Some problems are characterized by many mathematicians as exceptionally challenging, to the point that there are currently no known methods or branches of mathe

Some problems are characterized by many mathematicians as exceptionally challenging, to the point that there are currently no known methods or branches of mathematics capable of addressing them. For these issues, it is often proposed that a entirely new branch of mathematics needs to be developed to effectively address these types of challenges. And then there are other problems for which progress has been made over the past decades. At times, a weaker version may have been proved. Occasionally, new ideas emerge in the field regarding how to advance effectively. An upper or lower bound may be identified and gradually improved over time. Of course, while no one can predict the future, making an educated guess is of course interesting. I would appreciate it if Terry could share his thoughts on such estimates.