Why is the Yang–Mills existence and mass gap problem so fundamental?

Ref: Yang–Mills existence and mass gap

Can anyone please explain why the Yang–Mills Existence and Mass Gap problem is so important / fundamental to contemporary mathematics (and, presumably, theoretical / mathematical physics)?

If possible, please include the following in your answer / response:

(1) Why the problem is so fundamental / important - for both mathematics and theoretical / mathematical physics; (2) How the solution to the problem would impact research in the above two fields; (3) (If applicable) What progress has been made so far in resolving it; (references to papers, books, other resources would be helpful).

I'm an upper-level undergraduate in theoretical physics, and so am seeking an answer / response at such level.