{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-03-01-gauss-sphere-packing-formalization/","md":"https://postcutoff.com/e/2026-03-01-gauss-sphere-packing-formalization/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-03-01-gauss-sphere-packing-formalization","date":"2026-03-01","date_precision":"month","short_title":"Math Inc's Gauss formalises Viazovska's sphere-packing proofs in dimensions 8 and 24, fixing errors in the originals","deck":null,"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.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Formalizing sphere packing in dimensions 8 and 24 (arXiv 2604.23468)","url":"https://arxiv.org/abs/2604.23468","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"GitHub: math-inc/Sphere-Packing-Lean","url":"https://github.com/math-inc/Sphere-Packing-Lean","type":"code","group":"primary","domain":"github.com"}],"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Math Inc"],"title":"Math Inc's Gauss formalises Viazovska's sphere-packing proofs in dimensions 8 and 24, fixing errors in the originals","summary":"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"],"key_numbers":[],"tags":["math","lean","formalization","sphere-packing"],"science":{"field":"mathematics","subfield":"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.","open_since":"","ai_system":["Gauss"],"human_role":"AI-assisted: agent built on a human-started blueprint project","verification":{"key":"lean","label":"Lean-verified","text":"Formal proof in Lean"},"status":"confirmed","shock":"Weeks of agent time formalised a Fields-Medal proof and caught errors that human referees had missed."},"body_md":"## What happened\n\nGauss took over a partial human Lean project on sphere packing and finished both dimensions, reporting the errors it found in the literature.\n\n## Why it matters\n\nAI autoformalization reached Fields-Medal-level proofs, strengthening the case that formal verification can keep up with the flood of AI-generated mathematics.","disputed":[],"related":[{"id":"2026-09-04-claude-formalizes-fermats-last-theorem","url":"https://postcutoff.com/e/2026-09-04-claude-formalizes-fermats-last-theorem/","date":"2026-09-04","date_precision":"day","short_title":"Claude produces the first complete machine-checked proof of Fermat's Last Theorem in Lean, in 11 days","deck":null,"takeaway":"Formalising FLT had been a flagship multi-year human project.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":4,"official":2,"filed":"2026-09-29","updated":"2026-11-09","orgs":["Anthropic"]},{"id":"2025-09-10-math-inc-gauss-strong-pnt","url":"https://postcutoff.com/e/2025-09-10-math-inc-gauss-strong-pnt/","date":"2025-09-10","date_precision":"day","short_title":"Math Inc's Gauss agent completes the Strong Prime Number Theorem formalisation in Lean in three weeks","deck":null,"takeaway":"Autoformalization at this scale points to a future where new proofs, including AI-generated ones, are routinely machine-checked.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":3,"official":3,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Math Inc"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-09-29","human_review":null,"version":{"date":"2026-10-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":"https://postcutoff.com/s/math-inc-gauss-formalises"}