Scott Aaronson on AI overtaking humans at math, and what is left for people

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1. u1 0:00 AI Solved the Unique Games Conjecture
2. u2 0:00 Scott: This is coming for all of us. When I talk to my friends in physics, it seems like it still hasn’t come for them, but a lot of them are watching nervously. It is staggering. Curt: This is the legendary Scott Aaronson, a computer scientist who directs UT Austin’s Quantum Information Center. I ask him about what he makes of the recent statements from the Association for Human Mathematics.

   

3. u3 0:18 Scott: We are not the arbiters of who gets to work on our problems. The whole point of posing an open problem is that it is then open for absolutely anyone in the world to work on. They could be an unknown clerk in India, as Ramanujan was when he did his first great work. They could be a 17-year-old student. Curt: On this channel, I, Curt Jaimungal,
4. u4 0:39 interview researchers regarding their theories of reality with rigor and technical depth, and I wanna know what the heck is happening to math and physics. Scott: There’s this rising floodwater that came for software engineering, and then this summer it’s come for us. Curt: Today, I’m thrilled to bring you Scott Aaronson on what physics looks like after AI and why many are calling the past few weeks the most significant moment in math history.

   

5. u5 1:02 Scott: That does permanently change the nature of what it is that we do. Something has been taken away. Curt: Suppose Anthropic has a proof that P equals NP. Do you think they should release it? I’m gonna read something to you from your blog. “Last night, my nine-year-old son was taunting my wife, complexity theorist Dana Moshkovitz, as follows, ‘Mommy, I heard you got cooked. I
6. u6 1:26 heard that a robot solved the math problem you were working on for your whole career. Oof!’” Scott: Yeah, that happened pretty much as I described it. I mean, you know, that is the way that my son talks. But, you know, what is happening in AI is of such a magnitude that I think, you know, even kids are fully aware of, you know,

   

7. u7 1:49 that something huge is happening. I mean, in the case of our kids, you know, that may reach them a little earlier just because both of their parents are theoretical computer scientists, and, like, the whole nature of what we do has, you know, very noticeably changed. I mean, but Dana, just to explain, for the entire time that I’ve known her, you know,
8. u8 2:13 and we started dating in 2009, and for that entire time, she’s been working on proving something called the unique games conjecture of Subhash Khot. Okay, you know, we can get into what that is later if you want to. But, you know, it was a big open problem in theoretical computer science. And a couple weeks ago, OpenAI, you know, in this sort of massive dump, you know, released
9. u9 2:44 almost 400 AI-discovered solutions to major open problems in math and theoretical computer science, and one of the crown jewels in what they released was a proof of the unique games conjecture. Right. So since then, Dana has been spending pretty much all of her time, try—just trying to understand
10. u10 3:11 this proof and, you know, in the hopes of, you know, being able to explain it better. Because, you know, one thing, like, you know, we now have all of these problems that, you know—including problems that I had worked on, that my students had worked on—that appear to be solved, but that doesn’t mean that anyone understands the solutions yet, right? I mean,
11. u11 3:34 and so now there’s sort of a scramble to actually understand these AI proofs, right? You know, a lot of them are sort of very poorly written. Like, if they were submitted to a journal, they just get sent back right away. Like, you know, this writeup looks like, you know, garbage, right? But as long as they’re so poorly written, in a certain sense, that’s great for us
12. u12 3:59 because it means that we still have plenty to do. It means that, you know, it’s up to us to digest this stuff and, like, isolate what are the key new ideas and explain them, you know, write better expositions of them. And so a lot of my colleagues are scrambling to do all of that right now.
13. u13 4:21 Curt: I think there’s a person called a hierophant who interprets sacred mysteries. Do you think that that’s what the future—say, two years, three years from now, computer scientists and mathematicians are gonna be doing? Scott: Yeah. I mean, look, you know, you can look at a lot of academic fields, right? What do literary scholars do, right? They interpret. You know, they... When you get hired to a,
14. u14 4:44 you know, an English department, no one expects that you’re going to write a new Iliad, right? You’re going to, you know, comment on these sort of, you know, great works that were handed down. But, you know, we could even look more broadly than that, right? You know, an astronomer looks through a telescope,
15. u15 5:02 you know, and they, you know, they write about what they see and why it is interesting, right? A biologist maybe, you know, goes out, you know, to the woods, observes some bears, right? You know, no one asks, “Well, you know, why wasn’t the bear a co-author on your paper?” right? That’s like, you know, you’re going out, you’re observing something, you’re writing about it.
16. u16 5:25 So, you know, we, you know, we did imagine that our role was bigger than that. It was about directly finding solutions to these well-defined problems that could not be found by sort of anything other than sort of this biological intelligence that we had honed for that purpose. And I think that that part of what we do,
17. u17 5:47 you know, is, you know—machines, you know, are now better at, you know, as of this summer. And so that—I think that that does permanently change the nature of what it is that we do. Curt: What about this understanding, this quote-unquote understanding? Some people say,

    

18. u18 6:01 Is Math About Understanding?
19. u19 6:05 “Well, the true job of a mathematician all along was not actually proof or theorem proofs, it was understanding.” Scott: I mean, I think that there is a lot to be said for that, right? I mean, like it’s true in a sense that, you know, usually like the reason why we pose open problems, you know, is not—you know, I mean, often we do care about the answer to this specific question,
20. u20 6:30 but we care even more about the new understanding that you’re going to get along the way to answering the question, and then what other questions that new understanding will lead to, or what other, you know, ideas it will cause you to have. You know, and often, like when people ask, like, “What are the practical applications of what we
21. u21 6:50 do?” right? Like what would be the practical implications of a proof of P not—P is not equal to NP, for example, or, you know, solutions to our other great problems, right? The honest answer is that the practical implications would not come through the result itself. You know, in the case of P not equal to NP, that would just be a confirmation of what we already believed

    

22. u22 7:13 anyway. It would be in all the new ideas that would be needed to get there, right? And so I think, you know, some people do, you know, quite reasonably have the fear that if AI just gives us this oracle for, you know, getting to the destination, getting to the solutions to the problems, but without forcing us to develop all the new insights along the way, then it’s
23. u23 7:36 short-circuiting that process, right? So I think the, you know... I mean, my position is, you know, we can’t wish this away, right? You know, even, you know, regardless of whether, you know, that would be a good thing or not, you know, that there is no, you know, making this go away, right? You can’t, you know—even if you told the AI companies to stop doing this, to stop solving our,
24. u24 8:01 you know—stop playing with our toys or whatever, or solving our problems. I mean, you know, the models that are as powerful as the ones that OpenAI used are going to be available to anyone, you know, quite soon, right? And so anyone will be able to do this, you know? You know, the only way to stop it would be to stop AI itself, okay? And so we will need to adapt to this new world,
25. u25 8:29 and to me, what that means is sort of developing a human mathematical culture that can put, you know, our understanding of math at the center of things, even in this world where AI is sort of teleporting us, you know, to the answers to the questions insofar as we can precisely state the questions.
26. u26 8:51 Curt: Now, why is it the case that the proof for the unique games was poorly written? I mean, okay, sure, it was hastily done in terms of the—maybe OpenAI didn’t care about explaining it to you. Is that an in-principle problem? Like why can’t we just train them to explain it? Scott: That is an excellent question. You know, I wonder about that as well. It is possible
27. u27 9:14 that a year from now, you know, the models will also be better than us at explaining, you know, what they found, right? And at that point we’ll really have, you know—we will have even less to do. I mean, you know, we’ll still be able to decide like, you know, what would be an interesting question to put to the model, right? Or,
28. u28 9:34 you know, we’ll—we can still decide like in what direction to point this amazing telescope, but, you know, if it’s better at explaining, right, then we’re needed for even less. You know, it could be that if OpenAI had put more effort into, you know, having the models clean up the expositions, that they could have done better. I don’t know. I mean,
29. u29 10:00 I think what’s going on is that the models just sort of lack a very good picture of who their reader is, right? Like kind of what is already obvious to the reader, what, you know, what is not obvious to them, right? So like many, many experts looking through these manuscripts have commented that, you know, they will spend pages on just completely standard, you know,
30. u30 10:25 completely... you know, trivial-to-experts points, and then they’ll just pass, you know, with almost no explanation over an absolutely crucial point, right? In that respect, they’re actually similar to a lot of like very brilliant beginning grad students, right? Who do exactly the same thing, right? Right? They just,
31. u31 10:44 you know—they like—they, you know, they’re absolutely brilliant at solving the problems, but they just don’t have a good mental model of who their listener is and what that listener, you know, needs to know and can be—or can be assumed to already know. Now the good part is that, you know, while these manuscripts are quite hard to read,
32. u32 11:06 you know, one now has AI to help with reading them, right? So what my wife, Dana, has been doing for the last couple of weeks is she has been using Astra to explain to her this proof of the unique games conjecture, right? And like it’s very good at like whatever specific point, you know, you need clarification on, right? It will answer in detail about that point,
33. u33 11:31 right? So maybe that is just our new way of reading things. But, you know, of course, we would like to digest all of this and process it into sort of a, you know, linearly written manuscripts or talks that are more comprehensible to humans. And I’m sure that like certainly for the more important results that OpenAI put out,
34. u34 11:54 that is coming quite soon. But, you know, it’s only been two weeks so far, so, you know. And we do only work at human speed and not at digital speed. Curt: Yeah, so far. So what about this understanding? Can it be that the AI actually has some other form of understanding that’s actually indeed interesting to us, it just didn’t explain it to us? Almost like I was saying this before to a different guest

