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.
3 shown
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.
