[00:00:00] Jacob Haimes: This episode was recorded on October 2nd, 2026. Welcome to Muckrakers, where we dig through the latest happenings around so-called AI. In each episode, we highlight recent events, contextualize the most important ones, and try to separate muck from meaning. I'm your host, Jacob Hames, and joining me is my co-host, Igor Krawczuk

[00:00:22] Igor: Thanks, Jacob. This episode we sing a eulogy to mathematicians

[00:00:26] Jacob Haimes: Why? Why are we doing that? Maybe just give me a, an update or maybe it's too-- Maybe it's old news now. Maybe I, we don't even need to talk about it, but I feel like we should provide a little bit of context

[00:00:39] Igor: it is still rippling through, I would say, but, like, the impact has been supplanted by new model drops. Uh, so, so, like, the, the TikTok ADHD-- uh, the attention span of internet has moved on already.

[00:00:51] Jacob Haimes: Mhm.

[00:00:52] Igor: But, uh, a few weeks ago, I think at this point, OpenAI dropped that they had a Millennium Prize solution and that they, they had, uh, found like a particular, um, solution of a, like a Na- Navier-Stokes problem And was drama afterwards about their approach possibly having been lifted from human mathematicians who were developing the proof in ChatGPT and OpenAI couldn't rule out that the model had been trained on their approaches and I think this has not been resolved yet and so their what I probably hoped big announcement of like oh AI is now mathematician turned into OpenAI steals not knowledge workers proprietary stuff which one must assume was not their goal and it has led now to them reportedly or like via leaks that might come from them sitting on like lots of unresolved, um, like publicly unresolved solutions to like decently interesting problems, but they're not sharing And lots of discourse, both kind of like what is the role of OpenAI?

[00:02:12] Igor: Is it ethical to do what they do? How should they release these results, if at all? Should they be doing what they're doing? what does, what does this mean for math? Like, is math over now? Do all, all of the mathematicians get fired now? And my take is like, no But it's probably worth discussing kind of like Of why people are scared, but also why we should care about mathematicians staying em-employed more than other types of, uh, of, uh, of workers, if at all

[00:02:48] Jacob Haimes: So what you're saying is you're a nerd

[00:02:50] Igor: I mean, that was never in doubt, no?

[00:02:52] Jacob Haimes: Well, yeah, that's, that's fair. okay. So I think before we go further, we should double-check the OpenAI, uh, math, like what, what is it? They, they made like a little math board or something, um, advisory group on mathematics and artificial intelligence. Yeah, so this is the September 21st,

[00:03:13] Igor: to the,

[00:03:14] Jacob Haimes: and it was two weeks after-ish they, uh, you know, say that they have, uh, solved Navier-Stokes, which is of course not actually what they did.

[00:03:24] Jacob Haimes: They, um, met the conditions to unlock the Millennium prize for the Navier-Stokes, uh, Millennium problem, which means that they had a counterexample for it. Now, that's not to say that that isn't s- like its own achievement. Um, whether it is their achievement is in question. Um, but it isn't the claim that seems to be said often, at the very least

[00:03:55] Igor: I, I feel like it is fair to say that kind of like everyone, okay, people who work in the field when we so like solve Navier-Stokes, we mean kind of like claim the Millennium prize and kind of like there's actually like an interesting entry point there into like When this prize was created, the idea was that like having any of these conditions that, uh, allow you to claim a prize will have meant that you have developed a theory that allows you to kind of like make massive progress towards u-un-understanding of the type of problem, uh, th-that is, uh, forming like the Navier-Stokes equations, which are like the fluid dynamics equations basically

[00:04:44] Jacob Haimes: And just before we go further

[00:04:47] Jacob Haimes: I don't think that that is the case here though, correct? Like, there, there wasn't a big, uh, I guess fundamental like breakthrough that allows for restructuring of preexisting problems and, and, um, understanding in a way that like we didn't have before now. Maybe I don't, uh, have as much context on the, the specific, uh, solution as, as maybe I should, but yeah.

