bitter_lesson. In this case, there's other reason for it also. There's a lot of reasoning science and math discussions in non-specialized training data. For example, one paper I wrote with two coauthors started as a Reddit discussion. But there's also just a lot of subtle interaction that specialized models don't necessarily get. Math is easier to understand if one has a good command of physics. Engineering is better if one has math and physics. Etc. And sometimes a technique gets directly pulled over. For example, in the large OpenAI paper drop, one of the graph theory problems relied on a trick involving a weighing on the graph that involved complex numbers designed to cancel, where the trick came from a physics context that did something similar. A math specialized model would have been unlikely to find and import that trick.

Right, and the line here isn't clear. One take on NFTs is that they are nominally a tech but functioned purely as a commodity bubble. Or that NFT is a tech but it was used to make commodities which had a bubble. And the line between tech and commodity was blurry historically. When Spain entered the "platinum age," that was based in part on how to make nearly pure platinum was a tech, but the platinum itself was a commodity.

Since per a token output seems to be getting better also for open-weight models, this suggests this is more than just a business decision. And some of it is specific changes; we know that larger models with more training data for example will often produce higher quality output. But also aside from scaling, there have been architectural improvements. For example, one insight that occurred was that having lower precision weights which allowed more weights was often a positive tradeoff. That lead to changes in both the software and hardware ends, as the GPUs were modified as a result. Similar, there's been changes in what functions are used for the feedforward function.

The business case for LLMs is a bit broader than that. They don't need to replace that many workers if they make enough workers more efficient or more reliable (such as simply having LLMs look over drafts). There's also at this point, clear usage cases for scientific and mathematical research but that's using the very high end models, and admittedly is a pretty small market, not enough to justify massive expenditure at this level. The tulip example is interesting; what you are touching on their is the distinction between a "tech bubble" (like railroads or internet) and a "commodities bubble" (tulips, housing, Beanie Babies). Note that the degree to which the tulip bubble was real is questionable. See https://theconversation.com/tulip-mania-the-classic-story-of-a-dutch-financial-bubble-is-mostly-wrong-91413, and the line between a tech bubble and a commodity bubble itself can be blurry (see for example Bitcoin and NFTs). One of the difficulties here is that the LLMs keep improving, and the cost per token is going down, and the amount one can do per a token is going up. But that's happening in part due to massive investment in both infrastructure and research. How sustainable any of that is is unclear.

There are at least four problems with this. First, linear algebra is from a math standpoint insanely powerful. For example, all of representation theory https://en.wikipedia.org/wiki/Representation_theory is using linear algebra to understand groups. Much of the study of modular forms https://en.wikipedia.org/wiki/Modular_form involves understanding the behavior of modular forms over SL_2(Z) which has heavy linear algebra elements to it. People who see linear algebra as somehow a weak thing are often people who took a single semester of it and didn't do much else with it.

Second, the idea that these AI systems are just linear algebra isn't accurate anyhow. While there's a lot of linear involved, a major part of how transforms like LLMs work is the intervening non-linear layers, which use ReLu https://en.wikipedia.org/wiki/Rectified_linear_unit, Softplus, or a similar function. So, summarizing this as just linear algebra isn't accurate. It is linear algebra with some spice.

Third, even if this were somehow just linear algebra, that shouldn't therefore be a reason to think that there's any limits to what is going on. At the end of the day, the empirical success is what matter, and systems which can do things like prove the quasi-Riemann Hypothesis or solve other major math problems are pretty impressive regardless of what is under the hood. So, if one does think this is just linear algebra, that's not a reason to dismiss the systems but a reason to increase your estimate of what can be done with mere linear algebra.

Fourth, slowing down connections like this may make crashes *less likely.* In particular, the main way we could have a serious bubble here is over-investment. Delays including power grid delays force bottlenecks on the investment level, and make that sort of problem less likely.