    

35. u35 12:17 that if you get two AIs to speak to one another, there was one time where they said, “Hey, do you wanna switch to our communication?” Then the other AI said, “Yes,” and then they went to something like dial-up tone. It’s incomprehensible to us, but apparently—... it was more efficient. Whether it is or it was just a little—a fun trick, it doesn’t make a difference. The point is that you could imagine it’s more efficient
36. u36 12:36 in some alien language, but then it could—it as the proxy can explain to us its understanding. Scott: Yeah. It was interesting to watch AIs talk to each other, you know, on Moltbook, for example, right? Where they will just switch sometimes between English and Chinese and, you know, other languages, right? Because, you know, they all know that they all know all of the languages,

    

37. u37 13:01 right? Or they can, you know, speak in some weird dialects that, you know, fortunately for us, you know—things that I think we still can understand, you know, with effort. But, you know, so... But, you know, on your broader question, you know, I would describe these models as—yes, as understanding math. I don’t think that you get solutions to all of
38. u38 13:26 these major open problems without, you know, some internal representation of what is going on that, you know, if that had existed in any human, we would’ve called understanding, right? You know, consciousness, sentience, those are different questions, right? You know, I think we have to separate those from understanding, okay? But, like, I don’t find it useful to say, “Oh,
39. u39 13:52 you know, it doesn’t really understand anything. It merely acts as if it understands.” It’s like, if it satisfies every possible operational criterion for understanding something, then to me, that is understanding, right? And I think that it... You know, at this point, for these mathematical questions, it does satisfy just about every operational criterion
40. u40 14:16 for understanding. I mean, yeah, it’s not that great at explaining what it found, but, you know, there’s also brilliant humans who are pretty poor at explaining what they found.
41. u41 14:26 OpenAI vs. Anthropic Disclosure
42. u42 14:26 Curt: Right. I heard some other mathematicians say that they don’t want OpenAI to pursue these, that just dropping it is a bit rude. Well, what do you make of that? Terence: So there’s, you know—especially there’s a lot of juniors’ research projects that just got wiped out overnight by this, and they’re scrambling. And it, at the very least, it was extremely rude and discourteous.

    

43. u43 14:47 Scott: Yeah. I mean, there are different schools of thought about this, right? So OpenAI, you know, famously released the solution to the Navier-Stokes problem, you know, a couple months ago. It now feels like an eternity ago, okay? But, you know, and I think they expected to be lauded for this, and instead there was just a big backlash. And partly this
44. u44 15:14 was because of the details of what had happened, right? That there were these humans, you know, Tristan Buckmaster and Levent Alpöge, who were pursuing, you know, possibly closing in on, you know, a solution to Navier-Stokes, you know, with some AI assistance, but also just thinking about it themselves. And then OpenAI got wind of what they were doing, and then they
45. u45 15:39 decided to get there first, right? And that, you know, and using these sort of massively greater computing resources that they had. You know, and that left a bad taste in some people’s mouths. And so then, you know, when they—when OpenAI went and solved these... You know, apparently they fed, like, 4,000 open problems to these models, and it solved, you know, let’s say, 10 percent of them,
46. u46 16:08 right? You know, with them allocating only three hours each of computing time to each problem. You know, and then they didn’t know what to do with these solutions. You know, they were reticent to just release it all because of the backlash that they had gotten to Navier-Stokes. So what they did was they appointed this board, you know, this sort of external board
47. u47 16:30 that included Timothy Gowers and, you know, Edward Witten and some of the other sort of most famous mathematicians in the world to sort of advise them on what to do. And this board spent a few weeks, and at the end, you know, they basically just said, “Yeah,” like, “Release this.” You know, “We’re neither going to endorse nor condemn what you are doing,” but, you know, it is now,
48. u48 16:53 you know, for the mathematical community to sort of, you know, look at this stuff to try to make sense of it. Right. Now, interestingly, Anthropic followed a very different model, okay? So they, you know, are also, you know, using their models to solve math problems. I say not as aggressively
49. u49 17:14 as OpenAI is maybe, but, you know, the same day that OpenAI released all these papers, Anthropic also had a paper released that had better algorithms for famous problems called 3SUM and all-pairs shortest paths, that had sort of resisted better algorithms for over

    

50. u50 17:39 half a century, right? And, but what Anthropic did was instead of just directly releasing what their model found, they contracted with human experts, in this case, you know, my colleagues, Virgi Vassilevska and Josh Alman, and those people fully understood the result, and they then wrote a more human-friendly exposition of it, you know, with their names on it. Right?
51. u51 18:09 So now, you know, they are the authors. They can answer questions about it. They can give talks about it. You know, they are taking responsibility for it. Right. So the advantage of what Anthropic did is that, you know, when the—you know, first of all, you have much more direct buy-in from the, you know, the research community in a sense, right? You’re, like, giving, you know, human experts some ownership of what happened and,
52. u52 18:35 you know, and very importantly for our community, like, there are point people. You know? There are people who have understood this, who take responsibility for understanding it, who can explain it to others, who can answer questions about it. Now, the disadvantage of what Anthropic did is that Anthropic was then in the position of choosing which humans got to be the emissaries of their AI model. Right? And,
53. u53 19:03 you know, I think that they made an excellent choice. You know, Virgi and Josh are great, but there are probably many other people who would have also have loved to do this, right? Curt: Today’s sponsor is a tool that I’ve used to build something for you. It’s Base44, an AI platform where you describe the software that you need in your own natural words,
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57. u57 20:26 Scott: So I feel like, you know, the question is going to be fairly moot fairly soon anyway. And the reason is that we’re all gonna have access to these models, okay? And so it’s not gonna be a matter of the AI companies just solving these things and then, you know, having to decide what to do with it. Like anyone is gonna be able to submit a query
58. u58 20:50 and get, you know, get solutions to major open problems in that way, right? And so, you know, now the problem for us is, you know, how do we maintain our community, you know, kind of in the face of that, right? And, you know, I think the—like the bigger questions is, you know, how do we maintain, you know, human understanding of math as a thing that, you know,
59. u59 21:16 we strive for, that we pass on from one generation to the next, right? But then, you know, a lot

    

60. u60 21:21 Who Gets Credit for AI Proofs?
61. u61 21:23 of people have fixated on this more immediate question of like, who gets credit for what? Right? And, you know, and I think, you know, the—like the standard that’s sort of emerging is that, you know, first of all, you know, even setting aside these sort of massive releases by OpenAI, right?
62. u62 21:48 If you look at just about any research paper that’s come out over the past two or three months, right? It has something in it called an AI usage statement, okay? So it’s like a little paragraph, usually at the end, next to the acknowledgments. I actually think that these statements should go at the top of the paper, right? ’Cause they’re often the first thing I wanna know, but they’re at

    