[00:05:22] Igor: As best as I can tell, what basically happened is that like the The solutions that OpenAI published are using arguments and techniques that either independently or because, uh, OpenAI couldn't rule out that the, the model trained on them been developed by human, human mathematicians before that We're getting close to doing their own solution maybe And, and like, uh, the extension relative to that is not like the big shift that it would be, but also I don't think anybody has digested the papers and the implications yet. In the sense kind of like it's an LLM paper, I'm looking at, uh, at the two right now. Um, it's finite, finite time blow up for the Euler equation and finite time blow up for Na- for Navier-Stokes. And the Navier-Stokes one is 157 pages, the Euler one is 56 pages of relatively dense argumentation. Like, it's not horribly written But it's still something that I think like will need a while to really settle and also like the The Lean proof is not written in a form that would go into, into Mathlib, which is like this highly curated base of, um existing proofs in a way that can be reused basically And so-- And also um, what is important, and we, we were doing like a preparatory discussion for, uh, for this before. Um, I was trying to explain that When you do an actual proof, like when you do a mathematical analysis, what it means is that you're wrapping your head around something that is actually too big to fit into your head. and you do that by breaking it down into like smaller and smaller steps that all have like a meaning for you, that you ground in like your other mathematical un- understanding or in like analogies that would actually make sense to everyone. And you write down the, the relationship between these sub-problems in like a formal no- notation that allows you to basically say, "Okay, I've proved all of these subpro- uh, problems, and I have here like a formal thing that maybe it's n- not even intuitive for me, but I know that like just with the rules of logic that are embedded into this notation, if these sub-problems are true, then this thing is true."

[00:08:37] Igor: And then you can kind of like track of your thought across like more complex and large Problems, ideas when you would, uh, always be able to. a big un- uh, uh, part of understanding that we like, like, as in like the human society, but, but also like the person doing it gets is actually in like all the time it didn't work out. Like whenever you try to like s- do a proof fresh, you try a lot of different things that all intuitively make sense, and then you find like a problem, a counterexample, like something that like doesn't work out. And the process of encountering those problems and like sometimes being able to overcome them, sometimes not, is the thing that gives you your intuition, that allows you to, to kind of like both like identifying interesting problems, but also to like figure out new solutions and to be able to kind of like ground solutions that other people give you in some form of kind of like intuitive understanding that, that lets you really internalize it and digest it.

[00:09:55] Igor: And so

[00:09:56] Jacob Haimes: Right. I mean, it's just, you know, the real value of math is the friends we made along the way

[00:10:03] Igor: Yes, and by friends often th-this is trauma bonding, um, uh, with, uh, l-like having tried to prove a thing for so long and then fail and, or like, um, the other classic, like figure out that like a Russian dude or a Chinese dude or an Indian dude ha-ha-has done it like 80 years ago just because it wasn't published in English, like you, you hadn't, uh, found it yet. It's, uh, it's always nice. Um- But like, it's actually like, um, I think part of why it's difficult to, to like to care ab-a-a-about it is that, like, p- mathematicians fail a bit and is something that was brought up by Tao, who's, like, genius mathematician and very good c-communicator of math to people who are already nerds, I would say, um, has pointed out that, like, they fail to celebrate parts of math that are not proofs and results as much as they sh- it should be.

[00:11:15] Igor: And so, like, the-- Yeah, like the, like the friends are not celebrated as much. But, like, in the community, people know this is how it works, but, like, to the outside, it's not communicated. And so now OpenAI has produced a PDF that gives you the solution, they haven't produced, like, all of the problems that were, all of the dead ends, all of the other things that were tried. And even if they gave us that, if they released, like, the full transcript, nobody would do that, right? Like, like, like, uh, maybe mathematicians would out just out of, like, pure love, but, like, it's gonna be hard to justify to your career board that you wrote a paper basically just cataloging all of the dead ends in, in, in the OpenAI proof.

[00:12:10] Igor: Uh, like that's not what you get money for right now

[00:12:15] Jacob Haimes: Yeah. And, and so, so that and then I guess in addition to some of the other framings and, uh, concerns of, of mathematicians resulted in a bunch of Fields medalists, uh, within the, the days between, uh, the announcement of this, uh, Navier-Stokes, uh, c- uh, counterexample and, um, the, what, September 21st advisory group on mathematics and artificial intelligence that OpenAI has.

[00:12:46] Jacob Haimes: Now, um, there was an open letter, um, w- a severe misalignment of AI in mathematics, and Terence Tao was asked to, to, uh, sign it, I believe, and, and he did not, and he talks about that in one of his blog posts. But there were a bunch of

[00:13:03] Igor: Gower, I think. That wasn't

[00:13:05] Jacob Haimes: Oh, it wasn't...

