site banner
PaperclipPerfector  3d ago (text post)   1710 thread views

Friday Fun Thread for July 31, 2026

Be advised: this thread is not for serious in-depth discussion of weighty topics (we have a link for that), this thread is not for anything Culture War related. This thread is for Fun. You got jokes? Share 'em. You got silly questions? Ask 'em.

1
Top Bottom Old Controversial Comments
Jump in the discussion.

No email address required.

https://openai.com/index/ten-advances-in-mathematics/

Fellas, I regret to tell you something you should have realized last week at the latest: it's incredibly over.

This is quite exciting! Some scattered thoughts.

I definitely had the sense that we had hope for this type of thing, since math is (mostly) mechanically-verifiable. Lean is about to be getting even more attention than it had before, and it's important that these all come with Lean code attached. That said, my understanding is that it is still possible to do somewhat sketchy things in Lean. I'm expecting a lot more folks will see how important that concern is and really focus on either shoring it up or put together some set of principles like, "If you proof has X component in Lean, we're going to unfortunately simply discount it for now." But most results that come with Lean code will probably be just fine. (I certainly have no reasons to doubt any of these particular results, myself. Nor do have strong personal opinions about the edges of where possibly sketchy things can be done in Lean.)

On the use and human interpretability of results. This question is not new. Take, for example, the massive human-generated proof of Fermat's last theorem or the exhaustive computer-generated proof of the Four Color Theorem. Many many folks don't actually understand these proofs. Perhaps no one "understands" the proof of the Four Color Theorem, whereas at least the proof of Fermat's last theorem is understood well enough by an extremely small group of folks.

Using those results is easy. You don't have to understand them! If you're working on a problem, and you see that it would be useful for one of those things to be true, congrats! You can just use a pointer to the fact that it's true and move on. This is an unalloyed good.

Understanding those results is another matter. I was looking at a paper recently with some collaborators, and it was one of those situations where we were just failing to have much intuition about how to think about certain parts. (FYI, I think this paper was human-generated, but I don't know.) Multiple people in the group suggested that a few things could be, "They just tried a bunch of options, and found one where they could make the computation work out." And that's fine. I've done that before. Plenty of methods include, "You can just try stuff, and if one works, great!" I also happened to afterward figure out a different way to describe the same thing in a way that made intuitive sense out of it, which was extra neat. Maybe if we bang our head against their paper for long enough, we'll be able to find a way to make intuitive sense out of it, too. Maybe an LLM will help! Tao recently mentioned that he had a discussion with an LLM to help him grab some additional intuition around the counterexample to the jacobian conjecture.

At least in the near term, there will probably be a fair number of LLM-produced proofs that people look at and say, "How the hell does that work?" Plenty of time will be spent trying to understand them. Are there new concepts in there? Can you relate it to other math? Can you simplify it and make it more intuitive? Does something in the method raise new interesting questions?

Which leads me to the most hazy part; the somewhat longer term. Will LLMs be able to consistently make intuitive sense of their proofs for humans? Will they be able to help us understand the connections or identify new questions that we would understand as being interesting that are now relevant?

I certainly don't know how to prognosticate all that well, but I do think of some analogies to another domain that is (mostly) verifiable and where computers already significantly outperform humans - chess. Humans still try to understand something from the superhuman output of chess engines. Unfortunately, I can't find it immediately, but I very recently read (as in the last couple weeks, I believe) an argument that top human grandmaster play has barely improved outside of the opening phase, where folks are memorizing more and more of the output of engines. I'm not sure I believe this analysis (I didn't dig into the details of the methodology, and I can imagine plenty of methodological difficulties), but that's something somewhere in my mind. Another thing is that chess has one single extremely well-defined goal: win the game when you can, otherwise draw. This collapses neatly at any particular point in time to, "What is the objectively best move for this game state?" It is relatively easy to accept that the computer is just flatly going to estimate that far better than we are. It's harder to understand the reasons why that is the best move. It's harder (not necessarily impossible, but harder) to take a variety of examples like this from a computer and have a sense for how to built it into a broader understanding of the game. It's harder to make connections like, "The computer seems to value space in positions like X and Y, but not Z; why is that?"

We have plenty of mathematical "positions" teed up for this type of tool. We can hopefully just ask the LLM what the objective evaluation of these "positions" are. Where else it goes, how we understand the whole thing, and what we can do with it are open and exciting questions.

