Viazovska's optimal sphere packing theorem in dimension 8 has been fully formalized in Lean, with the final stages completed by Math, Inc.'s autoformalization model Gauss.
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Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical practice, and to respond appropriately to the challenges and opportunities we now face.
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Progress in Formalizing Sphere Packing in Dimension 8
Viazovska's optimal sphere packing theorem in dimension 8 has been fully formalized in Lean, with the final stages completed by Math, Inc.'s autoformalization model Gauss.