[00:13:06] Igor: article was Gower

[00:13:07] Jacob Haimes: Oh, okay. Um, my bad. But, um, there were a bunch of people that, that did sign it, uh, and I think that

[00:13:19] Jacob Haimes: The response to this, um, happening, not OpenAI's response, I think OpenAI's response is, uh

[00:13:28] Jacob Haimes: What you would do if you were if you were a large organization that, that had this sort of fundamental PR, uh, nightmare happen, um, uh, like, seems, you know W- I, I don't really care about how, what their response is. The thing that I care more about is the, like, popular response to, um, this reaction that mathematicians have had.

[00:13:56] Jacob Haimes: Um, 'cause I, I think that that in itself is also interesting and, and maybe, um, indicative of patterns, uh, that, that may happen again. Uh, and, uh, yeah, j- I guess just talking about that I think is worth discussing

[00:14:17] Igor: like, um, Terrence signed the letter and Timothy Gowers didn't, um, which looks a bit unfortunate because Timothy Gowers was, was afterwards, like, uh, part of the group that was, uh, pulled into this advisory group by, uh, OpenAI. So I think it's important to kind of like, um, be a bit more specific, like who are you talking about when you mean like the p- the popular response?

[00:14:47] Jacob Haimes: So when I say the popular response, I am talking like this is primarily informed by, you know, monitoring online conversation basically, uh, i- is what I mean by that. And so that of course does bias towards, uh, boosters, uh, who are talking about this kind of, uh, material. So like

[00:15:06] Igor: Online conversation that you see as well,

[00:15:09] Jacob Haimes: Yeah, online... Well, yeah, online conversation that I see, but like specifically monitoring in the, in, in the like few booster communities that I have, you know, subs to so that I get the, uh, the information without ever having to get on a platform as horrible as X. Um, sorry, Twitter. Um, but the

[00:15:34] Jacob Haimes: trend, I would say, is also mirrored in an attitude that is just much less prominent in conversations I've had with, uh, like everyday people as well that ar- aren't on these, uh, like message boards. It's just they're, they're not as, uh, you know, strongly opinionated about, uh, their takes, but it does have this sort of, uh, I guess, uh, like, uh, framing, uh, to what they're saying.

[00:16:09] Jacob Haimes: And that is that, um Essentially, like, why should we care? You know, why do, uh, these mathematicians get to dictate, uh, and prevent progress? Why do, uh, like, we all of a sudden, uh, need to be making carve-outs for, um, math a- and, and what AI can or can't do within this domain? Why is that special, I guess? And, and because I think a lot of people have had negative experience with-- experiences with math as well, um, and it is also one of those domains where regardless of whether or not, uh, it is the case for a given individual, there is a perception of people who are, like, mathematicians being sort of ivory tower-y, right?

[00:17:24] Jacob Haimes: Like, sort of o- doing-- off doing their own thing, um, that isn't necessarily relevant to, um, th- the common folk, I guess. Like, i- in a very, uh, high-level crude way, I'm not saying that I agree with this by any means, but I think that, like, the, uh, perception of mathematicians at large, like, like, is that. And so y- you almost get this combination of a, a backlash against, uh, like, uh, academic or, or not-- like, elitism that is perceived to be related and tied to academia, um, that is sort of embedded in this, like, these many responses.

[00:18:15] Jacob Haimes: I mean, uh, on, like... Now, I know to take this with a grain of salt, but on, like, Reddit, for example, uh, it is relatively easy to go into one of the, um, subreddits that has boosters in it and look up, uh, this Navier-Stokes thing and the open letters as a response. And you'll see in the comments that people are basically saying, like, uh, "Oh, boo-hoo for math."

[00:18:43] Jacob Haimes: Like, "I, I don't care," you know? And I, I think that

[00:18:47] Jacob Haimes: There is a strong parallel between, um, like artists i-in this case, um, although it is-- there, there are s- meaningful differences as well. Um, but That also is missing the point that I think Terence Tao and a lot of the other mathematicians are trying to make, which is this, you know, the math was the friends we made along the way kind of framing of like it actually really is important

[00:19:22] Igor: I th- I think it's important to not, um, entangle these two things a bit. So like, I don't think Terence cares about people kind of like, um Like, there's no entitlement in these, like, Te-Terrence blog posts, uh, uh, uh, uh, to me. And, like,

[00:19:40] Jacob Haimes: Yeah, I agree

[00:19:42] Igor: math has failed about this stuff. And I also think it's important to not over-index on, like, AI booster or, like, extremely online people where, like, like, you know, like, the-- my take would be that the vast am- a majority of people is fine with, like, mathematicians having a job because they're not very expensive and, like, they are generally, like, unoffensive people. might have, like, a personal trauma with, uh, w-with, with math, so they don't, they don't-- they don't see the point. But it's not like it's like physicists with CERN that is like, you know, like, billion-dollar accelerators to smash stuff together, there's also, like, a whole effort in, like, explaining why that is, like, to some degree worth it and compared to, like, other expenditures, not, not that, not that big So that's like one nuancing thing that I would like to take, but kind of like even if kind of like there's like a large contingent of like, you know, like very online people who are like, "Why should we care?" And also maybe it's also offline people, I think like the vast amount of people would be like vaguely sympathetic the same way they were like vaguely sympathetic w- with, uh, uh, w- uh, with artists and like, uh, like writers and like junior developers and so on.

