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I've been chatting with LLMs recently about classical modular forms, mostly o3 and gemini 2.5 pro. They seem to have strong and very sticky and totally false beliefs about congruence subgroups being generated by their upper + lower triangular subgroups,

e.g. that Gamma_1(N) is generated by (1 1) (0 1) and (1 0) (N 1). "Sticky" in the sense that no matter how often I correct it, it'll still argue this way in the next chat. (If you ask directly, it'll agree this is false, but it's eager to make arguments using this "fact".)

You can also now find AI-generated websites on congruence subgroups that contain this error, so it seems like this conviction is only going to get worse.

One great thing about the U.S. National Science Foundation is their broad mission to "promote the progress of science" both through new research and its public communication. See the following thread for #DMSFunded work describing recent developments in category theory, homotopy theory, and formalization:

What a run!

Congratulations!

I love this article which gives a beautiful and concise summary of the mathematics, as well as a great snapshot of the London Mathematical Society Hardy lecture tour:

Detailed comparison of the new DeepMind and OpenAI gold performances (to the extent that is even possible), co-written with Ernest Davis, only at Marcus on AI.

gay culture is synechdoche ("his roided biceps means the world to me"); lesbian culture is metonymy ("oh yes i'm flirting with her by talking to her ex"); straight culture is metaphor ("he doesn't mean it like that")