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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Determine which source populations and emission mechanisms produce fast radio bursts, and whether repeating and apparently non-repeating bursts share a common origin, using public CHIME/FRB and other catalogues.
Identify the pairing mechanism and the minimal theory that explains superconductivity, the pseudogap and the strange-metal normal state of the copper-oxide superconductors.
Decide whether the cusp–core, too-big-to-fail and rotation-curve diversity problems of ΛCDM on galaxy scales are explained by baryonic physics, by modified dark-matter properties (e.g. self-interactions), or by observational systematics.
Explain why the lithium-7 abundance observed in old metal-poor halo stars is a factor of about 3–4 below the prediction of standard Big Bang nucleosynthesis with the CMB baryon density.
Determine which physical mechanisms heat the solar corona to millions of kelvin above a photosphere of about 5,800 K, and in what proportion, using public spacecraft data and simulations.
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.
Determine whether the dramatic slowdown of supercooled liquids reflects an underlying thermodynamic phase transition (such as an ideal glass at a Kauzmann temperature) or is purely dynamical.
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).
