Joel David Hamkins: evaluation

Transcript context

…Before I forget, let me ask about your views on AI and LLMs that are getting better and better at mathematics. We’ve spoken about collaborators, and you have so many collaborators. Do you see AI as a potential great collaborator to you as a mathematician, and what do you think the future role of those… …Kinds of AI systems is? I guess I would draw a distinction between what we have currently and what might come in future years. I’ve played around with it and I’ve tried experimenting, but I haven’t found it helpful at all, basically zero. It’s not helpful to me. And, you know, I’ve used various systems and so on, the paid models and so on, and my typical experience interacting with AI on a mathematical question is that it gives me garbage answers that are not mathematically correct. And so I find that not helpful and also frustrating. If I was interacting with a person, the frustrating thing is when you have to argue about whether or not the argument they gave you is right, and you point out exactly the error— …in the AI saying, “Oh, it’s totally fine.” If I were having such an experience with a person, I would simply refuse to talk to that person again. But okay, one has to overlook these kind of flaws. And so I tend to be a skeptic about the current value of the current AI systems as far as mathematical reasoning is concerned. It seems not reliable. But I know for a fact that there are several prominent mathematicians who I have enormous respect for who are saying that they are using it in a way— …that’s helpful, and I’m often very surprised to hear that based on my own experience, which is quite the opposite. Maybe my process isn’t any good, although I use it for other things like programming or image generation and so on. It’s amazingly powerful and helpful. But for mathematical arguments, I haven’t found it helpful, and maybe I’m not interacting with it in the right way— …yet, or it could be. And so maybe I just need to improve my skill. But also maybe I wonder, like, these examples that are provided by other people maybe involve quite a huge amount of interaction, and so I wonder if maybe the mathematical ideas are really coming from the person, you know, these great mathematicians— …who are doing it rather than the AI. And so I tend to be skeptical. But also, I’m skeptical for another reason, and that is because of the nature of the large language model approach to AI doing mathematics. I recognize that the AI is trying to give me an argument that sounds like a proof rather than an argument that is a proof. The motivation is misplaced. And so I worry that this is a very dangerous source of error because it often happens in mathematics that… I mean, if I think back to when I was an undergrad, here at Caltech, I was a math major eventually, and at that time, LaTeX was a pretty new thing and I was learning LaTeX, and so I was typing up my homeworks in LaTeX and they looked beautiful. Actually, they looked like garbage. From my current standards— that time, LaTeX was a pretty new thing and I was learning LaTeX, and so I was typing up my homeworks in LaTeX and they looked beautiful. Actually, they looked like garbage. From my current standards— …I’m sure it was terrible. Except at the time, I didn’t know anything. I was an undergrad and LaTeX was sort of unheard of, and so I was producing these beautifully typeset, you know— …problem sets, solutions, and so on. And I would print it up and submit it and so on, and the grades would come back, terrible grades, and I realized what was happening— The copy was so beautiful, mathematically typeset in this way, it looked like the kind of mathematics you find in a book. Because basically, that’s the only time you saw that kind of mathematical typesetting was in a professional, published book. And that mathematics was almost always correct. …In a book, right? And so I had somehow lost my… …because it was so beautiful, and I’m used to only seeing that kind of typesetting when an argument was totally right. I wasn’t critical enough and was making these bonehead mistakes in the proofs. So, okay, I corrected this, of course.…

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