Sphere Packing Problem in Dimension 8 Formally Verified in Lean
Maryna Viazovska addressed the sphere packing challenge in eight dimensions in 2016, employing modular forms to create a 'magic' function that met the optimality criteria established by Henry Cohn and Noam Elkies in 2003. In March 2024, she, alongside Nivedita Hariharan, initiated a project aimed at formalizing this solution within the Lean Theorem Prover. A significant achievement occurred in February 2026 when the result received formal verification, with the concluding phases accomplished by the autoformalization model 'Gauss' from Math, Inc. This endeavor showcases a distinctive partnership between human intellect and artificial intelligence, with additional goals still to be pursued.
Key facts
- Maryna Viazovska solved the sphere packing problem in dimension 8 in 2016.
- The solution used modular forms to construct a 'magic' function.
- Optimality conditions were determined by Cohn and Elkies in 2003.
- Hariharan and Viazovska started a formalization project in March 2024.
- The formal verification was achieved in February 2026.
- Math, Inc.'s model 'Gauss' completed the final verification stages.
- The project uses the Lean Theorem Prover.
- The collaboration between humans and Gauss is described as unique.
Entities
Artists
- Maryna Viazovska
- Nivedita Hariharan
- Henry Cohn
- Noam Elkies
Institutions
- Math, Inc.