Mathematicians need to understand AI proofs, not dismiss them

Transcript

Transcribed by machine (Whisper) from the episode’s audio, so a word may be off here and there.

1. 4:32

   severe misalignment of ai in mathematics and i think that the general was this the association for human mathematics thing or um it's math and ai.org okay oh okay yes so i guess the core premise here is like uh there was a certain you know community effect of like mathematicians getting together um solving problems conceptually like discussing the conceptual leap whenever a problem was solved um this whole just like microcosm of humanity that they call it and now there's this sort of rush in the way that new solutions are announced and i guess it take away takes away from the thoughtfulness and community of mathematicians trying to understand so um what do you think are like the biggest risks of alignment between ai and mathematics is it really just that we're not fully understanding and like metabolizing the conceptual leaps yeah as a field

2. 5:27

   or what do you see yeah okay so so i think that it would be crazy to not be worried right now about the future of the mathematical community you know to whatever extent you someone cared about that community or was part of it or or or had hoped to join it uh you know i mean this is this is uh uh uh an asteroid you know has landed on our world right this is not something that you know you know people are in different stages of like you know denial grief bargaining acceptance right but i think you know a denial is just not going to be a a viable strategy you know this is this is not going away uh and in fact you know the uh the model that open a open ai used is something that will just plausibly be available to regular subscribers you know a few months from now right so anyone will be able to you know get results like this you know and i would i would say

3. 6:22

   that since the summer you know uh you know people have woken up to this like our whole way of doing research is different now right uh almost any paper that you read will contain you know near the end a little ai statement which explains like which parts of the paper did they think of which parts uh um came from astra or from or from claude uh so you know that that that is now just uh you know almost like without any fanfare just within the last few months that became you know part of writing a paper part of doing research uh and you know and of course things are moving so much faster it's like you know you can uh uh say oh you know it would be in you know it would be interesting to follow up you know this result you know with with by answering this other question and like normally you know like we used to like when you say that and then maybe over the next

4. 7:17

   six months over the next year people will think about that question and now it's like oh i actually already put that question into fable and i just got an answer right now right so you know i i still haven't adjusted to the speed that things are going at and and you know as you said uh uh you know there is a huge fear that things will just happen faster than we can metabolize them right that uh um you know that like like at some point it's just like okay i guess we should just give up we should just turn things over to the to the machines right you know but then you could say what uh what is the point then right because like these you know mathematical truths uh in some sense already existed put Yes. Right. We didn't, you know, we didn't need to bring them into existence. You know, they were already there. Right. What we care about is understanding. Right. We care about, you know, us actually understanding them and, you know, and eventually getting benefits for science and technology that are that are downstream from that understanding.

5. 8:21

   But, you know, for, you know, for us, it's mostly just about the understanding itself. And, you know, that, you know, maintaining a community that really values that understanding, you know, has taken centuries, right? I mean, it's been a sort of a painstaking effort of generations to build that up. And, you know, if you talk to grad students or to young researchers right now, you know, they're scared because, you know, they say, well, like, how will they sort of cut their teeth?

6. 8:56

   How will they sort of establish themselves, you know, when AI can just do everything, right? So we absolutely have to be figuring out how we're going to respond to this, what mathematical research looks like going forward. Now, what I don't think we get to do is to sort of declare, well, you know, the AI companies have to stop doing this and no one's allowed to do this, right? And you just have to stop, you know, ruining our playground by solving all our problems.

7. 9:30

   Like, you know, that is not our decision to make. You know, these problems are not, you know, we may have come up with the problems, but once you publish a problem, the whole point is that it is there for anyone in the world to try to solve, you know, even if they're a corporation that doesn't always behave the way you would want them to, right? you know a math problem once it's posed sort of belongs to to the whole world and so I don't think that we get to say you know you know people are not allowed to use AI or that you know we're not going to count you know AI solutions as being real solutions it's like okay you know it's true that the AI solutions you know that we've seen a lot of them are very poorly written by by our standards, right? And, you know, they're very confusing to read, you know, because like the

8. 10:23

   AIs, you could say they don't have a very good model yet of the human reader, you know, of like what an expert would find novel, what they would find obvious, right? They, you know, they may spend pages and pages on something that we would consider, you know, routine or uninteresting, and then just pass very quickly over the essential point. Now, you could say as long as they're so bad at writing, like that's great for us because it means that we still have plenty to do, right?

9. 10:55

   You know, and when they become, you know, wonderful writers too, right, then there will be an even bigger question about what is left for us. OK, but, you know, I think, you know, we we we neither get, you know, we we don't get get to say, oh, you know, this is this is it. Like, you know, we do need to digest these things and understand them and produce humanly comprehensible explanations of these results.

10. 11:25

    And that is what, you know, people all over the world who were experts on these problems are right now racing to do. and you know and that may then lead to papers that they write that they put their names on you know that they then take authorship or you know ownership over those papers uh and give talks about them and answer questions about them you know even if the original idea came from ai you know you know there you know there will still there will be all this human work uh that builds on it uh but you know and and like open ai is not you know submitting its GitHub repo to journals, right?

11. 12:04

    So it's like, it's not like we have a decision to make about whether to accept or to reject it or to, you know, grant or deny OpenAI academic credit. You know, they're not asking for academic credit, right? They're just, you know, they're just sharing this stuff, you know, with the world. What we don't get to do is say, oh, because these theorems are not certified organic, or they're not approved or released in the way that we would want, therefore we can ignore them, right?