Obviously, it is a bit early to judge the quality, accuracy and proofreading of OAI recent result, but assuming that their claims hold the ground and that many problems are indeed solved: which next advancements, “phases” or problems in the math get unlocked now?

I am not a mathematician, but I would assume that those problems were in focus of the scientists and mathematicians for a reason, and now we should expect certain new results on the ground of that breakthrough?