PPL 177 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerInstitutionalPPL 177Yang–Mills existence and mass gap

Permanent problem IDPPL 177

Verified openInstitutionalexistence

Mathematical physics

Yang–Mills existence and mass gap

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.

quantum field theorygauge theoryanalysis
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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
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Reward offers

Offer 01$1,000,000Clay Mathematics Institute
Institutional

Clay 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.

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Sources & reading