The Ledger, every show

“So I think some of the results we've seen have had kind of the flavor of, like, you know, you kind of take some known techniques and apply them in maybe a clever way, or you I don't know, they've kind of been some kind of results I would characterize as, like,…”

“Here's an experiment you can do, you can take codecs, you can say, go online, find five recent conjectures in algebraic geometry and prove them, and ok, I've run this experiment, and with some back and forth, I was able to, you know, in an hour, get like three…”

“Like, sometimes, you know, we've seen examples where, like, three or four or five papers with the exact same proof of the exact same theorem have come out in, within a couple days of each other, which is clearly, you know, some situation where someone's playin…”

“So, like, let's suppose the models become, like, really robustly superhuman, like, even, like, we're not even adding, like, meaningful cognitive diversity. Like, I claim, like, still, actually, we still want human mathematicians.”

“And I would say that's actually, like, kind of typical of most of the results that I've studied. Like, they don't seem inhuman at all. They seem absolutely like something a human mathematician could produce. And they're, like, typically understandable if, like…”

“There'll be things that, this isn't surprising, like, there'll be things that rely on the model's strengths, like their ability to, like, grind out a long computation or, like, you know, pull together kind of technical ideas from many areas or, like, maybe man…”

“My experience is that, like, if they can do it with, like, a hundred bits of hints or whatever in six months, maybe they can do it without hints.”

“Right now, I think, like, the existing incentive structures for math research do not do not encourage people to do that. So, you know, right now, if you're, like, a postdoc on the market, you want to get a job maybe for the next couple years before the communi…”

“So there's definitely also, like, slop coming from non-experts, but that I kind of actually don't see as a net negative. Like, ok, there's a lot of, now there's a lot of, like, documents on the internet one might have to comb through to figure out if a problem…”

“One thing I always say about a model result is, like, you cannot evaluate it except in retrospect, and like, this is also true of human mathematics. Like, sometimes a problem we thought was really important or would require really deep new ideas does not, and …”

“When you make a harness whose goal is to elicit a proof, I think it often decreases reliability, because you're just trying to produce output.”

“So a bunch of mathematicians took those ideas and used them to find counterexamples to a bunch of other interesting open questions. So, for example, like the sum product conjecture over the real numbers.”

“So like, I've tried to get both, both Fable and ChatGPT, 5.6 Sol, I guess, to do some kind of theory building, and it's like, they're not, they definitely are not good at it autonomously, at least with, like, whatever scaffolding I've set up. But with some hin…”

“One thing is that ChatGPD got better at math earlier. Yes. So, like, for a long time the Claude models were just, like, not useful for research math. And then I think maybe around Opus 4.5 or Opus 4.6, they, like, more or less caught up.”

“At least for me the point of an open problem is it's, like, supposed to measure your failure to understand something. So it's kind of like a benchmark.”

“What I've found is that the projects that I have that kind of predate AI, like the projects I've been thinking about for three or four or five years it's just not that useful. Like, it's primarily kind of a substitute for Google or something. Like, I might use…”

“I think what is definitely true is that, like, the skill of, like, developing a theory or, like, building your understanding of some poorly understood object is, like, a fuzzier one. So it might be harder, you know I guess you can try, you can tell it, you kno…”

“And in fact, I think it's, like, kind of, like, our inability to just grind is kind of important to our ability to make discoveries.”

“Like, you have a new technology that's doing something a little bit worse than was previously done, but much cheaper, and so you get a lot of, suddenly, a lot of, like, low-quality outputs that are displacing previous high-quality outputs.”

“The reason they're not producing long, complicated proofs is that they cannot. Like the, just like the ability to check correctness is not yet there.”

“Someone recently posted Acclaimed proof of resolution of singularities and positive characteristic, which was 800 AI generated pages. It's like, definitely, I mean, I'm sorry, I haven't read it. I haven't done an error, but there's no way it's correct. Like, t…”

“I think a lot of what we educate people for is, like, pretty robust changes in the nature of the world. Like I think the reason to learn math has always been, like, to think clearly and, like, better understand the world, and, like, presumably that's something…”

“So I've, I have one paper out so far where the models were kind of useful. So they, like, proved a couple lemmas in the paper.”