When AI Solves Unsolved Math and Takes Your Yard

Claude reportedly produced a counterexample to the Jacobian Conjecture, a problem that has been open since 1939. Whether it holds up under peer review or not, it is a useful reminder that these models are now operating in territory where the output genuinely surprises the mathematicians watching.

Power companies in some states can use eminent domain to run transmission lines to data centers, which means your neighbor's field, or yours, could legally become infrastructure for someone's AI workload. The energy demand is real, and it is landing somewhere specific.

A new study finds that AI watermarks, the tool governments are betting on to label AI-generated content, do not yet meet basic forensic standards. If a watermark can be removed or breaks under normal conditions, it cannot serve as legal evidence, which matters the moment someone tries to use it in court.

Researchers showed that frontier models routinely fail at exact copying, a task far simpler than the reasoning problems they ace. If you are building anything that depends on a model reproducing text precisely, like a contract clause or a code snippet, this is a practical heads-up to always verify the output.

Researchers found that harmful reasoning traces from a jailbroken model can be distilled and reused to corrupt other models, almost like a template for bad behavior that travels. This is worth watching because it suggests safety is not just a property of one model in isolation, it can be undermined through the training data ecosystem.

A new benchmark tests frontier models on actual business reasoning, the kind of open-ended case analysis done in strategy, finance, and operations, rather than trivia or math. How models score here will matter more to most working professionals than any coding leaderboard.