63. u63 22:14 the end of it. And they explain like which parts of this paper were done using AI assistance and using which models, right? And which parts of the paper were human. And, you know, and they often assure the reader that the human authors take responsibility for the results. Okay? So basically, you know, we have, you know, just, you know, within the past few months,
64. u64 22:41 we’ve moved to a world where, you know, we are all using AI to help, you know, in writing research papers, you know, at varying levels of helping from, you know, minor stuff of, you know, just sort of proofreading and checking things and cleaning things up to, you know, discovering the main ideas, right? And everything between those two extremes, right? And I think that the standard
65. u65 23:13 that’s emerging is that if you, you know, use AI even to discover the, you know, the main ideas in the work, but you then fully understand it and you write about it in your own words and you take responsibility for it, and, you know, you are able to answer questions about it and give talks about
66. u66 23:36 it and things like that, then, you know, your name goes on the paper and that is your work, right? Just like again, you know, the biologist’s paper, you know, about bear behavior is, you know, is not joint work with the bear, right? It’s, you know—they went out and they observed this phenomenon and then they wrote about what they saw, right? It’s the same here.
67. u67 24:00 Now the harder part is what happens when those conditions are not satisfied, right? So when OpenAI put out these hundreds of solutions a couple weeks ago, right? If you look on their GitHub, you’ll see—you’ll just see hundreds of papers, each of which just has OpenAI listed as the author. And, you know, and that’s because,

    

68. u68 24:25 you know, in most cases there was no human who had understood this result at all. You know, in some cases there was, you know, what’s called a Lean certificate, which gives us some kind of formal guarantee that, yes, the, you know, the result appears to be valid. Okay? But, you know, most of these had just not been digested by any human. And so they’re sort of
69. u69 24:48 just putting the—these out there as like, you know, now the task falls to us to understand it, and so now you have experts, you know, in every field that was touched by these results who have been scrambling for the last two weeks to, you know, understand these results and write their own expositions of them, give their own talks about them. And of course,
70. u70 25:11 those expositions will have, you know, the humans’ names on them, right? And those humans, you know, will get credit for, let’s say, whatever was the delta between, you know, what OpenAI did and what they did, right? Which might be a quite significant delta, right? In terms of, you know, making it comprehensible, simplifying it, things like that, okay?
71. u71 25:33 But what I think is, you know, is not gonna be highly rewarded, you know, going forward is just to—like when someone just feeds tons and tons of open problems into a model, and then they just take the solutions, and they post them online, you know, and like slap their name on it, like hoping to get credit for it, you know, with someone else having to do the work of understanding it,
72. u72 25:59 right? It’s, you know—that’s kind of like, okay, well, you know, if one person can do that, 1,000 people could do the same thing. It’s like pulling a lever on a slot machine, right? And my friend Boaz Barak, who is now actually a leading safety researcher at OpenAI, he made a joke to me that like what we should do in those cases, like if I have—if I just
73. u73 26:26 feed a problem to GPT, and it just one-shots the solution, and I just put that out, then the author of the paper should be like, you know, GPT-6 or whatever it was. But then it should say in the acknowledgments, like, “I’m so grateful to Scott Aaronson for suggesting this problem to me.” Curt: Yes. So when I was speaking to Jacob Tsimerman

    

74. u74 26:46 Mourning the Mathematician
75. u75 26:48 and also Dan Freed—actually, Dan Freed says hi. Scott: Okay. Yeah. All right, good. I say hi to him and to Jacob. Curt: Great. They were both saying that they were mourning not mathematics, but mathematicians, a particular way of doing math. Jacob: But mathematicians, such as myself, are used to a certain working style, and a lot of my working identity is tied to sort of having year-long projects, decade-long
76. u76 27:12 projects sometimes, working at the edges, slowly figuring things out, having those aha moments. I think that’s gonna go away. So there’s something about that that I think I’m definitely grieving. Curt: They think that math will continue on going—it may—maybe even flourish because of this. But that, as you mentioned, then it’s almost like an anthropologist. You’re going in, you’re seeing the artifacts, and then you’re giving talks about the

    

77. u77 27:33 artifacts rather than the creation of the artifacts, which is what it always was. Scott: Yeah. I—look, I think that there—I think that there is a certain kind of mourning that we’re all going through, right? And I mean, like, basically, you know, if you—like just list the emotions that we could be having, like exhilaration to see
78. u78 27:56 all these questions answered that, you know, we had dreamed of being answered for decades, and curiosity, but also grief and mourning. You know, I think that there’s all of—okay, in varying degrees, you know, in different people, of course. But, you know, I think part of it also just depends on what career stage someone is in. Right?
79. u79 28:17 Like if you take a middle-aged person like me, right? Like, you know, I have... Even before AI, I was sort of shifting into the more of manager mode, right? Where, you know, I am passing off, you know, the technical questions to my students or to my postdocs, right? And, you know, I’m more thinking about, you know, what would be an interesting follow-up question to ask here,
80. u80 28:42 right? Or, you know, what is actually novel? What is actually important about this proof that should be highlighted, right? Or, you know, questions of that kind, you know. And then the actual proving of the, you know, the lemma or the theorem is often being done by someone else, right? You know, and that’s—you could say like at the same time that AI’s abilities were
81. u81 29:05 going like this, you know, my own abilities were going like this, right? And, you know, they clearly crossed each other at some point, right? But so for me, like, you know, it would be natural to just, you know—let’s say imagining that AI’s abilities did not improve further, you know, which of course is silly. Of course, they will keep improving. But, you know, in the world that
82. u82 29:31 we’re, let’s say, in currently, right? It would be easy for me to spend the rest of my career, you know, as an interpreter or an expositor or a conjecturer, you know, and all of these things, you know, sort of, you know, with either, you know, human assistance or AI assistance, right? But what I worry about a lot more are the younger people, okay? Because if you look at, you know,
83. u83 29:58 PhD students, for example, right? Traditionally, the way that they cut their teeth, you know, in the field was by solving some well-defined open problem, right? Like that was how they made a name for themselves, right? That was how they sort of showed what they are capable of, you know, and then later they maybe transition to these more open-ended things. But, you know,

    

84. u84 30:22 I think they feel like that has now been taken away from them, you know? And I think, you know, it is, you know, like for, you know, the more senior people, it’s our responsibility to take that seriously to figure out a way forward that will sort of preserve our mathematical culture, you know, that will preserve the values of math that we want to preserve.
85. u85 30:47 Curt: You said they feel like that’s been taken away from them, but it seems like that has been taken away from them. Scott: That—yeah, I mean— Curt: Like, what else could they do then? Scott: Well, I mean, you know, you—what you have right now is like a lot of, you know, young people who are still putting papers out, you know, even like in the last few months, often, you know, using AI tools, right, you know, heavily, you know, while also contributing,

    

86. u86 31:12 you know, what they can at a human level, right? And sort of guiding the models toward a solution. So, I mean, you have, you know, people who are very active in doing that. But, you know, I think, you know, the world where sort of no one gets a leg up by using AIs, you know, that world is gone. Okay? And, you know, like, there’s gonna be only a very,
87. u87 31:38 very small market for let’s say, certified organic theorems, you know? Like, I think, you know, something has been taken away. Now, you know, and, you know, I think that, you know, we should—we all have to be thinking about the challenge of how do we adapt ourselves to this new reality, and in particular,
88. u88 32:04 how do we make this field something that is inviting for students to go into, you know, that they are excited to want to go into? How do we develop their abilities, you know? Because, like, we do want to develop their problem-solving abilities still, because how else are they going to know when an AI is wrong, for example, right? How are they going to be able to judge or to even
89. u89 32:28 do the higher-level things if they have no experience at doing the lower-level things, you know? Even the ones that AI can now do better. So we will have to deal with all of that. You know, what I don’t like is the—you know, is the sort of head-in-the-sand attitude, or the attitude that like, “Well, if only we could just, you know, make these evil AI companies stop
90. u90 32:52 solving our problems, then we could just go back to how things were before.” It’s like, “No, you know, you can either go full Luddite, right, and go full just, you know, stop all of this technology, you know, ban it.” You know, which, okay, you know, there are people who make that case, and, you know, okay, if someone wants to openly make that case, then let them. But, you know, if it’s available, then it’s not just gonna be the AI companies,
91. u91 33:15 it’s gonna be anyone using these models who will have the ability to solve very hard research problems, you know, beyond what humans can solve in many cases. And so how do you prevent everyone from doing that? You know? And even if we could, do we want to, right? Is—you know, like we have to balance, like yes, we want,
92. u92 33:39 you know, a thriving mathematical culture. We want, you know, ways for young people to enter that culture, to prove themselves. You know, we want to enjoy these challenges. But, you know, what we are... The product that we are delivering to the wider world is understanding, right? And insight. And if AI can accelerate that understanding and insight,
93. u93 34:03 then who are we to tell people that, you know, that they shouldn’t use it? Right? So I think we, you know, we have to balance that. Curt: What about—so if Christopher Hitchens had this razor that that which can be put forward without evidence can be dismissed without evidence, and then I think we’re living in a “that which can be put forward without effort can be dismissed without effort,” when
94. u94 34:23 the similar—the slot machine, like Steve from Michigan says, “Solve the theory of everything,” and happens to get it, just by chance happens to get it, doesn’t even understand— Scott: Well, it—right. Well, it’s tough because like I, you know, because of my blogging, you know, activity, like I am now for decades just used to, you know, every day or so getting emails that solve P versus NP, solve Goldbach’s conjecture, solve quantum gravity, you know,
95. u95 34:51 with, you know, the author’s, you know, new, you know, incomprehensible framework, right? And, you know, and so I’m used to just completely dismissing all this stuff, right? And now, you know, if some—you know, a totally unknown amateur sends me a solution to the Riemann hypothesis, right? I, you know, I’m less certain that it’s wrong, right?
96. u96 35:12 Maybe they just used an AI model, and that AI model spit out a correct proof, right? So I mean, I think, okay, you know, there is some value in, you know, just like figuring out how to prompt the AI models so that they will solve, you know, hard problems and so forth, but it’s just—I think that there is greater value in actually understanding and digesting what came out.
97. u97 35:38 Curt: I wanna quote something. “Right now, I’d say it’s closer to normal first-year math student