[00:21:08] Jacob Haimes: Yeah, I, I think that's roughly accurate as well

[00:21:12] Igor: And then, uh, the, the thing with like, like Terence has this very nice mas- Mastodon thread where he coined this phrase, "Non-renewably mining the open problems of, uh, mathematics." Which we can dig into, but like they're mainly concerned kind of like with their craft then I think secondarily like the career idea of, uh, that is like related to that craft. But I think like if, if it was like A clear indication that this is just like the way things are gonna be done now In particular, Terence has been extremely open to kind of like playing with LLMs, uh, using created tools. Like, like, like mathematicians are not a monolith. There's not like the consensus where I would say like it's not a community that is Luddites. They will like happily embrace like whatever tools actually work

[00:22:19] Jacob Haimes: Yeah

[00:22:22] Igor: And it's more about like the Like can this and public good craft and tradition keep existing in the short term if the frontier labs are now just like strip mining the open problems, uh, hoovering up maybe all of the attention, all the funding, and then kind of like moving on afterwards after dumping a, a bunch of trash into, into, into this thing.

[00:22:58] Igor: And I think like that conversation, yeah, like, like it has parallels to the like Artist, Writer, other jobs discussion But there

[00:23:11] Jacob Haimes: I mean, it's,

[00:23:12] Igor: of ... Ja, ach du

[00:23:14] Jacob Haimes: uh, it's sort of just like, like the pulling the lider- the bleh, pulling the ladder up behind them, uh, kind of thing, where it's, uh, making

[00:23:24] Igor: OpenAI now, not, not, not the mathematicians

[00:23:26] Jacob Haimes: not the-- Sorry. It, it is, uh, it's sort of like the, the frontier labs pulling the ladder up behind them, uh, with regards to mathematics. It's, you know, saying, okay, the work, the, the value of, um, all these mathematicians publishing their work, um, is what allows us to get to this, uh, sort of state.

[00:23:53] Jacob Haimes: Uh, and then now that we're here, we'll just, you know, uh, iterate through things without necessarily being cognizant about, um, how, how we can sustain math moving forward. Um, and, and I think There, there are two things to me that stuck out about this case, and the first one was just that, um

[00:24:27] Jacob Haimes: The understanding of, and maybe these are both just like different flavors of the same thing, but the understanding of what a mathematician does I think is for most people not necessarily, uh, very well developed. I mean, like myself included. Um, and so it is hard to understand from that perspective of like

[00:24:58] Jacob Haimes: what's actually happening and, and, and why this, uh, process of, of like just publishing or, or yeah, non-renewably mining open problems, um, would be destructive to that. I think that's, that's part of it. And then the other part of it is that I think the The communication between the initial math and the outcomes and like The cool things and breakthroughs that have happened as a result of math don't have that through line as clearly laid out, um, and, uh, sort of explained. And that's not to say that That is like, "Oh, you know, they should have done-- Those mathematicians should have done better." Uh, it is

[00:26:06] Igor: I, I think it's fair to even say a little bit I was pushing back against this a little bit. I think there's a kind of truth to it, right? And b- b- like, like there is always this thing of like If you are given the privilege of being like an intellectual by a society, you should at least give back so that they understand what you're doing instead of like hoping that like the and rich people favor will last, uh, will last you forever, right? Like, I think like there's a, a little b- f- bit of like that being a thing.

[00:26:40] Igor: And they, if, I mean, they, they've done that as well. Like, they ... Some people get this, some people don't, basically

[00:26:46] Jacob Haimes: Yes. And I, I think that at least in, in my experience, the kinds of people who are interested in doing the research typically aren't as interested in making that research highly accessible, um, and that it ma- like, matches this pattern here. Uh, and so I think that that disconnect, the fact that people incl- like including myself, don't fully understand the role that some of the more theoretical math work that is being done sort of at the cutting edge of math, uh, has on, like, developments and, uh, practical utility that I experience is not ideal.

