Similar to the story of George Dantzig, who was late to class and solved two open problems in statistics because he mistook them for homework, I think the current batch of frontier LLMs are chained up by knowing which problems are supposed to be unsolved. If they're let free (probably via some targeted RLHF) we might get a flurry of solutions to open problems.
But a property of intelligence is to know when to stop, if we treat intelligence as some sort of search and not some a priori intuition of the entire space. Seems kind of hard, if not impossible, to train for specifically that.