Math Inc's Gauss formalises Viazovska's sphere-packing proofs in dimensions 8 and 24, fixing errors in the originals
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. Along the way it found and fixed a sign error and an incomplete step in the published proofs.
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
Science result
- Field
- mathematics / discrete geometry / formal verification
- Problem
- Formal verification of optimal sphere packing in dimensions 8 and 24 (Viazovska 2016; Cohn–Kumar–Miller–Radchenko–Viazovska 2017)
- Result
- Complete Lean formalisations of both theorems, correcting minor errors in the published proofs.
- AI system
- Gauss
- Human role
- AI-assisted: agent built on a human-started blueprint project
- Verification
- Formal proof in Lean
- Status
- confirmed
- Why surprising
- Weeks of agent time formalised a Fields-Medal proof and caught errors that human referees had missed.
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.
Changelog
- 2026-09-29: created
Related events
- Math Inc's Gauss agent completes the Strong Prime Number Theorem formalisation in Lean in three weeks ★★★★
- Claude produces the first complete machine-checked proof of Fermat's Last Theorem in Lean, in 11 days ★★★★★
Sources (2)
- paperFormalizing sphere packing in dimensions 8 and 24 (arXiv 2604.23468)
- codeGitHub: math-inc/Sphere-Packing-Lean
id: 2026-03-01-gauss-sphere-packing-formalization · updated 2026-09-29 · open in the interactive timeline