01
The problem
For every compact simple gauge group, construct a non-trivial quantum Yang–Mills theory on four-dimensional space that satisfies the official axioms and has a positive mass gap.
Date noteYang–Mills theory began in 1954; the precise prize problem used for age sorting was formulated in 2000.
Open since2000canonical formulation
Last checked2026.07.26Catalog verification
02
Reward offers
Offer 01$1,000,000Clay Mathematics Institute
InstitutionalClay does not accept direct submissions. A proposed solution must be published in a qualifying outlet, at least two years must pass, and the work must gain general acceptance in the mathematics community while resolving the complete official formulation.