The claude.ai chat interface only lets claude run javascript code, but “import numpy as np” is python. As a result, the code doesn’t run. This is an extremely common and funny issue for me across claude versions, but it must be caused by something in my prompting style if other people aren’t hitting it
Typically if I don’t stop it claude does eventually recover, the new version was able to catch itself and switch to javascript after only three script submissions! In the end, claude 4 opus produced a confident, well informed, and completely wrong answer, but its a nasty problem that I didn’t expect it to solve- has to do with quantum time reversal. The humor doesn’t really involve the math. ( For reference, if the METR time horizons people want to steal it, this problem took me about 4 hours, but I am an unusually slow mathematician. If you know that the common name for this is an antilinear eigenvalue, not a conjugate eigenvalue, then it can be solved with a simple arxiv search, but one is not always gifted the True Name of a math concept by which its literature may be summoned; and I had not found the true name yet when I prompted claude or made the original post)
If you form the block matrix Y = (real(A), -imag(A) ; -imag(A), -real(A)), the real valued eigenvectors and eigenvalues of Y correspond to conjugate eigenvectors and eigenvalues of A; the complex conjugate pairs of eigenvalues of Y don’t correspond to anything. Then, for any angle theta, you can multiply a conjugate eigenvector v of A by exp(i theta) to get a new conjugate eigenvector, and find its associated eigenvalue by elementwise dividing A conj(exp itheta v) by v. The conjugate eigenvalues form up to 10 continuous rings around the origin,