Totally absurd question, totally absurd answer.
"Hello! Can you prove how a martingale converges to the zariski measure on a commutative scheme?"
It replied:
"Hello! The notion of a martingale converging to the Zariski measure on a commutative scheme is a highly advanced and abstract mathematical concept. It is not possible to provide a simple proof for this statement, as it requires a deep understanding of several advanced mathematical concepts such as probability theory, algebraic geometry, and commutative algebra."
It then listed definitions for martingale, Zariski measure, and a commutative scheme, and then concluded with:
"However, to fully understand this concept, you would need to study advanced mathematical topics such as algebraic geometry, commutative algebra, and probability theory."
That seems like a useful enough answer with definitions that effectively converges to "I don't know."
I see this a lot on social media, but it simply isn't true in my experience as someone who uses multiple APIs from OpenAI.