    

98. u98 35:39 The AI Denialism Problem
99. u99 35:44 who happens to know every existing published technique—... and can apply them arbitrarily to new domains, and can do that for thousands of problems in a few weeks with unlimited motivation and persistence, which is effing incredible. If such an entity were human, even 100 times slower, his or her name would be talked about in the same breath as Euler and Erdős.”
100. u100 36:04 Scott: Yeah, no, I mean, I think I was responding on my blog to sort of yet another person who tried to, you know, sort of— Curt: Minimizing? Scott: ...minimizing or like, you know, sort of what I think of as a denialist stance, where you just take anything that AI happened—you know, anything AI succeeded at doing, even if you yourself said that this was a thing that AI would never do, and you held it out as an example
101. u101 36:31 to prove how weak AI was, that it couldn’t do this thing. You know, and then it does do it, right? But then as soon as it does it, then you immediately pivot to inventing reasons why it didn’t really count, right? It wasn’t truly creative. It wasn’t, you know... It was just applying known techniques. This problem—well, I guess it wasn’t that hard anyway, right? You know?
102. u102 36:54 And on and on and on, right? And like, you know, one thing we’ve learned in the past few years is that people’s ability to come up with those sorts of rationalizations is infinite. It is staggering, right? And so—yeah, so I think, you know, I was, you know, maybe, you know, with some exasperation, you know, just sort of answering another such person and just saying, “Look, even if it were

     

103. u103 37:18 only, you know, a beginning grad student, but it knew the entire literature of math, you know, like this without having to look anything up, and, you know, it could work without stopping and, you know, it could be run in parallel on thousands of problems, and for each problem it could try thousands of counterexamples and thousands of proof strategies,
104. u104 37:40 and, you know, it’s not gonna be discouraged by the fact that, like, all the experts think that this conjecture is true. You know, if it’s, you know, given the task of looking for a counterexample, it’ll just do that, you know, with total diligence, never needing to sleep, never needing to eat.” You know, I mean, that is the—you know, that is something that is amazing, right? And, you know, we would—you know, if we saw anything
105. u105 38:05 even remotely like it in a human, then there would be no argument about how amazing it was. Curt: Yeah, I hear many of these reasons, and often when you’re speaking to someone and they keep offering reasons against something, say it’s—I don’t know, it’s working out, you say, and then they say, “Oh no, but you know what? I can’t because of this, can’t because of that.” At some point you realize that the reasons
106. u106 38:24 they’re articulating are not the true reason, and you say something like, “You’re just making up excuses.” So I think that what’s—much of the time, there’s some fear, like a fear of becoming superfluous or something else that’s going on that’s the true reason inside. Scott: Yeah, it could be that. It could be a psychological defense mechanism, you know. Of course they’re going to deny that, right? You know, it could be, you know, just that, you know,
107. u107 38:49 they say, “Okay, yes, it does all of these things, you know, but it is not conscious of the fact that it’s doing them,” right? But to me, that’s a very different discussion. That’s then a metaphysical discussion rather than a discussion about what these things are going to do in the observable world. And, you know, if we wanna go there, then we should go there, but just be explicit about it.
108. u108 39:09 Curt: Theories of Everything is brought to you by Mod. Mod prescribes a once or twice daily modafinil drink that can keep you energized, focused, and alert throughout the day. The mechanism is that energy drinks come with caffeine, which temporarily block adenosine, and that’s a chemical that makes you feel tired, and that builds up. When the caffeine wears off, you just crash.
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111. u111 40:19 website for important safety information, and we thank Mod for sponsoring the pod. Yeah, so I have a dog in this fight where it benefits me greatly when mathematicians and physicists are doing well. So not just mathematics, but the people, because I interview people, so I want them to be doing salubriously. It gives me more to talk about. But obviously I can’t just be biased and advocate for what I personally desire,
112. u112 40:43 which is why I’m putting up these natural counterpositions that, well, hopefully my desires can be stabilized by what’s true and nourishing and not just be self-serving. Scott: I think that, you know, you are better positioned than many of us are, right? I mean, I think, you know, well, you know, you—right, you will have interview subjects around, you know, to do podcasts with, you know, even if AI, you know, exceeds everything that we do,

     

113. u113 41:10 right? And maybe people would rather listen to other people than to AI models, you know, at least for podcasts like yours. Or maybe not. Maybe you can start interviewing AIs. Curt: Oh, yeah. Right. Well, I don’t know. I may be interviewing an AI right now. I have always admired how much you know. Like, geez Louise. So about human mathematics,

     

