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.