Math Inc’s Gauss formalises Viazovska’s sphere-packing proofs in dimensions 8 and 24, fixing errors in the originals
Result confirmed
Importance: major (4 of 5)The takeaway
Math Inc’s Gauss agent completed the Lean formalisation of Maryna Viazovska’s Fields-Medal proofs of optimal sphere packing in dimensions 8 (5 days) and 24 (~2 weeks), about 180,000 lines.
Status
- Claim
Result confirmed
- Our reporting
- High confidence
- Verification
- Lean-verified
- Importance
- Major (4 of 5)
- Last verified
- 29 September 2026
Your AI and this story
- GPT-6 AstraIn its training data
- Claude Opus 5.5In its training data
- Gemini 4 HydrogenIn its training data
- Grok 4.7In its training data
It happened before the cutoffs of all four assistants, so it can be in their training data.
Key facts
- Dimension 8: 5 days, code grew from ~20k to ~60k lines; dimension 24: ~2 weeks
- Final code ~180k lines (some sources say ~200k)
- Found a sign error in Proposition 7 (dim 8) and an incomplete step in Appendix A (dim 24)
- Write-up arXiv 2604.23468; exact announcement day not verified
What happened
Gauss took over a partial human Lean project on sphere packing and finished both dimensions, reporting the errors it found in the literature.
Why it matters
AI autoformalization reached Fields-Medal-level proofs, strengthening the case that formal verification can keep up with the flood of AI-generated mathematics.
Sources
2 sources from 2 sites. Numbers match the chips in the text.
2 sources: 2 primary
Primary
- Formalizing sphere packing in dimensions 8 and 24 (arXiv 2604.23468)arxiv.org, paper
- GitHub: math-inc/Sphere-Packing-Leangithub.com, code
Changes
- Filed