1011 problems

Open problems

Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.

All fields Mathematics 4 Computer science 2 Physics & astronomy 1

Theoretical physics 1

Source Any Curated here 1

Verification Any A · Machine-checkable B · Reproducible C · Reviewed Tier Any Standard Hard Grand challenges

1 shown

C Grand challenge Theoretical physics

Yang–Mills existence and mass gap

Prove that for every compact simple gauge group a non-trivial quantum Yang–Mills theory exists on R^4 and has a mass gap Δ > 0 (Clay Millennium Prize Problem).

0claims

0verified

Yang–Mills existence and mass gap

Browse by field