About this episode
We unpack Marina Viazovska’s landmark proofs that the E8 lattice in eight dimensions and the Leech lattice in twenty-four dimensions realize the densest sphere packings, and then examine the leap from human insight to machine-checked certainty via Lean4. The auto-formalization agent Gauss wrote the formal arguments—five days for the eight-dimensional case and two weeks for the twenty-four-dimensional case—building a 200,000+ line codebase that's verified by the Lean kernel. This episode explores the symmetries that make these dimensions special, the role of humans in guiding AI, and what this collaboration could unlock in the future.
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