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arXiv:1603.04246math.NT

The sphere packing problem in dimension 8

Maryna Viazovska

Abstract

In this paper we prove that no packing of unit balls in Euclidean space $\mathbb{R}^8$ has density greater than that of the $E_8$-lattice packing.

arXiv comments
22 pages, 2 figures
Journal reference
Annals of Mathematics, Pages 991-1015 from Volume 185 (2017), Issue 3
DOI
doi:10.4007/annals.2017.185.3.7
Subjects
math.NTNumber Theory math.MGMetric Geometry

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Linked by 2 identifiable commenters in 2 comments across 2 threads, from Mar 2016 to Jul 2022. Found in 1 HN submission from Jun 2026 to Jun 2026. Open submission discussions.

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Discussed in comments2 threads

  1. Fields Medals 2022 1 comment
    • No no no, she is legit, no doubt here. She was a star way before the current events. She solved a long-standing open problem in fundamental maths. This is the holy grail in maths research. The main resulting paper is single-author, so there is no doubt who did the work. She got…

      stnclsView on HNParent context

    • The paper [0] was linked, the article gave context to the problem and outlined the approach. What more do you want? [0] http://arxiv.org/abs/1603.04246

      ecmaView on HNParent context

Submitted to Hacker News

  • Show HN: Glq LLM quantization using E8 lattice

    I have with the help of AI create an open source method of E8 LLM code book quantization library called glq. I was interested in creating Glq as a PC gamer and devops, interested in both LLMs and AI. The current high RAM prices and LLM resource usage also inspired me to write glq. A question arises could you try and squeeze more out a gaming GPU with limited VRAM size by using alternative LLM compression methods? Glq is effective compared to other LLM quantization algorithms at between 2-bits…

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