Kissing numbers (AlphaEvolve problem 8)
Kissing numbers (AlphaEvolve problem 8). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
For a dimension , define the kissing number to be the maximum number of non-overlapping unit spheres that can be arranged to simultaneously touch a central unit sphere in -dimensional space. Establish upper and lower bounds on that are as strong as possible.
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Repository result category: world record — AlphaEvolve improved on the best known result recorded at the time. See Section 6.4 in "Mathematical Exploration and Discovery at Scale" paper: arXiv:2511.02864.
Progress & source assessment
Henry Cohn maintains a list of record upper and lower bounds for kissing numbers.
Some new kissing number constructions in medium dimensions were recently constructed (with AI assistance) in this recent paper.
- [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Kissing numbers (AlphaEvolve problem 8) linkApache-2.0 (repository license); problem pages reproduced with attribution.
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
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Discussion
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