I asked Claude (Opus and Fable 5) to work on unsolved problems in math, and it found the new lowest-ever counterexample to Borsuk's conjecture (https://en.wikipedia.org/wiki/Borsuk%27s_conjecture), N=63. The last one found was in 2014 (N=64). I posted Claude’s writeup and verification code on my website here: https://nickk124.github.io/borsuk.

So far, Claude verified the counterexample in four independent ways: an exact rational/algebraic-arithmetic certificate, two independently-written max-clique algorithms, an ILP solver, and CP-SAT, all agreeing that no valid partition into 64 smaller-diameter parts exists. Actively working to get it verified by a proper mathematician!