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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 12Computer science 1Physics & astronomy 5Chemistry & materials 2Life sciences 2Earth & society 2
Combinatorics 3Number theory 5Graph theory 2Algebra 1Analysis 1
Source Any Curated here 1
Verification AnyA · Machine-checkableB · ReproducibleC · Reviewed Tier AnyStandardHardGrand challenges

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B Hard Algebra

The inverse Galois problem over Q

Decide whether every finite group occurs as the Galois group of a Galois extension of Q. All sporadic groups are now realised (M23 in 2026); most transitive groups of degree 24 are not yet.

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