# Yang–Mills existence and mass gap

- kind: problem
- status: open
- year: 2000
- authors: Clay Mathematics Institute, after Yang and Mills (1954)

**Statement.** Prove that quantum Yang–Mills theory exists rigorously in four dimensions and has a positive mass gap.

Physicists compute with Yang–Mills theory every day, and lattice simulations show the gap clearly. Nobody can yet construct the theory with mathematical rigor. It is a physics problem whose resolution would be a theorem.

Posed 2000, Clay Mathematics Institute, after Yang and Mills (1954).

## Prize

$1,000,000 Clay Millennium Prize

## Sources

- [Wikipedia: Yang–Mills existence and mass gap](https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap)

[The Standard Model's loose ends](/wiki/Space:standard-model.md) · [Physics](/wiki/Continent:physics.md)

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