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.
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Identify the pairing mechanism and the minimal theory that explains superconductivity, the pseudogap and the strange-metal normal state of the copper-oxide superconductors.
Explain why the CP-violating θ parameter of QCD is experimentally smaller than about 10^-10 when nothing in the Standard Model requires it to be small.
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).