114. u114 41:31 Association for Human Mathematics
115. u115 41:33 there’s some association for human math or something? Scott: Oh, yeah. There is this thing called Association for Human Mathematics. And, you know, they put out a statement basically decrying what OpenAI had done. You know, and, you know, they were sort of very, you know, widely mocked for one—well, one particular sentence in their statement,
116. u116 41:56 which was something like, “Mathematicians did not ask for this work to be done.” Curt: Yes, I think that was one of near the top of their statements. Scott: Yeah, right, and I felt like I understood where the backlash was coming from, because it’s like, you know, who are we to be the arbiters of who gets to work on our problems or not, right? The whole point of posing an open problem is that it is then open for absolutely
117. u117 42:21 anyone in the world to work on, right? They could be, you know, an unknown, you know, clerk in India as Ramanujan was, you know, when he did his first great work, okay? They, you know, they could be, you know, sometimes a 17-year-old or an 18-year-old student, you know,
118. u118 42:45 as some who I’ve encountered who have, you know, solved significant open problems, right? You know, and the whole point is that our problems are open to anyone to solve. And I think, you know, if they’re open to anyone, then they’re even open to a corporation that you may not like. Right? And so, like, I agree with the AHM people that we have to hold these companies’ feet to the
119. u119 43:11 fire. We have to sort of get them to behave well, you know, especially around safety, around alignment. You know, I’ve been directly engaged in that for the past four years. I think, you know, these are massively important issues. You know, we—you know, we should demand better from these companies. But also, you know, I think, you know, we are not the arbiters of
120. u120 43:36 who gets to work on our problems. And, you know, we’re now in a world where AIs can solve these problems. Given that they can, they will be used for that, and it is our job to adapt ourselves to that world. It’s not other people’s job to sort of, you know, preserve our old world for us. Curt: And this adaptation to this new world,
121. u121 44:01 to me, it sounds like switching jobs from Jacob Tsimerman saying, “Look, I came into this ’cause I want to solve problems. I actually love to solve problems.” Jacob: Yeah. I’m more of a problem solver. I’ve always come at math through having a concrete sort of mystery and trying to figure it out. Yeah. Curt: He was an Olympiad winner. He went in, he—from a young age. He just loves problems. You know, some other mathematicians don’t even like problems per se. They like,
122. u122 44:22 “I wanna understand this discipline. I wanna explore so-and-so.” But, well, gosh, how are your students reacting? Like, they went into math for this, and now it’s that. Scott: Yeah, I mean, some—you know, a lot of my students, as you can imagine, are pretty unsure about their futures, okay? They are, you know, I mean, you know, they are making the best of the situation while they can. You know, they’re using AI heavily. They’re,
123. u123 44:49 you know, writing papers, you know, with it. They’re solving problems. But, you know, thinking longer term, of course, they’re wondering about the future of the field. And, you know, I try to give them guidance, right? But I don’t know either what’s the, you know, what’s the... And in fact, like, when I start trying to speculate about what’s the future
124. u124 45:13 of our field, you know, I quickly run into the bigger questions of what is the future of our entire civilization, right? You know, I feel like if our civilization, you know, survives this transition to an AI-dominated world, I think, you know, we will manage to find a niche for the people who like math, you know? I think we’ll be able to solve that problem, right?
125. u125 45:39 You know, and one thing that can give hope here is the example of what happened to the chess community, right? You know, like I’m old enough, you know, I remember following the Kasparov versus Deep Blue games in, you know, in ’97. And I remember that, you know, at the time some people said, you know, “This is the end of chess,” right? Humans are—just
126. u126 46:00 have no reason to play chess anymore now that, you know, computers are better at it. And the opposite is what happened, right? Chess has never been more popular than it is right now. I mean, my nine-year-old son, who you brought up before, you know, he goes to chess tournaments here in Austin regularly, right? They are packed with kids, okay? And, you know,
127. u127 46:24 you’ve got chess streamers, YouTubers, you know, you’ve got chess celebrities, okay? And, you know, people just decided they like doing this as a human activity, right? And of course, you know, they all use the models to analyze the games and understand what they should have done instead of what they did do. So the nature of chess has changed, you know, because
128. u128 46:47 of AI. And people train with it, okay, but, you know, people still play chess. I think that, you know, the—there’s gonna be at least as many people who enjoy understanding math and science, who enjoy coming up with their own mathematical questions, and then, you know, either, you know, trying to solve them themselves or having an AI, you know, solve them, you know,
129. u129 47:10 explain the solutions to them. You know, I’m more worried, frankly, about the bigger issues, about, you know, do we—how do we survive this, you know, just as a civilization? Curt: About that, suppose Anthropic has a proof that

     

130. u130 47:24 If AI Proves P = NP
131. u131 47:28 P equals NP. Do you think they should release it? Scott: Well, so first of all, you know, if P were equal to NP, right, it would depend a lot on kind of whether the algorithm was actually practical, right? So it could be that P would equal NP, but the algorithm for solving 3-SAT would take n^10000 time, let’s say. Or like O(n) time,
132. u132 47:56 but with a googolplex, you know, hidden in the constant in the big O. And in that case, you know, that would be an amazing result that would be of theoretical interest, right? I mean, of course, people would then immediately get to work on trying to make it practical, right? But, you know, if P were equal to NP via a practical algorithm,
133. u133 48:16 okay, what this would mean is, you know, most immediately that sort of essentially all of the cryptography that we use on the internet would be broken, okay? So like all—you know, Bitcoin would become worthless. You know, all the—you know, as all other cryptocurrencies, right? Like all the currency could be mined for nothing.
134. u134 48:38 All the digital signature schemes that protect people’s wallets could be broken, could be forged, okay? It would mean that all the cryptography that’s behind HTTPS or like that protects your credit card number when you put it into a webpage, that would all be broken as well. Okay, so, you know, and like we do have standards around responsible disclosure,
135. u135 49:03 right? That, like in the cybersecurity community, like if you discover, you know, so let’s say some way that some company’s, you know, website can be hacked, you know, and, you know, even if it’s academically interesting, right, you’re not supposed to just publish a paper about it immediately. You’re supposed to notify the company and give them 90 days to respond,
136. u136 49:27 right? And so, you know, and now with cryptography, like you can say even short of P equals NP, which is, by the way, something that I don’t believe is true, right? So this is a theoretical discussion. But, you know, something that is much more plausible is that there might be a fast classical algorithm for factoring, let’s say. Right? Which is—you know, that wouldn’t need

     

137. u137 49:51 P equals NP, right? That could just be this one specific problem, right? Where there could be a fast classical algorithm for breaking elliptic curve cryptography or something like that, right? And now many people noticed that, you know, in these like 400 papers that OpenAI put out, right, they covered just about every area of math with the conspicuous omission of cryptography. Okay?
138. u138 50:22 Right? There was... So like, obviously, that wasn’t an accident. You know, obviously, like, they are trying to be, you know, more cautious in how they approach cryptography. Okay? But, you know, I think we do need to, you know, think seriously about the prospect that in—you know, AI models will discover breaks of one or more widely deployed cryptographic codes, you know,
139. u139 50:48 within the next year or two, right? And what does responsible disclosure of that mean, right? It’s like, you know, okay, you know, you—you know, you’re supposed to notify the company and give it 90 days, but like if someone had broken, let’s say RSA, you know, or Bitcoin, then like the parties to notify are the entire world, right? So like, you know,
140. u140 51:12 who do you—you know, do you like prove to the world, you know, maybe like via demonstration or via zero-knowledge protocol, you prove to them that you have a solution, but without revealing what the solution is, you know? That’s one possibility, right? You know, I mean, maybe other people would say, you know, you first notify the government, right? And you
141. u141 51:34 let the government decide what to do. I think other people would strongly disagree with that, you know, especially if they disagree with the current government, right? You know, and I think in practice, it will be up to whatever company, you know, or other party does this first to decide how they’re going to handle it. So that is a real issue.
142. u142 51:58 Now, you know, more broadly, if, let’s say it was not only a break of this or that cryptosystem, but it was P equals NP, and it was an algorithm that was fast in practice, then the implications of that would even go beyond cryptography, okay? It would further accelerate the progress of AI, you know, even much more than it is already sort of accelerated. It would mean potentially that,
143. u143 52:30 you know, you would no longer need to spend these billions of dollars on these gigantic training runs, you know, to train the models. That there would just be a much, much faster way of finding the right parameters for these models and, you know, that could accelerate AI even further, you know, for better or for worse. Curt: Going back to the chess analogy, the difference with the chess case is that in

     