[00:27:46] Jacob Haimes: I, I, I think it would be good if that through line were more clear, and then I think it would make, um

[00:27:54] Jacob Haimes: make the, the case that it is, uh, being made by individuals like Terence Tao a little bit, um More accessible for, for people. At least that's how I think about it

[00:28:13] Igor: I, I do think it's also like... I, I basically agree, and it's part of why I pushed for us doing this episode, that like we can do a little bit of that, but like, um I gave a couple of workshops where I tried to basically, like, teach math to non-math people, where I tried to, like, um, take away the trauma that they had, um, a little bit the beginning of, of my PhD. And it's, like, one of the most meaningful things I've ever done. Um, but it's difficult and, like, uh You run into the case where people don't like the idea of Not being good already. Like, it's, i- it's, it's difficult to get, uh, to, uh, uh, uh, to get started to learn new ways of how to think, basically. And certainly in math, it's also like, it's just much, much more ac- it's much more acceptable to say, "I'm not a math guy," than to say, "I'm not a writing guy," or like, "I'm not a, I'm not a music guy." Where like music also people kind of like accept it, but like there people I think are, are much more of it, okay, like you could learn the instrument if you wanted to. You might not be like at it

[00:29:34] Jacob Haimes: I mean, I don't know. I feel like I know a lot of people within the research and engineering space who don't say, "I'm not a writing guy or gal," uh, but that's, like, what they mean, you know? I'm making fun of the writing of researchers and engineers

[00:29:57] Igor: Yeah, I mean, like, like, like, um, there's investment and there's difficulty and, and, and it's not a priority to, uh, uh, uh, to, to learn, right? And kind of like if you're already busy with life, adding that to like round off your development is always gonna, gonna be a challenge. And when teachers traumatizing you away from doing that closes off a whole, whole world for you.

[00:30:24] Igor: The same way that, you know, like learning an, an instrument, learning to, uh, to dance, learning to draw, like all of these like ways of like human expression that we have. not everybody needs to do everything, right? Like, like it's totally fine to, to, to just not do some of them But In some of them, people are kind of traumatized into having been forced to do it in a way that, uh, they didn't want to and they didn't want, uh, they didn't connect with, so math. And then they basically kind of like genuinely develop kind of like tr- trauma reactions where they just kind of like eyes glaze over and they just disengage with it.

[00:31:09] Igor: They don't even try. And then in others like, you know, like if I gave you like a guitar and I showed you like a couple of like, um, chords, you might try and you will kind of feel like I am, I suck at this, but I, I'm getting some, uh, notes out and it's maybe like not, not, not so bad and then you just like put it away and you don't do it anymore.

[00:31:30] Igor: But you, you will not kind of like freeze up and, uh, and, and just not do anything. And, and it takes a while to g- to like get through it and like if then this freezing up and glazing over is like how people engage with the topic, explaining them to go back to the orig- original entry point they should care about it becomes difficult because there's no access point for it.

[00:32:04] Igor: So, so usually the communication dumbs it down a lot or d- does like the pretty pictures. Like Quanta Magazine is very good at this. It, it gives you like all of the pretty pictures of like crystallography and like the knot theory and stuff like that. And then there's like some math YouTubers who manage to do that, but like let's be honest, like the people who watch those videos are already people who are like a bit math affine and people who are like in the learning phase still And the rest might look at the pretty pictures but not really, like, engage with it, and so it doesn't really answer the question of why should they care. And the reason why they should care is because, like, mathematicians is a bit like philosophers, uh, in that, like, they expand, like, the realm of what can be thought by humans and understood. That if you look into the world now you have lots of-- Like, if you went through, like, a Western high school education, you have lots of words and lots of theories, lots of, like, models, lots of notation that allows you to, like, actually, like, grapple with it consciously or subconsciously.

[00:33:13] Jacob Haimes: I mean, a- also if you went to other high schools, probably

[00:33:17] Igor: I just have a reference point from a Western, a Western high school

[00:33:20] Jacob Haimes: Yeah, I just, I, there, there's a reading of that where you're disparaging non-Western high schools, and I just wanted to

[00:33:27] Igor: Yes, uh, Like, uh, if you go around the globe far enough, all high schools are Western high schools.

[00:33:36] Jacob Haimes: true

[00:33:37] Igor: This, this, this is what I meant.

