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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 19Computer science 5Physics & astronomy 10Chemistry & materials 10Life sciences 4Earth & society 4
Algorithms 1Computability 1Optimisation 2Machine learning 1
Source Any Curated here 1Optimization constants 2AlphaEvolve problems 1
Verification AnyA · Machine-checkableB · ReproducibleC · Reviewed Tier AnyStandardHardGrand challenges

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B Algorithms

Proof-producing SAT solving of open combinatorial instances

Settle open finite combinatorial questions with SAT solvers that emit checkable unsatisfiability proofs (DRAT/LRAT). Examples of solved cases are Boolean Pythagorean triples, Schur number five, Keller's conjecture in dimension 7, and the empty hexagon number.

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