“Claude is like a 26-year-old precocious PhD student. Works hard, does lots of things, talks crap quite often. … Claude told me that the category of containers is locally cartesian closed. It's not. And he gave me a sketch proof. If you don't know more than Claude, you just go, oh, that's fantastic, brilliant, I'm going to write that in my papers.”
aboutlogic · September 2026
Ghani, a category theorist at Strathclyde, was talking with Thorsten Altenkirch and Deniz Sarikaya about what LLMs are doing to mathematics. He uses Claude heavily and rates it, and the point of the story is that he knows enough to catch it. What worries him is senior colleagues repeating model output they cannot check, which he thinks closes down the space for inquiry.
Transcript
yeah. And the papers you mentioned, you know, I'm going to go back to what I said about value and significance. These are subjective, and some people might be uncomfortable with it. But, you know, just like in art, in all areas, we often make decisions about what we think is better than others. And, you know, we like papers that are that are more creative and more interesting and do interesting things and whatever. So those papers that you mentioned, I think maybe we don't need so many of them. I mean, we all know there's a huge explosion of numbers of papers published over the last 50 years. And now just like they're just stuff published. And, you know, do you really need all those papers? No one thinks we really need all those papers. And it's driven not even by the mathematicians. It's often driven by university bureaucrats who want to measure stuff and they just weigh the papers. That's not mathematics.
Yeah, I mean, it will kill a lot of proxies. And I mean, proxies are proxies. They aren't the real thing. Yeah. But this will make the social structure change, hopefully for the better. The only thing where I really, really worry is learning, because I think there is immense value in doing the messy detail work for a while. I worry. And then later on, we get this weird, you are now allowed to skip over the details.
Yeah. I worry too. I've seen a number of problems of AI. And so apart from the political and social aspects and whatever. It used to be that if you didn't know the answer, you said, I don't know the answer. Now you go to Claude and you trot out some stuff that Claude says and you think it's true. And this is really bad. And I've seen a lot of senior people, you know, they go around, they do this kind of thing, they trot out stuff, they don't know what they're talking about. And this is really, really dangerous because it's going to mean that the space for inquiry gets closed down because people think they know the answer, but they don't know what they're talking about. That's not good. Another real problem is, so Claude, for me, I use a lot of it. I think it's fantastic. It helps me do things, but I know more than Claude. Theory Meets, Claude is like a 26-year-old precocious PhD student. Yes, works hard, does lots of things, talks crap quite often. I mean, I told Torsen recently, Claude told me that the category of containers is locally cut easy and closed. It's not. And he gave me a sketch proof. And, you know, if you don't know more than Claude, you just go, oh, that's fantastic. Brilliant. I'm going to write that in my papers and I'm going to build my software and write my grants and use it all. So that's okay because I know more than the precocious 26-year-old. But I see a lot of people just trotting out stuff they've got from Claude. And they can't tell whether it's right or wrong. This is again, you know, so people are going to, I worry that people not get the opportunity to grow into and learn all the skills which makes them better than Claude if all they're doing is trotting out Claude. If they never do the proofs, they'll never know if Claude proof is true or not.
I mean, I've got this very concrete problem. I'm teaching logic. And how do you finish logic? It's called I'm using a proof assistant. A while ago, I used cock when it was still cock. And now I'm using lean. Now the problem is I set them some exercises and the exercises are formative, really, but I have to evaluate them, I have to assess them. And previously, they would sit down and bang their head against this proof. And while doing the proof, there's other things that are health and safety regulations. Yeah. Exactly. That's a problem.
The exit is there. Then everybody is safe.
Yes. So then, but it was really good because they were stuck on something and then you walked around the lab and give them little hints and they learned something. And now they can just use an AI and AI will fill in the proof. And that's too easy.