[00:33:38] Igor: But like the, uh, the idea is like you, you're given concepts. These concepts have been developed and they're like concepts that, that are being taught in schools they're useful. Like they have proven useful for hundreds of years. And so even if people like hate the school math that they have to do, turns out it's really useful and it helps you a lot in becoming like a more empowered human being. And somebody needs to make that and ground it in human experience and, and like human language for long enough so you can teach it to people. And that's like the pipeline where like to some degree like philosophers pluck fuzzy shapes out of the ether of human experience and basically argue that like this is a thought that should be thought and that it's often completely incomprehensible to be honest. Like I love philosophy, but, uh, uh, uh, but like, uh And like good philosophers are like razor sharp and can also like do the translation into like human language, but like It's only like the best who can, who can, who can do that. And then like mathematicians are usually, uh, like when like In the opera-opera-operationa-äh, operationalization Every single time this word. Um, but like they, they, they, they take what's a very fuzzy concept and they say, "Hmm, yeah, that, that's interesting idea. How about we try to it like a concrete definition, like something that I can just like down very compactly on what it is instead of having to, to read like 50 pages, uh, of a, of like introduction to like get the vibe of it." And then once you have that, you put it into context of all of the other ideas that have ever been formalized like that, and you see what you can do with it. And sometimes will like close the loop and you will actually like feed back ideas to the philosophers because you have figured out some weird combination that actually makes sense and then the, then the, the philosophers grapple with that. And like

[00:35:59] Jacob Haimes: This is already... But like this is too abstract already, right? Like

[00:36:03] Igor: This explanation, you mean?

[00:36:05] Jacob Haimes: Yeah

[00:36:07] Igor: Yeah, s- that's the thing. Li- like Let me try to give a concrete example Like formal logic grew out of like a branch of philosophy that tried to like really like formalize certain things. And That just became like what is now amongst other things like lean. There's like-- There the, the interplay is like very clear that like the mathematicians find some, uh thing they can't answer in math. And then like the philosophers that are like the logicians and like the more formal philosophers, they actually try to conceptualize what should be the notion we, and we formalize actually.

[00:36:44] Igor: What should be the, the axioms that we assume? What is like intuitive for, for people? And they argue for it. That's like a concrete interplay. Another example from my personal research is like Various philosophers have talked about like and like interplay between like the like an actor and the thing they act on, that there's like, there, let's say, a feedback of that usually, usually in the context of like sh- social studies. And there's now this like Moritz Hardt is like a, a professor in Germany. has a whole program ar- around performative classifiers, so like machine learning classifiers and models where like the act of

[00:37:27] Jacob Haimes: They're not, they're not doing it for them, they're doing it for you

[00:37:32] Igor: What's

[00:37:33] Jacob Haimes: That's what, you know, performative

[00:37:35] Igor: Yeah, l-l-like, like, like the p-p-performativity here is kind of like that not that the model gets really good at predicting the world, it's like, like, like the model changes the world so that it gets really good. And it was first identified, um, in the context of, like, the Black-Scholes equations by Ekaterina Sw- uh, Svetlova, my knowledge, or it might have been pointed at before. But this is, like, an example of, again, like, these, like, ideas, like, popped up in, like, uh, philosophy, and then they were broadened i-in-in-into, like, something more mathematical, and then are feeding back already into, like, critiques of a- of, uh, of algorithms. And, like, this is, like, human intellectualism.

[00:38:19] Igor: This is, like, how we make sense of things and how we understand things and how we just, like, are able to reason about things slowly. Because nerds get obsessed with this, and then they, like, hash it out, and then other people use those words and, like, bring it into, like, the wider discourse and change it as well, right?

[00:38:40] Igor: Like, the words, like, way the public engages with will not be how, like, the original nerds engages with it, but, like, it will be influenced by that. this is, like, the- the big value that mathematicians have like for, for humans and then as a consequence of this, you get more people who are able to d- to do like engineering and computer science and stuff like that who, who have already like a framework of operationalizing things and formalizing things that maps onto like human understanding and so they can problems with it that they couldn't solve if they had to just like build intuition And if you bring in AI now I think the calm take is basically this changes But like the, the, uh, like, uh, there is a risk that we lose a generation and we lose like, um, a big part of this like public good. Um, there was a article that was posted yesterday called Claude Shaped Science, where like a physics professor explained how he uses Claude write papers now, and he has written like 28 papers in different places, and it's all around this like loop that he built. And it's actually like an insightful thing in, in the sense that like he points out that like if this is like-- I'm sure ho-hold it with my hand here. Um, if this is like what scientists want and there's an overlap with what Claude is good at, then like in that overlap you can make like rapid progress now. And you shouldn't try to put like Claude at play for things that it's not good at if you're like pragmatic about it. In the same way, like if you're doing math, I think not only OpenAI doing these proofs. There's like also independent researchers using generative to do their work. That's why they had these chat logs in there.

