This is one of the seven
Millennium Prize Problems proposed by the
Clay Mathematics Institute in April 2000.
Almost half a century ago Yang and Mills discovered that
quantum physics reveals a remarkable relationship between the physics of elementary
particles and the
mathematics of
geometric objects. Although the theory has been verified in
particle accelerators all over the world, there are no mathematically
rigorous solutions to the governing equations for
massive particles. In particular, the Mass Gap hypothesis has never received satisfactory justification. The Millennium Problem is concerned with resolving this.