I just don't understand how Alpöge can get Claude to construct so many complex mathematical objects. He must already have some deep insight into the structure these things are likely to take. Naive prompting, or naive search would not have found pretty much any of the object he's found in the past month.
He has an AB in Math from Harvard with a senior thesis "The average elliptic curve has few integral points", and a PhD in Math from Princeton with thesis "Points on Curves", so it's fair to say he has some deep insight. (https://alpo.ge/cv.pdf)
Okay this result may well be in his expertise wheelhouse but what about the recent smooth Carathéodory conjecture disproof? Or the Jacobian, or the Hadamard matrices? It seems to span a pretty wide range. I know others are getting good results too, but his really stand out.
It wouldn't surprise me if he is given access to a more advanced model or more compute, since he is an Anthropic employee. Add to that the fact that this makes great PR and that he has not shown any of his prompts, it's more than likely in my opinion that this is the case.
I just don't understand how Alpöge can get Claude to construct so many complex mathematical objects. He must already have some deep insight into the structure these things are likely to take. Naive prompting, or naive search would not have found pretty much any of the object he's found in the past month.
He has an AB in Math from Harvard with a senior thesis "The average elliptic curve has few integral points", and a PhD in Math from Princeton with thesis "Points on Curves", so it's fair to say he has some deep insight. (https://alpo.ge/cv.pdf)
Okay this result may well be in his expertise wheelhouse but what about the recent smooth Carathéodory conjecture disproof? Or the Jacobian, or the Hadamard matrices? It seems to span a pretty wide range. I know others are getting good results too, but his really stand out.
It wouldn't surprise me if he is given access to a more advanced model or more compute, since he is an Anthropic employee. Add to that the fact that this makes great PR and that he has not shown any of his prompts, it's more than likely in my opinion that this is the case.