I have spent a small fortune in tokens trying to get Anthropic models to attempt proofs of things like the irrationality of the Euler-Mascheroni constant, and to make lattice reduction / SVP algorithms that rival SOTA methods like the G6K sieve, and all sorts of difficult frontier problems. It says 'honest' as a euphemism for giving up, because it knows I'm being a crank, and because the training data contains a lot of pessimism.

But I can get around this by first having it write a prompt for itself discussing the problem followed by a rousing speech about never giving in and admitting defeat, but pressing on towards results regardless of how hard matching SOTA results is.