I told Gemini Pro I woke up after having dreamt that polynomial and asked if it was related to the Jacobian conjecture. It spent some time thinking and referenced this tweet announcement, saying:

"If you truly dreamt about that specific polynomial, you might be mathematically clairvoyant."

In the rest of the answer, it maintained a cautious skepticism about my claim, saying:

"Here is exactly why the math world is currently scrambling to verify the polynomial you "dreamt" about."

I love how it put "dreamt" in quotes.