GoKawiil
Tech News
Alongside its human-readable proof resolving a longstanding Navier-Stokes question, OpenAI also released a machine-checkable Lean 4 formal proof, completed in about 17 hours. The author contrasts this with historical estimates that formalizing research-level math could take tens of thousands of person-hours by hand.
A researcher evaluated 26 different prompt conditions—ranging from 'use TDD' to formal methods like Lean 4, TLA+, and SMT solvers—to see whether simply instructing coding agents to apply specific testing techniques or libraries improves the correctness of Rust implementations of Zstd. Four popular testing 'skills,' including ones with hundreds of thousands of GitHub stars, were also tested alongside a self-written skill, using the same Zstd benchmark from prior agentic programming comparisons.
A complete formalization of Fermat's Last Theorem has been written and verified in the Lean 4 proof assistant, built atop the Mathlib library and following the Frey-Serre-Ribet-Wiles-Taylor-Wiles argument. The repository builds all 60,475 modules from scratch, with every declaration checked by the Lean kernel, and the final theorem relies solely on Lean's three standard axioms rather than any sorry or added axiom. An independent tool, leanprover/comparator, confirmed the proved statement matches a separately stated Mathlib-only challenge and that the entire proof chain replays correctly.
A new repository presents a Lean 4 formal proof deriving the bound liminf(p_{n+1}-p_n) ≤ 186 for consecutive primes, building on the Maynard-Tao style DHL[40,2] admissible-tuple framework. The proof chain is conditional on three explicit input axioms covering Kloosterman sum bounds and related estimates, which have not themselves been formalized as Lean proofs despite being backed by established results like Deligne's theorem via Katz's monograph.