But most results that come with Lean code will probably be just fine.

Most results produced with an honest human who understands what they're doing will be fine. There were a few corner-case bugs in Lean itself discovered recently, and those might not be the last, but they'll at least be rare. And although you can slip in an "just assume X" to get you to your proof of Y, meaning it's then really a proof of X⇒Y, anyone who really understands the problem will understand that "see what you can prove assuming X" is an intermediate step to proving Y, not the final result.

I still have to say "most" here, because the trouble with a proof written in Lean is that it is written in Lean. If you're working on the frontiers of mathematics then you're almost certainly going to have to formalize your own definitions, and a mistake in formalizing a definition is not a mistake a formal system can detect. A verifier will simply verify that you did indeed prove the precise thing you told it you were proving, even if that thing is not precisely the thing that you were writing in English about proving.

But the big catch here is "honest human who understands what they're doing". There will be people who add new axioms (or who are happy when their LLM adds new axioms) "because that made it run" without realizing that's what they've done. There will be jerks or cranks who do this deliberately. IIRC there was a guy on Twitter X a month or two ago ranting about his wonderful new major proof, all formalized in Lean and everything, who apparently didn't pay attention when his use of the sorry placeholder triggered its warnings. And at the frontiers of mathematics, the honest human who understands what they're doing may end up vastly outnumbered by jerks and cranks after the latter feel "empowered" by AI. Even before LLMs there were relatively low-level bits of mathematics famous for breaking amateurs' minds and turning them into cranks. I assume we'll stave off most of them by getting into the habit of checking new Lean code for "hacks" rather than pure technical validity, and that'll work for any proof regarding stuff that's already defined in mathlib, but it still won't stop the cranks altogether.

Posting separately and prior to the above, so it appears separately and below; this is much less important.

IMHO, this topic is a culture war topic (or at least, it can be, depending upon the presentation). Given that premise, the root comment is a nearly contentless bare link with a one liner snipe of the commenter's outgroup. For example questions, what is "it" and what does it mean for "it" to be "over"? It is plausible that these sorts of questions could have coherent answers that make the original comment benign, but they were not included in the original.

An alternative interpretation is that it is a "First"-post, though I would still probably characterize it at first impression as being paired with a one liner snipe of the commenter's outgroup.

Indeed, I think that the same sense that there even is such a thing as a commenter's "outgroup" on the topic in an indicator in favor of the premise that the topic (or at least a presentation of the topic such as this) is culture war.

EDIT: I should clarify that I am NOT asking for the comment to be modded. I am not entirely confident of my interpretation, and I'm not at all confident that the mods would think so, either. I did not report it because I don't have a strong opinion that it should be modded. I am merely expressing my opinion on some things that I did not like, and I am very open to contrary perspectives.

The rules for "low effort" are somewhat relaxed for the Friday Fun Thread, and "this is culture war" could arguably apply to anything with such a broad interpretation as "there exist people who disagree with you."

"It's over" is in common use as a humorous meme phrase on 4chan. I don't see any examples in the catalogs of /v/ and /g/ at this time, but an OP like "Humanbros… it's over……" would be similarly humorous in this context. (I do see one OP of simply "Bros…" on /g/, and "Soulsbros… *cough* I don't feel so good" and "Nuly bros……" on /v/.)

@ControlsFreak

ToaKraka of all people (much love to him) managed to figure this out. This gentleman. Level -1 Autism. I am very fond of him.

And you couldn't. You produced four paragraphs of appellate briefing on whether a shitpost belongs in the Friday Fun Thread, followed by an edit clarifying that you were not, in fact, filing charges. I'm grateful for your forbearance. However: the Fun Thread is the one venue where a bare link plus a one-liner isn't merely tolerated, but entirely accepted. Dawg. I'm at a loss for words. Is this why Opus 5 performs worse when set to maximum reasoning, because it uses those reasoning tokens unproductively? Much to ponder on.

I am happy to conduct an assessment if you'll pay. I'll probably charge extra, FYI.

Thanks for clarifying something in my thinking. It is a shitpost. That is, it is shit. It is bad. It is not good. Coupled with the primary purpose being to get a dig in on your outgroup, it is quite off-putting. I feel like a simple bare link would have been far better. Even a not-dumb one-liner would have been nice. It's that you're faking like you're making an argument, but without making an argument. It's like "clown hat on; clown hat off" tier of feces.

