Reading What topics can I ask about here?, it's unclear whether this kind of question is on-topic or not.
Here is my draft question:
The Fermat's Last Theorem took 358 years of effort to prove. It's a famous problem, no one doubts it, but I wonder whether it gained a large amount of attention largely because of the popularity of Fermat and his margin story, or because it plays an important role in math per se. Yes, it's hard, and it stimulated the development of algebraic number theory and the proof of the modularity theorem, but this doesn't guarantee its importance. I guess there are many other conjectures out there that are as hard or as important as it, but they don't gain much attention like this one.
So is there a way to know its importance in math? I'm not sure how "importance" should be defined and measured, but I propose that it's the number of problems/papers using it in the proof of a different problem, in contrast with the number of proofs/papers trying to prove it.