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 12 Computer science 4

Combinatorics 6 Number theory 1 Graph theory 2 Geometry 2 Logic & formalisation 1

Source Any Curated here 2 Formal Conjectures (Lean) 39

Verification Any A · Machine-checkable B · Reproducible C · Reviewed Tier Any Standard Hard Grand challenges

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A Geometry

Kissing configurations in dimensions 10–31

Find sphere arrangements that improve the best known lower bounds on kissing numbers in selected dimensions.

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A Hard Geometry

The kissing number in dimension 5

Determine τ5, the maximum number of non-overlapping unit spheres touching a central unit sphere in R^5. Currently 40 ≤ τ5 ≤ 44.

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