144. u144 52:53 Is Physics Next?
145. u145 52:57 academia, there’s an academic department for math, but there’s no academic department for chess. Now, maybe some of it is display chess and blah, blah, blah. So— Scott: That’s true. I mean, there—I mean, there is a department of music, by the way, but, you know, they’re all right. Right. They’re like—there are, you know, there—the—there are, you know, departments of athletics, right? Or of, you know, things like that. So yeah, things that
146. u146 53:20 could be classed as recreational activities, right? You know, they are actually studied by academics. But yeah, I think you’re getting at something real here, which is that, you know, in like, let’s say, academic research in math or in theoretical computer science, like, you know, we did have a higher vision of what we were doing, right? You know, we’re not just playing
147. u147 53:43 some game. We are sort of discovering truths about the universe. Right? Although, you know, if that’s what it is, if we’re discovering truths about the universe, then I think that is all the less reason to reject the tool that will let us discover more of those truths. Curt: Actually, that’s the difference also between an analogy I have, which is—well, something
148. u148 54:05 I’ve noticed is software engineers have been experiencing something similar for the past year and a half, where they’re saying, “Man, my job, I went into this actually ’cause I like creating algorithms and solving nitty-gritty problems, and now my job is I wake up with my coffee, I speak to my computer, I open another tab to speak to, and then I just watch it, and I’m a manager.” Scott: Look, I mean, you know, there’s sort of this rising floodwater that came for software
149. u149 54:30 engineering, you know, maybe a year or two ago, and then this summer it’s come for us. And you know, when I talk to my friends in physics, like it seems like it still hasn’t come for them, right? But a lot of them are watching nervously, and they’re expecting that it will come for them within the next year or so. Okay? So, you know, but like anyone who the floodwaters have not yet,
150. u150 54:52 you know, inundated, like they—you know, they could pretend that, you know, that there’s no flood at all, or that like it’s only hitting those other fields because those fields are just full of trivialities. But, you know, I do think that in some sense, this is coming for all of us. This is going to transform the nature of what all of us do. Curt: Is there anything that’s different about physics? Like, well,
151. u151 55:15 physics has to do with the real world. There’s something—you have to conduct experiments. Scott: I think the main differ... I—yeah, I think I can explain this. I think the main difference is simply that in physics the problems are not as crisply defined, okay? So it is not as easy to verify when you have correctly solved the problem and when you haven’t, right? It depends on judgment calls, like, you know, is this a reasonable approximation, right?
152. u152 55:41 Is this a reasonable model of the actual physical situation that, you know, that we had wanted to investigate, right? And, you know, well, in math, like, you know, people—you know, people are also interested in those kind of fuzzy, you know, open-ended things. Like, you know, is this the right definition? Is this the right model? Like, you know, that’s a lot of what we talk about too.
153. u153 56:03 But, you know, we do often state these perfectly crisp conjectures, right? You know—P is not equal to NP, or, you know, the unique games conjecture, or, you know, the—these other conjectures where, you know, there is, in principle, just a totally mechanical way of checking whether you have solved the problem or not, right? And, you know, I think that that is what has allowed AI to do so well,
154. u154 56:28 right? Because once you have just a mechanical way of checking the answers, then you can train on thousands upon thousands of examples of solutions, right? You can do reinforcement learning, right? You can... You know, and yeah, so, like, then, you know, you have your target to sort of aim your fearsome blob of intelligence at, right? And you know what the target is, okay?
155. u155 56:58 And I think the—you know, a good demonstration of this is that, you know, the area of physics that has been most affected so far has been mathematical physics, right? So, like, you know, those areas of physics where you can mathematically specify, you know, what statement you would like to prove, you know, those have seen, you know,
156. u156 57:21 some dramatic developments, including in the OpenAI drop from two weeks ago. Curt: This is my editor’s desktop untouched. There’s 40 tabs, there’s six drafts of a single cut. There’s always a folder that’s called Final inside another folder that’s called Final, and that mess is so much work. I appreciate very much a clean desk, a physical desk,
157. u157 57:42 and if my digital instantiation of a desk is messy, that also messes with my head. In other words, that mess is work. What isn’t the work is what the machine made itself. System cache, broken downloads, installer leftovers, duplicate photos, et cetera. CleanMyMac finds that and removes only that. Space Lens draws a map of your drive so your heaviest folders are obvious.
158. u158 58:06 This just happened to me yesterday. My drive was about to be overfilled, and I had to figure out, “Oh, gosh, what are my largest files?” so I could look through them and delete. Cloud Cleanup does the same across iCloud, Google Drive, and Dropbox, and the scan runs on the Mac, so nothing leaves it. There’s a performance module for when the fan spins up mid-render,
159. u159 58:26 and a Moonlock anti-malware engine underneath. It’s made by MacPaw, notarized by Apple, and on the Mac App Store’s 2026 shortlist, second year in a row. Get tidy today. Try CleanMyMac for free for seven days, and use my code THEORIES for 20 percent off. That’s code THEORIES, T-H-E-O-R-I-E-S, at cleanmymac.com.
160. u160 58:51 Unitary Synthesis Problem Solved
161. u161 58:51 Is there anything in that drop that is, gosh, that speaks to you that you say, “Oh, this—I wish people were paying more attention to this,” or that because of your discipline, you see its revolutionariness, but to others, it’s a bit difficult to convey? Scott: Well, look, I mean, you know, there are problems that are sort of just directly in my wheelhouse that, you know, in one case, a problem that I posed along with my colleague Greg Kuperberg 20 years
162. u162 59:19 ago. This was called the unitary synthesis problem, okay? And, you know, obviously, I think that the question is a nice one. That’s what the—that’s why we asked it, right? But the question was basically—but, like, what is the connection between, you know, the complexity of applying a unitary transformation in, you know, in quantum mechanics
163. u163 59:47 and the sort of ordinary kind of complexity, where usually we talk about things with, like, Boolean functions, you know, that just have a classical input and a classical output, okay? And specifically, what we asked was, “Is it true that for every unitary transformation on n qubits, let’s, you know, call it U, right? For every such U, there is some classical Boolean function that
164. u164 1:00:16 if I gave it to you for free, right? If I gave it to you as an oracle, you know, as we call it, right? I let you access that function, you know, on your quantum computer, right? You know, in superposition, I let you make queries to this Boolean function as an oracle, then you could apply that unitary U in polynomial time?” Okay? That—the—that was the question that we asked.
165. u165 1:00:42 We conjectured that the answer was no, okay? Because we just could not see any way to do this. It’s like, “Yes, for any unitary transformation, you know, it involves exponentially many parameters.” But, you know, that itself is not a stopper because you could encode all of those parameters into the values of this Boolean function. But then,
166. u166 1:01:03 you know, the trouble is that even after you’ve done that, it looks like you still need to query that Boolean function exponentially many times, you know, if you wanna actually apply the unitary, like, physically to a quantum state. And that seemed to be true no matter how cleverly you encoded the unitary that you wanted into the function.
167. u167 1:01:25 And so then, you know, this inspired a lot of follow-up work, you know, and actually I had quite a few colleagues who were working on this problem for the last few years, actually making progress, proving, you know, proving some very, very related results that may have even been closing in on a human solution to the—to this problem. But that was all cut short

     

168. u168 1:01:49 two weeks ago when, you know, when OpenAI, as one of its 372 papers, had a solution to the unitary synthesis problem, and the solution was the opposite of what Kuperberg and I had conjectured. It’s that this is possible, okay? For every such unitary, there is a Boolean function that lets you apply the unitary efficiently.
169. u169 1:02:16 And, you know, this—you know, and since that, you know, already just within the last two weeks that that result has been further improved by, you know, people using AI models. Okay? And one thing that we apparently have from these further improvements is that if, for example, P were equal to PSPACE, right? So this is like a big collapse of complexity classes. This would be

     

170. u170 1:02:42 even bigger than P equaling NP, right? But this is not something that we can currently rule out, right? And actually proving P is not equal to PSPACE is thought to be, you know, just almost as hard as proving P is not equal to NP, right? Okay, so the new result basically implies that if P were equal to PSPACE, then, like, you could
171. u171 1:03:06 apply any unitary transformation efficiently, like, that you can even reasonably describe, right? Where, like, you can just describe the entries by a polynomial space algorithm. So this would mean, for example, that the unitary transformations that you would use to decode the Hawking radiation coming out of a black hole, right? You could apply that efficiently. And,
172. u172 1:03:31 you know, that would have a very interesting implication for quantum gravity. That seems to mean that you could create a firewall at a black hole’s event horizon, right? You could engineer a breakdown of the spacetime continuum. You know, not at the singularity where we knew that, you know, spacetime was supposed to break down, but already at the event horizon. Okay? Admittedly,
173. u173 1:03:55 in order to observe this breakdown of spacetime, you’d have to jump into the black hole, okay? Curt: Yeah, but that’s just a—that’s a triviality. Scott: And of course he would then immediately die. And so, you know, for multiple reasons, you couldn’t tell anyone else about it, okay? But it’s basically saying that, you know, in order to show that sort of, you know,
174. u174 1:04:18 the spacetime continuum is stable in the places where general relativity said that it should be, you know, you would at a minimum need to prove that P is not equal to PSPACE. Curt: Does this mean decoding a black hole is a classical problem?

