Progress in Formalizing Sphere Packing in Dimension 8
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914617356189696 |
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| author | Hariharan, Sidharth Birkbeck, Christopher Lee, Seewoo Ma, Ho Kiu Gareth Mehta, Bhavik Poiroux, Auguste Viazovska, Maryna |
| author_facet | Hariharan, Sidharth Birkbeck, Christopher Lee, Seewoo Ma, Ho Kiu Gareth Mehta, Bhavik Poiroux, Auguste Viazovska, Maryna |
| contents | In 2016, Viazovska famously solved the sphere packing problem in dimension $8$, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 2003. In March 2024, Hariharan and Viazovska launched a project to formalize this solution and related mathematical facts in the Lean Theorem Prover. A significant milestone was achieved in February 2026: the result was formally verified, with the final stages of the verification done by Math, Inc.'s autoformalization model 'Gauss'. We discuss the techniques used to achieve this milestone, reflect on the unique collaboration between humans and Gauss, and discuss project objectives that remain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23468 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Progress in Formalizing Sphere Packing in Dimension 8 Hariharan, Sidharth Birkbeck, Christopher Lee, Seewoo Ma, Ho Kiu Gareth Mehta, Bhavik Poiroux, Auguste Viazovska, Maryna Metric Geometry Artificial Intelligence Logic in Computer Science Number Theory In 2016, Viazovska famously solved the sphere packing problem in dimension $8$, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 2003. In March 2024, Hariharan and Viazovska launched a project to formalize this solution and related mathematical facts in the Lean Theorem Prover. A significant milestone was achieved in February 2026: the result was formally verified, with the final stages of the verification done by Math, Inc.'s autoformalization model 'Gauss'. We discuss the techniques used to achieve this milestone, reflect on the unique collaboration between humans and Gauss, and discuss project objectives that remain. |
| title | Progress in Formalizing Sphere Packing in Dimension 8 |
| topic | Metric Geometry Artificial Intelligence Logic in Computer Science Number Theory |
| url | https://arxiv.org/abs/2604.23468 |