TL;DR
This paper reports on the formal verification of the 2016 solution to the sphere packing problem in dimension 8, using Lean Theorem Prover and autoformalization techniques, marking a significant milestone.
Contribution
It presents the first formal verification of the sphere packing solution in dimension 8, integrating human and AI-assisted formalization methods.
Findings
The solution was formally verified in February 2026.
Autoformalization with Gauss significantly contributed to the verification process.
The project demonstrates effective collaboration between humans and AI in formal mathematics.
Abstract
In 2016, Viazovska famously solved the sphere packing problem in dimension , 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