I'll be happy to conduct an assessment of how you could improve such posts if you'll pay. I'll probably charge extra, FYI. (That is to say, this new habit of you also insulting your interlocutors by demanding that they pay for you to offload your thinking to Claude contains no meaningful content, is also extremely off-putting, and it should be beneath you.)

Gee buddy, I don't like you either. I'm sure we'll both live.

Had you restricted yourself to a perfectly welcome take on the actual ramifications of said mathematical breakthroughs, I'd have been perfectly happy. Instead you were remarkably obtuse, and engaged in backseat modding while appending an edit clarifying that you weren't engaging in backseat modding. I appreciate the disclaimer roughly as much as I'd appreciate someone explaining at length why my house is an eyesore and then adding that they haven't called the HOA about it and aren't sure they would win if they did.

Consider what you've talked yourself into. The post is culture war because it has an outgroup, and we know it has an outgroup because you can imagine someone objecting to it. Run that rule over the rest of the thread and see what survives. Somebody's cat photo has an outgroup, namely dog people. I would ask what isn't culture war under this standard, but I have a guess.

It's especially funny given that my far more detailed AI updates have been accused of not being Culture War material, in the CWR thread. It's almost like reasonable people might disagree, and that a four-paragraph brief on the taxonomy of a shitpost is not the quality contribution you think it is.

In fact, I recall, multiple times, asking you to avoid interacting with me. I have a strong preference not to block anyone at all, but if you're not going to listen, we'll see how far my patience holds. I won't miss you.

God knows I'm not giving you any money, unless $ 0.00... counts, and I'm also not particularly beholden to your preferences on what I write in my spare time. And for the record, I have been offered (and tentatively accepted) @Primaprimaprima 's deal on not using LLMs. Which is quite the opposite of your nonsensical claim, and would have been discoverable by the ancient technique of asking. To him: I've been busy, and I'll get around to the logistics at some point.

Is this really what you've got? C'mon man.

Instead you were remarkably obtuse, and engaged in backseat modding while appending an edit clarifying that you weren't engaging in backseat modding. I appreciate the disclaimer roughly as much as I'd appreciate someone explaining at length why my house is an eyesore and then adding that they haven't called the HOA about it and aren't sure they would win if they did.

I did not think it was necessarily moddable. I realized that someone might think so, and I made sure to clarify. My point was that it was bad. It is, indeed, bad. You're so desperate to avoid that issue that you must try to make the conversation about something else, and this is the best that you have?! Your complaint is that it must boggle the mind for someone to think that a post is bad, but not necessarily moddable? C'mon man. Be serious.

The post is culture war because it has an outgroup

Read again. I said that it was an "indicator". I have separately believed and stated that certain AI issues appear to be culture war these days.

It's especially funny given that my far more detailed AI updates have been accused of not being Culture War material, in the CWR thread.

Read again. I specifically said, "it can be, depending upon the presentation".

a four-paragraph brief on the taxonomy of a shitpost is not the quality contribution you think it is.

Read again. Where did I ever say that I thought it was a quality contribution? I said that it was much less important. Please stop just making up bollocks shit to try to insult your interlocutors.

If you would like my help in using Claude to read better, pay me. See again how completely contentless that sort of shit is? How it's nothing but an insult? You can't even bring yourself to consider your own behavior, so you must deflect and insult again.

I will align my stated and revealed preferences: I am quite done talking with you, even if that implies I was particularly interested anytime lately. Good luck anyway.

Sure that's impressive, meanwhile Google's AI is letting you fabricate satellite images (was, they removed it after coming to their senses).

A non-sequitur to end all others really. What about it?

For context, Google has long been trying to compete with the big AI labs, and failing spectacularly. Ironic for the company that discovered/invented the transformer, Gemini is regarded as much worse than ChatGPT and Claude, and they keep making embarrassments, for example bad AI overviews in search (the article is >2 years old but it still occasionally happens).

So this past week OpenAI has solved multiple Erdos problems, and all Google has made is this silly feature.

