> This obviously raises the question of how LLMs can now routinely solve open mathematical problems

Because many open math problems can be solved by synthesizing two disparate ideas and then cranking the handle for hours and hours. I don't think applying idea X + idea Y to identify a good subset of the search space, and then exhaustively searching that subset, is --necessarily-- a process that involves reasoning. I think this is why so many LLM results in mathematics are counterexamples that disprove open conjectures.

When I look back at the reasoning process after an LLM completes a task where I expected it to fail, I usually find many approaches that make no sense and are doomed to failure, before it lands by drunkard's walk on a method that happens to work.

(This does not mean LLMs are useless or that I necessarily agree with the claim that they never do reasoning.)