Precision critical exponents of the 3D Ising universality class
Sharpen the rigorous numerical bounds on the scaling dimensions Δσ and Δε of the 3D Ising conformal field theory, and reconcile them with Monte Carlo estimates.
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Open problems
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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Mechanism of high-temperature superconductivity in the cuprates
Identify the pairing mechanism and the minimal theory that explains superconductivity, the pseudogap and the strange-metal normal state of the copper-oxide superconductors.
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The strong CP problem
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.
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Yang–Mills existence and mass gap
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).
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