I ran into a quagmire with Gemini recently and getting it to reverse an input is impossible and it stubbornly refuses to revert back to its previous state of knowledge. I’m quickly running out of uses and even interest in general beyond treating it as a plugin. ChatGPT hasn’t faired well either.

It's a gross mistake to conflate a setback with defeat, when it comes to Google. They were floundering with Bard. They made a strong recovery, and were competitive again, falling back only after Gemini 3.1 Pro was a disappointment.

Gemini 3.6 Flash has just been knee-capped by OAI making 5.6 Luna 80% cheaper. But this is the company that invented Transformers, and which has talent, TPUs and more money than God. I don't have very high expectations of the upcoming 3.5 Pro, but it only takes a bit of huffing and puffing to get back to the frontier for another month or two.

Their AI overviews use a cheap and cheerful model, simply because of the ridiculous scale of implementation. You're not going to devote 5.6 Sol levels of intelligence for "cheap chippie in Bristol" and thereabouts.

Also, in the locally-hosted ~1-2 graphics card space, their Gemma 4 local models have been quite good for general-purpose use, even if its tool use was a bit broken. (Qwen3.6, or the really big Qwen 3.5 is still the practical frontier for coding AFAICT.)

Google having more money than God is part of their problem. It's like asking why a fat old guy is losing a footrace.

That does not outweigh their other, very real advantages. You do not want to be a cash and compute-poor lab.

You do not want to be a cash and compute-poor lab.

Hmm. Like Moonshot or DeepSeek? Every lab is cash and compute poor compared to Google.

Yes? That is not in conflict with anything I've said.

You've quite literally got the CEO of DeepSeek complaining that they can't get the GPUs necessary to reach the frontier:

https://news.ycombinator.com/item?id=49052912

https://www.cyberkendra.com/2026/07/deepseek-pauses-fundraising-amid.html?m=1

In it, Liang reportedly framed China's disadvantage as an arithmetic problem rather than a talent one: "The biggest gap between us and the US is in resources."

The specifics were unusually candid. Liang is said to have told investors he needed 200,000 Huawei 950 chips to train a frontier model but received 16,000, adding that "Huawei's problem is still insufficient capacity" and expecting the crunch to last at least three years. He also floated narrowing the gap with US labs to three to six months using a fraction of their computing.

You can do remarkable things with grit, determination, the willingness to eat unsalted rice (and by distilling Claude), but that won't get you to the frontier before the frontier moves on.

Liang laments not having enough compute, you know. It is a handicap.

More comments

Google needs to keep acquiring hungry talent and keep it away from the warm, suffocating embrace of their internal bureaucracy - not an easy problem to solve. Cash and compute are the table stakes to compete, but they don't win you the competition.

What is this place?

This website is a place for people who want to move past shady thinking and test their ideas in a court of people who don't all share the same biases. Our goal is to optimize for light, not heat; this is a group effort, and all commentators are asked to do their part.

The weekly Culture War threads host the most controversial topics and are the most visible aspect of The Motte. However, many other topics are appropriate here. We encourage people to post anything related to science, politics, or philosophy; if in doubt, post!

Check out The Vault for an archive of old quality posts. You are encouraged to crosspost these elsewhere.


Why are you called The Motte?

A motte is a stone keep on a raised earthwork common in early medieval fortifications. More pertinently, it's an element in a rhetorical move called a "Motte-and-Bailey", originally identified by philosopher Nicholas Shackel. It describes the tendency in discourse for people to move from a controversial but high value claim to a defensible but less exciting one upon any resistance to the former. He likens this to the medieval fortification, where a desirable land (the bailey) is abandoned when in danger for the more easily defended motte. In Shackel's words, "The Motte represents the defensible but undesired propositions to which one retreats when hard pressed."

On The Motte, always attempt to remain inside your defensible territory, even if you are not being pressed.


New post guidelines

If you're posting something that isn't related to the culture war, we encourage you to post a thread for it. A submission statement is highly appreciated, but isn't necessary for text posts or links to largely-text posts such as blogs or news articles; if we're unsure of the value of your post, we might remove it until you add a submission statement. A submission statement is required for non-text sources (videos, podcasts, images).

Culture war posts go in the culture war thread; all links must either include a submission statement or significant commentary. Bare links without those will be removed.

If in doubt, please post it!


Rules


Recommended Posts And Communities

Recommended Realtime Chats