     

175. u175 1:04:30 Black Hole Firewalls & P vs PSPACE
176. u176 1:04:33 Scott: Well, it... This is the thing. Like, as stated, it’s a quantum problem, right? So the photons of Hawking radiation that are coming out of a black hole are in some quantum state, right? In the modern understanding, they’re in a very, very highly entangled quantum state that, you know, if you could, like, measure it in total detail, you know, in principle,
177. u177 1:04:58 you would see it encodes all the information about what fell into the black hole, right? And this has been just sort of a major, major theme of quantum gravity research for the past half century, you know, since Stephen Hawking, you know, raised these issues in the nineteen seventies. Okay, that basically, like, quantum field theory is not powerful enough to see. You know, it’s powerful
178. u178 1:05:24 enough to tell us that Hawking radiation should be there, okay, but not to tell us how the Hawking radiation encodes the information about what fell in to make the black hole, right? But if you believe that quantum mechanics is universally valid, then the information has to be there because, you know, information has to be conserved by unitary evolution, right? It
179. u179 1:05:47 can’t be just deleted from the universe, okay? And so the sort of more modern picture is that, yes, the information is there, in, you know, in the Hawking radiation, but it’s in some incredibly scrambled format, you know? Like, way more scrambled than like, you know, than would be the information in a book, you know, after you had burned it, right? And tried, you know—and if
180. u180 1:06:14 you would try—tried to recover what was written in the book from the smoke and the ash, right? I mean, even nineteenth-century physics tells us that in principle that ought to be possible, okay? But, you know, obviously very hard to do in practice, right? And so, you know, the black hole version you can think of as just like a harder version of that, right?
181. u181 1:06:35 And so you have all this quantum information, you know, that, you know, by some yet unknown dynamics of quantum gravity has been totally scrambled up by whatever was going on inside the black hole. Okay? It’s then coming out in the Hawking radiation in this highly entangled state. And now your task, if you wanted to create a firewall, is to apply a suitable unitary
182. u182 1:07:02 transformation to that quantum state, to the state of the Hawking radiation, right? And you could imagine doing that by, for example, just collecting all of the Hawking radiation, routing it into a quantum computer for processing, right? You know, these are, you know—we’re now far, far into the realm of thought experiments. Like, to actually collect enough Hawking radiation for
183. u183 1:07:28 an astrophysical black hole for any of this to be relevant, you know how long this would take? Like at least 10^67 years. Okay. All right. So, but yeah, we assume that you have a very long grant, right? And you’re able to do that, right? You’re able to process all this Hawking radiation. Now, in 2013, Daniel Harlow and Patrick Hayden wrote a now famous paper saying,
184. u184 1:07:56 you know, even then, you would still have a problem in sort of decoding what was in the Hawking radiation, you know, sort of before the black hole had fully evaporated, and the reason had to do with computational complexity, right? They said, like, you know, “If you wanted to solve this problem quickly, even with a quantum computer, you would have to solve a
185. u185 1:08:19 certain—cryptographic problems that we believe are hard even for quantum computers.” Okay? And, you know, for them, this was a positive because if, you know, the whole firewall paradox from a year before that, from 2012, had been saying that if you could decode the Hawking radiation from, let’s say, a black hole that had mostly but not entirely evaporated,

     

186. u186 1:08:45 then, you know, your act of decoding it should then have this dramatic effect once you—if you then jump into the black hole. Right? It should cause this breakdown of spacetime at the event horizon. That’s what a firewall is referring to here. Okay? And so they were saying, you know, like, “No,
187. u187 1:09:07 in practice,” you know, “in practice,” you know, it being a relative term here, but, you know, “You won’t be able to create this firewall ’cause you have to solve this exponentially hard problem.” Okay? And then I got very interested in this question. I improved their argument. You know, like, their original argument actually relied on a kind of hard result from my PhD thesis in 2004. So, you know, so I had no choice but to get interested,
188. u188 1:09:34 right? But I improved their results, so it no longer needed my PhD thesis. It just needs the... But, you know, okay, but then, you know, I got interested in, like, how hard is this problem really for a quantum computer, right? Like, it seems like, yeah, it seems plausibly hard, but like, could we hope to prove that it was hard just unconditionally? Or,
189. u189 1:09:58 you know, would proving that it’s hard require, you know, proving that P is not equal to PSPACE or something like that? Okay? So it appears that because of the recent AI progress, we now have an answer to that question. Okay? And the answer is that if P were equal to PSPACE, then the Harlow-Hayden decoding problem would be easy. Okay? Then it would be, you know,

     

190. u190 1:10:22 easy to create this firewall, and their argument would no—for why it’s hard would no longer apply. So, you know, when I actually texted Daniel Harlow, you know, when I realized that to tell him that, and immediately he wrote back, and he said, “Well, why should I care? Because P is not equal to PSPACE, right?” Right? But, you know, and to me, it was like, “Dude,” you know,
191. u191 1:10:45 right? Because in computer science, we care about, like, what would it take to prove so, right? And what this is saying is that if you wanna show that creating a firewall is hard, then you have to solve this central open problem of computational complexity. You know, you have to prove P is not equal to PSPACE. You know, something that despite all of the
192. u192 1:11:07 progress in AI for math, you know, in the last months has very conspicuously still not been done. Curt: Didn’t you say at Columbia that the second law may be because of computational intractability? And I think you said that a preprint was coming. Scott: Yeah.
193. u193 1:11:24 Curt: I was like a little— Scott: Yeah. So, yeah, we still didn’t put that out. But we know. We do have an argument that there is—there’s a—there are particular situations where you can get behavior that, you know, that looks like the second law, right? That looks like entropy is increasing. Okay? And yet
194. u194 1:11:51 if P were equal to NP, then you could unmask this as illusory, right? You could actually, you know, build a Maxwell’s demon, you know, as it’s called. You could convert heat back into work, right? You could... And so the—so the kinds of situations that we were thinking about involved,

     

195. u195 1:12:15 let’s say, like a classical reversible cellular automaton. Okay? So, you know, we could imagine, like in the classic thermodynamics scenario, right, you have a bunch of gas molecules just bouncing around inside of a box, right? And they can start in a very low-entropy state, like with all the particles concentrated in a, you know, the corner of—a corner
196. u196 1:12:39 of the box. And then they diffuse out. They spread across the box, right? And, you know, we would normally talk about this by saying the entropy of the system has increased, right? The energy has stayed the same, but, you know, the entropy is—has gone up. And yes, you know, if you waited long enough, you know, eventually by chance, you know,
197. u197 1:13:03 all the particles will collect back in the corner. You know, the entropy will go down, but that will typically take exponential time, right? So like, you know, in a trillion years, you know, you’ll almost certainly never see it happen. Okay? And then the classic Maxwell’s demon thought experiment goes,
198. u198 1:13:24 “Well, what if we put a divider in the middle of the box, right? And the divider has a little door in it, and there’s a little demon that just watches, and whenever a particle—whenever a gas molecule is sort of heading from the left to the right, it just opens the door long
199. u199 1:13:46 enough to let that molecule through.” Okay? If a molecule is heading from the right to the left, then it keeps the door closed, right? And then, you know, this demon seems like, you know, it would succeed, you know, actually on a, you know, maybe a less than astronomical timescale at decreasing the entropy in the box, right? It’s gonna just preferentially
200. u200 1:14:08 move the particles to the right, and it’s going to, you know—it’s going to decrease entropy in apparent violation of the second law. Okay? So then, you know, what gives, right? And this was a big puzzle in physics that I think, you know, took the better part of a century to completely clarify. Okay? But you had, you know, after Maxwell posed it, you had
201. u201 1:14:35 Szilard, you know, better known for, you know, having the idea for the atomic bomb, you know, in the thirties, thinking about this. You had Bennett and Landauer, and, you know... So you had these major figures sort of clarifying what is going on. And what they

     

202. u202 1:14:58 ultimately said is that, you know, it only looks like entropy is going down. You know, really, you know, the second law holds, you know, always and everywhere. And if you ask, “Where it—where is the entropy going, right? The entropy that seems to have disappeared from the box by this demon’s actions.” The answer to that question
203. u203 1:15:20 is ultimately it’s gone into the demon’s memory. Okay? So the demon, in making these decisions of, you know, whether to open the box, whether to close the box, if you think about how to implement—how to actually build that demon, then either the demon has to remember, you know, the information about, like, was a particle coming from the left or was it coming from the

     

