OpenAI published a paper claiming an unreleased model coordinated up to 10,000 AI agents over 88 hours to produce a formal Lean proof addressing the Navier-Stokes existence and smoothness Millennium Prize Problem. The company says the proof identifies conditions under which the equations develop a mathematical singularity, not evidence that real fluids behave impossibly. Outside mathematicians have yet to verify the claim.
techspot.com
· 2026-09-09
OpenAI says an internal AI model, more capable than GPT-6 Astra, generated a solution to part of the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. The proof demonstrates that three-dimensional incompressible fluid dynamics governed by these equations can develop a singularity—unbounded speed growth—in finite time, even from smooth initial conditions. OpenAI released both a written explanation of the proof and a formal verification built in the Lean proof assistant.
openai.com
· 2026-09-08
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.
danluu.com
· 2026-09-08
Mathematicians Wang and Wu of Hunan University released a preprint proving the Spherical Hadwiger Conjecture, an integral-geometry problem unsolved since 1974, using OpenAI Codex to help develop proof details, spot gaps, and draft the manuscript. The authors say they verified all AI-generated mathematical content themselves and take full responsibility for the final result, following disclosure practices similar to the Leiden Declaration guidelines for AI use in research.
mbmccoy.dev
· 2026-09-06
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.
github.com
· 2026-09-04
Anthropic researcher Tianyi Peng tested whether the Claude AI model could formalize Fermat's Last Theorem in the Lean proof assistant, and over 11 days of largely autonomous work, Claude generated an end-to-end, machine-checked proof. The system wrote roughly 13 million lines of Lean code and proved about 29,500 intermediate theorems, building on decades of prior work including Andrew Wiles's 1995 proof and a community formalization effort led by Kevin Buzzard since 2024.
anthropic.com
· 2026-09-04
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.
github.com
· 2026-09-03
GoKawiil