In that vein, this post points out how subtly the messaging can be when an AI company claims to solve a problem, in this case the Jacobian conjecture:

"I found that the most historically concerned version [of the Jacobian conjecture] n=2 remains open, while Anthropic claimed that they “resolved the Jacobian conjecture”. This is highly misleading, because it is mostly dimension-indexed, just like the Kakeya conjecture or generalized Poincaré conjecture; also, at least for a group of mathematicians, this name only referred to the 2-dimensional case (since there’re many positive results/evidence in this case), and the higher-dimensional versions were frequently labeled with “almost no evidence“."

https://proofsandprompts.com/2026/08/18/on-protecting-mathematics-from-llm-companies-monopoly/