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

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)?

(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.

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To demonstrate it and win the $1 million from the Clay Institute, she has to define the quantum field theory at a rigorous mathematical level and master much of its physics in an equally rigorous way. So it's a good, simple enough to be formulated, mathematical problem whose solution would bring mathematicians' mastery to a higher level. At the same moment, the paper that would win the$1 million award would almost certainly not be very important for physicists. Physicists have found lots of complementary ways and insights that made them sure that the mass gap exists. Harboring doubts about the mass gap or trying to "totally" eliminate these doubts is simply not what theoretical physicists in this discipline spend most of their man-hours.