Especially since it's a recursive problem so each step is naturally broken up into subtasks. And the algorithm of what subtasks to break it up in to is public. This makes it much easier for it to get down to a case that the LLM can reliable solve.
I guess that the subtask decomposition of many (sub)problems is known and in the training distribution. How many real-world problems are resistant to divide-and-conquer? Presumably most/all of the unsolved mathematics conjectures. What else?