We may be in a bubble here. Certainly some elements look very bubble-like. In the late 1990s, during the dot-com boom, one had people making perfectly normal businesses but just tacking on "on the internet" to it and it would get millions of dollars of funding automatically. See for example pets.com . And we're seeing some of that now; we've had a whole bunch of businesses see their stock price shootup just because they mention AI. So we may be in a bubble, and it may crash now, or might crash never or decades from now. (Arguably the US had an 80 year automobile bubble that didn't crash until the late 2000s which then forced the auto bailout.) But the other thing to keep in mind is that a crash does not mean the tech goes away. In 1873, the US had a devastating collapse of the railroad bubble, and yet railroads continued to grow, with the amount of track not peaking until around 1910 https://transportgeography.org/contents/chapter5/rail-transportation-pipelines/rail-track-mileage-united-states/. Similarly, although the internet bubble burst, by 2015, one had more internet use than even the most internet hyping person in 1998 would have likely dreamed of. A bubble bursting does not mean the tech itself goes away.

The set of problems that only a human can solve is getting rapidly smaller. The set of puzzles that a human can solve, that an AI cannot, and which take a small amount of time for a human and aren't highly inconvenient may already be empty.

Jumping a car with compressed air isn't a technological miracle. It is a useless stunt, and one which if went into production cars would be dangerous to both those in the car and people around them.

I don't know what field you are in, but in my area, math, this is wildly not the case. They are much, much better. And the next line of the public frontier models are obviously even better judging from everything that we've seen drop from OpenAI and Anthropic. The large OpenAI release would by itself would have four or five results which would arguably be a Fields Medal if a human had done that, and quasi-RH which would if a human did it be almost definitely a Fields Medal result.

On the contrary. The people trying to make this sort of claim at this point are overwhelmingly the non-mathematicians. To the mathematicians the number of new proofs of genuinely difficult problems and the use of novel techniques like those in the Unique Games Conjecture proof and Hadwiger-Nelson make us generally have the exact position you are claiming is something that is believed by the non-mathematicians. Even the most anti-AI mathematicians like Tasmin Chu agree that the AIs are producing novel, major work at this point.

Seriously? They proved the quasi-Riemann Hypothesis. Are you seriously going to argue that that was stolen somehow and not a useful contribution?

You seem to be conflating two very different things. There's a massive difference between an LLM connecting ideas that hasn't previously been connected, while using ideas from humans, and claiming that all they are doing is rearranging data.

This gets to some extent into the issue of what we mean by "novel" and admittedly that has some subjectivity to it. One take on what is going on here is that this should be showing us how much that we thought of as creative was just rearranging things. There's a legitimate argument that the AI isn't doing anything creative or clever here, and that if someone says, "Well, by that metric the vast majority of human mathematicians aren't doing anything creative or clever," and while I see that as a pretty hard response, one response is to just say "Yeah, go bite that bullet."

Here? None.

I'm not sure where the line is there. For at least some of these, part of it seems to be the AI importing pieces of techniques used in other areas of math. In general, no human discovery is completely novel. Newton's work relied on prior work of Galileo, Oresme and many others. Einstein's work relied on ideas of hundreds before-hand. At the same time, there's people whose work really does look like it is fundamentally different in many ways than what went before, and both of those are examples. In math, Peter Scholze's perfectoids for example clearly build on existing ideas, but there's a lot of stuff that looks deeply new. How to draw the line here isn't always clear. For what it is worth, Harald Helfgott, who is a much smarter and more knowledgeable mathematician than I am thinks that of what he's looked at it seems like the AI is still producing things in what amounts to almost the "convex hull" of known math or close to it. But his idea of what that looks like may be much bigger than my idea.

No one saw quasi-RH coming or many of the others here. So that is unlikely. And the last batch of 10 problems they released a few weeks ago which were impressive enough were all novel results. There have been issues with them using techniques or ideas that should be better credited to where some of those approaches are coming from. But that's the sort of thing that often happens at a preprint stage. When I referee a paper, if this happens, you just request they cite the relevant papers and move on. This isn't at all stealing things.

