Sphere packing is formal in dimensions 8 and 24
The Lean project Sidharth Hariharan and Maryna Viazovska started in March 2024 reached a sorry-free main theorem in February 2026, with the last stages closed by Math, Inc.'s autoformalization model Gauss — five days for dimension 8, and dimension 24's two hundred thousand-odd lines in about two weeks. A Fields-Medal proof from 2016 is now machine-checked end to end.
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The Lean project Sidharth Hariharan and Maryna Viazovska started in March 2024 reached a sorry-free main theorem in February 2026, with the last stages closed by Math, Inc.'s autoformalization model Gauss — five days for dimension 8, and dimension 24's two hundred thousand-odd lines in about two weeks.
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A Fields-Medal proof from 2016 is now machine-checked end to end.
- 01EPFL
- 02IEEE Spectrum
- 03Sphere-Packing-Lean