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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Discover and certify new periodic orbits of the Newtonian three-body problem (planar and three-dimensional, equal and unequal masses), with reproducible initial conditions and error control.
Determine reliably, with controlled numerics, where the doped two-dimensional Hubbard model (with and without next-nearest-neighbour hopping t′) is superconducting, striped or otherwise ordered.
Resolve the disagreement between lattice-QCD and data-driven (e+e− → hadrons) evaluations of the leading hadronic vacuum polarisation contribution to the muon anomalous magnetic moment.
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.
