Yes mathematicians chose problems for the LLM to solve, and then the LLM solved them. That's how we know they were good open problems and that this is research level math.
The LLMs generated candidate solutions which were evaluated by a scoring function written by hand by the mathematicians. No LLM produced these results by itself
Yes, some good ones and some garbage, and the LLMs had no idea which was which. The good solutions were arrived at by an iterative procedure which depended on the scoring function written by the mathematicians, and it seems plenty of other ingenuity besides.
It's a fascinating use of LLMs by mathematicians to produce new results, but the LLMs are just one component of the tools used to get the results.
