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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Combine public NICER pulse-profile posteriors, gravitational-wave tidal-deformability constraints and pulsar masses into reproducible, well-calibrated constraints on the neutron-star equation of state.
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.
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.
Explain why local distance-ladder measurements of the Hubble constant H0 disagree with the value inferred from the cosmic microwave background under ΛCDM, or show that the disagreement is systematic.
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.