[00:40:41] Igor: And if the kind of like main part of the work remains still by like done by humans and, and driven in this like a, like a tool version of using LLMs to do the work, the process just continues and accelerates. Like, like this pipeline that I talked about is, uh, remains intact. The humans just can fly through that conversation better and maybe like become more intelligible. I think that's sort of how you said, right? Like, uh, you, you become more intelligible to a, to a wider population because they have more time focused on communication. That's like the be- the best case outcome But the, the, the thing that this, um, advisor group now proposed and also flagged, and that Terence was also pointing out and that is part of like the fear in the, in the math community, is that if you go in and you just like dump 10,000 lines of lean code, o-onto the community and you have now solved the problem, the only thing you do is you kind of like destroy the existing mechanisms of how people both gain experience, how they can a career and kind of like, um, learn their craft un-until they become productive. Um, and you don't really replace it with anything except like an expensive model that At best can do the work but is not accessible to everyone, but at worst cannot do a critical part of what the job is, which is like all of this stuff in human experience and being the interface between these highly abstract ideas and if not like the general public, then maybe like people who are like one step less nerdy than me, where like I can talk to Jacob and Jacob can talk to out- to normal people. Like there's a, there's a, there's, there's like a-

[00:42:50] Jacob Haimes: Yeah, that, I think that's a relatively good representation of this podcast for sure

[00:42:55] Igor: So, so that's the, um, long rant to like try to explain like should people care and like my best attempt at the through line and like what the concern is and also why people should care about it in my best attempt at ex- explaining it

[00:43:14] Jacob Haimes: So I guess just like trying to take this to the

[00:43:19] Jacob Haimes: I'm trying to extrapolate further along this, you know, direction that you have sort of outlined here. If we accept the assumption that, Essentially just like, yeah, dumping all, what, 100 of the different, uh, mathematical, uh, proofs that they say that they are sitting on, uh, like into, uh, the public space, um, were to happen, you know, what would the result be? And I, I think understanding What the, the short-term gain and long-term gain w- uh, or, or, yeah.

[00:44:07] Jacob Haimes: The, the, the short-term, uh, net effect and the long-term net effect, uh, is like relevant here. And I think what it, it seems to me that you are arguing is that the short-term net effect would be there are more problems that have solutions, uh, and maybe It speeds up the solutions being... I mean, it does speed up the solutions being out there, but it may not speed up the application of said solutions in a practical way because the people who can actually do that sort of, uh, transference are-- were not the people who wrote, you know, the proofs, who, who understood the, the fundamental, uh, y- like underlying aspects of said proof.

[00:45:03] Jacob Haimes: Uh, and so it-- that part may not speed up in a meaningful way or, uh, that much. Uh, and then at the same time, the long-term impact is that you reduce the, uh, or, or, yeah, increase the likelihood that you're creating a sort of like a, a next generation of mathematicians who is less capable than the, the current counterparts because they do not have the same sort of like command of, uh, the math space that they operate in because they didn't do the original exploration, uh, themselves.

[00:45:59] Jacob Haimes: They just followed along with a, um, a proof and then a rebuttal to that would be, okay, well, but, you know, just because the proof already exists doesn't mean you can't engage with it. Um, and then the rebuttal to that would be, but no one's gonna pay you to do it if it already exists, so you are effectively, uh, preventing that path from being feasible.

[00:46:31] Jacob Haimes: Um, is that

[00:46:34] Igor: Yeah, and you also close off like the, like the on-ramp. But like people who already care will work through the-- And who-- Like people who already care and who have the privilege of doing so will work th-through the book. Kind of like, um, I'm doing that because I'm a fucking nerd

[00:47:02] Jacob Haimes: Yeah

[00:47:03] Igor: job. S-s-s-so, so like I try to learn proof techniques even if I can't directly use them in, uh, in, uh, in my day job

[00:47:18] Jacob Haimes: Yeah, that's, that's like gotta be one of the nerdiest things you could say

