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 accelerator
s 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.