#lean

Anthropic set dozens of Claude agents loose on Fermat's Last Theorem. They wrote 13 million lines of Lean, proved 30,300 theorems, and burned 6 billion tokens — with humans offering only the occasional nudge.

A public Anthropic Lean repository contains a complete formalization of a classical Fermat's Last Theorem proof route, which mathematician Kevin Buzzard says compiles and checks.

The AI Adoption Playbook for Lean Startup Teams: Ship Smarter, Not Harder Look, I’m going...

introduction: Understanding the Quran in its original language is a goal every Muslim aspires to...

leanblueprint methodology adoption on a real Rei stack subset (STEP 614-624 THE_THEOREM chain, 48 theorems, zero sorry). Archival preservation redundancy tier: ZERO new IP claim beyond wrapping existing GitHub-public content and Paper 55 GitHub Release collatz-proof-v1 in leanblueprint format. Zenodo DOI 10.5281/zenodo.22051191 (working paper, close). Three-party co-authorship per OUKC charter v1.0.

TL;DR I want to hand an AI agent a multi-day job and have it run to completion. This post...

If you've ever argued about whether your team should be doing value stream mapping or process...

Learn how to combine Lean 4 for formal verification of AI logic with ClickHouse for real-time analytics, creating a robust, verifiable, and high-performance AI infrastructure.

The Real Story Isn't the Proofs—It's the Price Tag OpenAI just dropped ten solved open...

OpenAI's Astra solved 10 open problems for $2,000: the lesson is the verifier Summary. On...

Chapter 3 of OpenAI's new manuscript claims to have constructed a non-sofic group, settling a long-open question, and ships roughly 34,000 lines of Lean code with no unproved placeholders so outsiders can verify it.

v0.1 (2026-07-30) first formal Paper 176 publication. Empirical measurement of v_2(omega_{F_n}(3)) for n = 5..11 with excess above Lucas 1878 lower bound n+2. Excess sequence 0,0,0,1,5,0,0 is highly irregular. F_9 excess=5 driven by small factor 2424833 = 37 * 2^16 + 1 whose v_2(p-1) = 16 (max of three factors). Characterization excess = v_2(k) where p_max = k * 2^(n+2) + 1 matches 7/7 in range n = 5..11 when driving factor satisfies v_2(ord_p(3)) = v_2(p-1). Lean 4 axiom-free F_9 divisibility witness: 2424833 divides F_9 = 2^512+1 via Pratt-style iterative squaring sqIterMod k = 2^(2^k) mod 2424833, kernel-verified sqIterMod 9 = 2424832 ≡ -1 mod 2424833. This §7 replaces external Selfridge-Hurwitz 1963 attribution with Lean-internal kernel-verified computation; native_decide NOT used = Lean.ofReduceBool axiom NOT added. 44 axiom-free theorems combined (26 FermatNineExcessWitness + 18 ZcsgMdnstModularBoundary STEP 1306). Zero sorry, zero native_decide, zero user axioms. Refutes §7 hypothesis 'n-monotonic function predicts excess' at n=9 (excess=5 while n=10,11 return to excess=0). Honest positioning (6 non-claims): (1) No world-first — Lucas 1878 + Selfridge-Hurwitz 1963 + Euler/Landry/Morrison/Brent-Pollard/Lenstra/Brent factor discoveries prior art; Rei differentiator = specific n=5..11 empirical table + Lean 4 axiom-free F_9 witness (Pratt-style replacement) + 7/7 characterization within bounded range. (2) No claim Fermat compositeness resolved. (3) No claim excess unbounded — 7/7 in n=5..11 does not imply anything about n → ∞. (4) No claim ZCSG/MDNST containers refuted (only specific §7 monotonic hypothesis refuted). (5) No claim SELF-loop = multiplicative order (chat-Claude 2026-07-20 syntactic resemblance noted but formal identity explicitly rejected per evaluation symmetry principle). (6) No claim Pratt-style Lean 4 proof scales beyond small kernel arithmetic (F_n n ≥ 12 not asserted). Zenodo v0.1 DOI 10.5281/zenodo.21694136. Three-party co-authorship per OUKC charter v1.0.