This is really not accurate. There's Fields Medal level work here with quasi-RH for example. And for Hadwiger-Nelson it took an approach that doesn't seem to be in in the literature. These things really are doing novel math. I've personally seen this is in a bunch of situations. Here's a personal example, much smaller than anything like these problems. I have a recent preprint with a student here https://arxiv.org/abs/2609.36068 (about 90% of this was done by her. She's very good.) But part of this came from when I ran a version of Proposition 13 in that paper through Claude just to clean up the draft of that bit before I sent it to her. Claude informed me (essentially unprompted) that the argument had a whole in it (in addition to pointing out grammar errors, unbalanced parentheses and some other embarrassing minor mistakes). I then fixed the hole, and gave it back to Claude. Claude thought for a few minutes, and then informed me that I had *not* fixed the hole, and the reason was that my version of the proposition was missing an entire infinite family which it constructed. The literature on this problem is small, and I'm very familiar with it. The family it produced is straightforward (see Prop 8), but definitely was not in the existing literature. So yes, these systems really can do novel math, and can even do so in an essentially minimally prompted fashion, in this case, explaining to the meat mathematician why his proof is wrong. My student and I then generalized Claude's family to Theorem 9 in that paper, but the AI definitely had an impact.

At some level this was actually not a good thing. I'm trying to encourage students to *not* rely on the AI for research so they develop basic research skills. So if the AI had not volunteered the family I wouldn't have had to tell her that the AI had discovered it, but honestly required noting it. So I had a conflict between intellectual honesty and being a good role model.

Mathematician here specializing in number theory with a side-order of graph theory. I've only had time to start looking at two of them. First, is the Hadwiger-Nelson/chromatic number of the plane https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem proof. As far as I'm aware (and I could be wrong) the technique it uses here is not in the literature, so this is a genuine construction of a new technique. Second is the Erdos Egyptian fraction bound, and for that one it looks like the techniques are about what I'd expect, but I'm definitely still digesting both of these.

For the quasi-Riemann Hypothesis the striking thing is almost the opposite direction. It looks like the AI used standard complex analytic techniques to get the result. But many mathematicians have often thought for years that those techniques would not likely be strong enough to get this sort of result.

I know less about the Unique Games Conjecture https://en.wikipedia.org/wiki/Unique_games_conjecture but having talked with some of the people there it looks like it took a somewhat standard set of ideas and then combined them with multiple just weird stuff and sort of took a hard left turn at one point for no clear reason and ended up at the result.

It is also worth noting that while many of these have Lean code confirming their correctness (quasi-RH for example) others do not. The three I mentioned above have all also been looked at at this point by human mathematicians who have not found issues; that's likely true for others, but those three I'm aware at least of people doing so. Not all the claims have Lean code though; a bit under half. One of the non-formalized problems also has been withdrawn due to what essentially amounts to a sign error https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/paper.pdf. It is likely others will be withdrawn also by the end, but I'd be surprised if more than 10 are. And even if everything single one without Lean code turned out to be wrong (which seems very unlikely), this would still be an amazing set of math. I commented elsewhere that if a human mathematician had made the quasi-RH result they'd be likely a shoe-in for the Fields Medal, and another mathematician replied saying "delete likely."

Now a more editorial comment: There are legitimate concerns about what this is doing to mathematics. This sort of thing is very cool. But it also is part of a trend that may make it much harder to train young mathematicians or get them to exist at all. If the AIs are limited in how genuinely novel their ideas can be, then we may end up in a situation where we get a massive burst in math over the next few years, and then math stalls out because we don't have enough good really high caliber mathematicians (Not the mathematicians like me, but people like Serre, Tao, Scholze, Clausen,etc.) to come up with deeply new ideas that the AIs can build on.

"Guarantee" isn't what matters here. Likelihood is what matters. They provide predictions better than random chance. That's the central point.