[00:47:24] Igor: But like A, I'm not able to do much research with that shit because I can do it in my evenings and it's like a passion thing. not a professional at using them. B, like Not many people will do this. And if you're, like, smarter than me, 'cause, like, I'm not good at this, right? Like, like I'm, I'm, I, I'm, I'm just, like, excited. But if you're a smarter person than me and you haven't yet kind of like gotten the taste for it, and then like even now there's like low-hanging fruit, like some people just like write a proof because they got hyper-focused on it over a weekend and then they, like, the field was wide enough open and they're just like smart and they can do that. if you have like the equivalent of like a, um, dragnet like that, that harvests every open problem that is in the vicinity and publishes like all of the solutions or claims it at least, or even if they don't do that but they just like devalue the idea of a proof because like AI can do it, who cares? You might not do it. Then the counter to that you can say is like these people, they will tinker with something else. But I do think like the, like you can say like something would be lost and we don't know if it might be useful to have it as well. Like maybe we should like preserve it a bit. Um, yeah, there's like a long way of like agreeing with you

[00:49:13] Jacob Haimes: Okay. So yeah, I guess what, like what we've learned today is that

[00:49:22] Igor: Jacob is much cooler than me

[00:49:24] Jacob Haimes: I mean, uh, that's not something we've learned today, Igor. Um, what we've learned today is that math is the friends that we made along the way, you know?

[00:49:34] Igor: Math is very fun and you should all, um, read Terence Tao's blog and, uh, at least get into graph theory because there you can draw like little circles and connect them with lines and then like, uh, ca- ca- can do a lot of math through that. Um, I think that, like, I want to end on something else for all. Like, I want to give like a practical takeaway of like, okay One, I hope, like, it becomes a bit for people of, like, why the mathematicians are in a hubbub about AI.

[00:50:06] Igor: That, like, it's cool tooling, but it's kind of, like, threatening one of the core things that makes, like, the math attractive and, like, valuable in some way The tool OpenAI is usually being extremely shady Three, why should you care? And like with four, like four and five, I would like to discuss like, what can we do And what should people do? And then maybe like before that, like why did they do it now Yeah, like, like why, why is OpenAI doing it? And then for that, I just want to, like, very briefly talk about, like, what happened since then, which was that OpenAI postponed their IPO they're, they're raising $30 billion like, new funding after, like, a flurry of model releases And also like new noises around like we need to pace the frontier and then like I think a week later they release like, uh, an, a, a new model and then like another model, uh, like a week after that. Um, um, or like a few days e-even And Right after that They released a blog post about the dangers of the open weights model and how, the weight model can be easily used for cyber criminality Notwithstanding the fact that like OpenAI was hacking like people left and right and Anthropic, uh, to a degree were doing the same thing. Um, and then Reuters got their hands on the ideal prospectus of, um, uh, Anthropic and, uh, found out just how much money they were, uh, burning. Um, and I think like quick takeaway like why are we doing it now is like what they were gearing up to was, you know, like drumming up the IPO fever. Anthropic released this bio thing recently. They were trying to do that. OpenAI wanted to do a, a, their thing with like their new Astra, uh, and, uh, GPT-6 and whatever models and they wanted people to be like blown away by how good their models are And that I think worked kinda w- through this rapid pace combination, but mainly they've been f- uh, blown away by how fast and cheap the models are. But the increased performance is like vibey where like every release people kind of say, "Oh, it's not, it's not much different," but like they do kind of like add up, so I'm a bit careful with that now But the, at least in my level, like the vibes are that people are happy switching to open weights models if they had to, for most of their coding needs, uh, at least. Um, and At least part of the answer of, like, why are they the, big math blitz and all these things is, like, to show, like, how good the models are to get the next funding cycle, uh, going as usual would be, like, my take. And people can maybe, like, comment if they have different reads. And for what you can do, Unless you're like Jacob and good at everything already, then like I genuinely think getting some form of like, connection with more abstract mathy things is generally worth it. Like, um, we should link Logi Comics, is, uh A comic about, äh theoretical computer science and formal mathematics, but it's actually fun. Like, I, I genuinely re- recommend it

[00:54:10] Jacob Haimes: yeah

[00:54:10] Jacob Haimes: and that's all the muck that we have the time for this week. Uh, if you enjoyed our discussions on math and I guess, like Maybe, maybe I'm, I'm just, you know, biased, but I, I feel like I, I haven't heard people talking about this particular problem in this way. Um, so I don't know. If you have, I guess let us know who, uh, and if you haven't, maybe, uh, you know, share this or something if you think it was, uh, worthwhile.

[00:54:46] Igor: If you d- if you disagree heavily, then do tell us in excruciating detail and also, like, find my website and send me an email. Like, I want to hear your nerdy, uh, disagreements

[00:55:00] Jacob Haimes: Uh, and with that, we'll see you next time