This came as a result of reading this document relating to the prompt of the jacobian conjecture. I attach a picture of page-2:
As can be seen there seems to be some nuance into how the prompt is constructed, it just didn't go "go solve this problem". So, I'd like to think there is a meta level "art" to prompting an AI to think about solving a math problem, and that maybe this meta level thinking capabilities are something that mathematicians can abstract much more easier than AI can at this point.
Hence, my question, what are some observations you have made in your own experiments with AI in mathematics research related to prompting? or maybe even before that, how much of a scope exists in this?
source & further reading
mathoverflow.net — original article
Do people actually believe Jacob Tsimerman (or is he just cashing out the fields medal)?
Examples for use of AI and especially LLMs in major mathematical developments
What does one do when one accidentally stumbles upon an LLM-generated counterexample to a conjecture far outside one’s area of expertise