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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.

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