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1011 problems

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.

All fields Mathematics 10Computer science 5Physics & astronomy 6Chemistry & materials 2Life sciences 1Earth & society 2
Combinatorics 3Number theory 2Graph theory 1Algebra 1Geometry 1Analysis 2
Source Any Curated here 1
Verification AnyA · Machine-checkableB · ReproducibleC · Reviewed Tier AnyStandardHardGrand challenges

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C Hard Algebra

The Jacobian conjecture in two variables

Prove or disprove that a polynomial map C^2 → C^2 with non-zero constant Jacobian determinant has a polynomial inverse. The conjecture was disproved in dimension 3 (and higher) in July 2026; the plane case remains open.

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