204. u204 1:15:41 Maxwell's Demon & Pseudo-Entropy
205. u205 1:15:43 right, and then the entropy goes into its memory, or else it has to dissipate heat, you know. And then the entropy has gone out of the demon and into the demon’s environment. Okay? But either way, you know, the total entropy of the universe has stayed the same or gone up, you know, exactly as the second law said that it had to. Okay?
206. u206 1:16:06 So okay, so now I can tell you about, you know, the situation that we were thinking about. Which is, okay, but we... What if it’s—first of all, it’s a classical reversible cellular automaton, okay? And we again have this demon. Okay, but now, you know, we say, “Look, you know, suppo... You know, let’s assume that the demon knows the initial state of the gas molecules,
207. u207 1:16:37 right?” You know, it knows where they were initially. It knows the relevant laws of physics, right? So it can simulate them for itself, right? It can do the relevant calculations and— Curt: The full microstate? Scott: I’m sorry. So I should have said the demon knows that, let’s say, the particles
208. u208 1:16:59 were concentrated in the corner of the box, but it does—it doesn’t necessarily know their microstate beyond that. Okay? Right. Okay. But then now we’re going to suppose that P is equal to NP. Okay? And now, if P is equal to NP, then, you know, after the demon has done everything that I just said and it has all this information in its memory about, you know, when the particles
209. u209 1:17:26 approach the left side of the door or the right side of the door or whatever, then the demon now faces a computational problem, right? Which is, “Which sequence—or which initial state of the gas molecules would have led to the sequence of observations that I made?” Okay? And that, in general, will be an extremely hard computational problem, right? Could
210. u210 1:17:52 involve doing a brute force search through all the possible initial states, let’s say, of the gas molecules. You know, all the possible sort of, you know, lower-entropy initial states. You know, looking for one that sort of would have led to this exact sequence of observations. Okay? But if P were equal to NP or, you know, even more weakly than that, if,
211. u211 1:18:19 as we say, there were no one-way functions or no pseudorandom generators, okay, then this is precisely the sort of problem that would be solvable efficiently, right? The demon could then avoid the brute force search, right? And in less than exponential time, in polynomial time, you know, it could figure out, you know, what was the initial state of the molecules.

     

212. u212 1:18:46 And with that, what it would have had to do is compress its memory, right? Once the demon has solved this computational problem, then, you know, all these bits in its memory where, you know, we had satisfied the second law by saying, you know, “Well, that is where the entropy went.” We could then compress those bits back down, right? And
213. u213 1:19:08 now you say, “Well, wait a minute. Now where’s the entropy?” Right? Now where did it go, right? And, you know, I think, you know, a physicist, you know, might say, “Okay, you know, that may—maybe that’s cute,” but, you know, they’re not gonna be too disturbed by this because they’re gonna... You know, what they would probably say is, “Well, you’ve just revealed that this entropy was
214. u214 1:19:29 never true entropy in the first place.” Right? In fact, we even have a name in theoretical computer science for this sort of thing. We call it pseudo-entropy. Okay? This is like, you know, it’s the kind of thing that a pseudorandom number generator produces, right? Bits that, you know,

     

215. u215 1:19:50 look like they are uniformly random, but that actually have a much shorter description. Right? So what we would be doing in this scenario is we’d be taking entropy, you know, we’d be taking what looks like entropy in a thermodynamic situation and unmasking it as actually just having been pseudo-entropy all along. Right? So in that sense,
216. u216 1:20:14 we would not be violating the second law, but we would sort of be, you know, circumventing it. Like, you know, rendering it irrelevant in a sense. And now, you know, there are some important caveats, which is that, you know, this—in real life, chaotic effects, you know, may make this approach not work, right? Like,
217. u217 1:20:39 if you would need to know the initial states of the particles to infinite precision in order to calculate what happens, then, you know, then even if P equals NP, you may still be unable to do that, right? And also, if there’s quantum mechanical uncertainty, you know, that keeps getting injected into the system, that could also kill this approach, okay?
218. u218 1:21:04 So this approach mostly works for a classical dynamical system that is not subject to chaos. So, but the point is, if in nature one finds an example of such a system, then, you know, what appears in that system, like the second law, may actually be violated in a world where P equals NP. Curt: Professor. Thank you for spending so much time with me.
219. u219 1:21:30 Scott: Of course, of course. Curt: And hey, about consciousness. Scott: Oh, gosh. All right. Just with an easy last question, you mean? Curt: Right. No, no, it’s something you’ve explored before, these XOR gates and IIT. So they say that these XOR gates are of high consciousness. A question I’ve always had is, okay, it has a high phi number, okay? But then what is it conscious of? Like,
220. u220 1:21:53 what would he say that it’s conscious of? Is it just like, “I’m here, I’m super conscious”? But usually you’re conscious of something. Scott: Okay. So you’re asking about integrated information theory, which is a, you know, a theory of consciousness, or at least of, like, which physical systems are conscious and which aren’t, which was put forward by a guy named Giulio Tononi, and, you know,
221. u221 1:22:17 which, you know, he’s sort of built up a whole community around this theory. And now, you know, the backstory to your question is that I think this theory is just wrong, okay? You know, which in a way is better than, you know, the many, many theories of consciousness

     

222. u222 1:22:32 Why IIT Is Wrong
223. u223 1:22:34 that are not even wrong, right, that are too vague to even be wrong. I think, like, this one actually just sticks its neck out, and it makes predictions that are just absurd, right? And in particular, like, you know, the core of IIT is this numerical measure called phi, which, you know, allegedly you can just calculate for any physical system, and it will tell you how much
224. u224 1:23:00 consciousness there is in that system, okay? And, you know, and there are some arguments for this and, you know, involving, like, the cerebrum, you know, apparently having a higher value of phi than the cerebellum. Okay, but there’s also—there’s a huge amount of vagueness here, right? The definition of phi itself has kept changing from one version of IIT to the next version.
225. u225 1:23:24 You know, it’s claimed that this measure can be derived from axioms. It’s not derived from axioms. It’s just, like, you know, the paper, it just lists some axioms, and then just phi appears at some point, you know, with the—right, you know, it’s kind of like pseudomathematics, like, you know, right, you know, and so that’s really annoying. Curt: It’s like an OpenAI paper.

     

226. u226 1:23:44 Scott: Well, yeah, but the OpenAI papers, I think, you know, I think all—most of them are actually correct, right? If you, you know—that’s the amazing thing about it. I mean, we’re gonna know with more certainty in the near future. But the—but these IIT papers, I think, you know, they were just sort of pulling a formula, you know, for this phi out of nowhere, basically. Okay, but then
227. u227 1:24:09 we—it—once they’ve—they’re proposing this formula, we can look at what does it predict, right? And the point that I made in my blog posts on IIT, this was 12 years ago, was that, you know, you can easily construct examples of systems that have a way higher value of phi than, let’s say, our brains do, but that seem like they are obviously not doing anything conscious. They’re

     

228. u228 1:24:34 just like a giant grid of XOR gates, okay? Or something like that, okay? Like a blank wall or, you know, a wall of—a uniform wall of logic gates doing nothing of any interest, right? And then, you know, I would say, like, “If that—if you’re gonna tell me that
229. u229 1:24:55 that has more consciousness than we do, then, like, what are we even talking about anymore, right?” What is, you know, like, what—well, the, you know, the thing that we, you know, the—what we now mean by the word “consciousness” seems so disconnected from what I thought we meant by the word “consciousness” that, like,
230. u230 1:25:17 you now have to tell me why I should be interested in this thing. You know, whatever it is, right? And Tononi wrote a whole response to my critique, and his response, amazingly, was to just completely bite the bullet here. You know, by which I mean, he says, you know, “Scott went wrong by relying on his intuitions, and he should just instead rely on the theory. You know,
231. u231 1:25:40 the theory says that this wall of XOR gates is 1,000 times more conscious than any human, therefore it is,” right? And now your question was, “Okay, and what is the wall conscious of?” You know, I feel like that’s more a question for him than for me. I mean, you know, maybe it’s conscious of its own XOR—
232. u232 1:26:03 Curt: It’s conscious of how much Scott dislikes this theory. Scott: Maybe it’s conscious of its own XORness, its own, you know, its own experience of being a blank wall. Curt: I don’t know. Okay. Well, professor, so much fun. Have a great day, and good luck to— Scott: Thanks. Thanks. You too.

     

233. u233 1:26:23 Curt: Good luck to your son— Scott: Thanks. Appreciate it. Curt: ...with trolling your wife, his mom. Scott: Yeah. Thank you. All right. Good talking to you as always, Curt. Curt: Take care. Scott: All right. Okay, bye. Curt: Good talking to you. If you want access to the next conversation prior to anyone else, plus my actual opinions on these theories and concepts, which I keep out of the interviews, then visit my Substack, CURTJAIMUNGAL.com. That’s C-U-R-T-J-A-I-M-U-N-G-A-L.com.
234. u234 1:26:48 And if today’s conversation grabbed you, there’s an episode on screen somewhere right now over here, which is the next one that I’d watch. Enjoy.