Lean (theorem prover)

2026-10-27

RESEARCH · 2 SOURCES · The Decoder · TechCrunch AI

OpenAI asks outside experts to vet AI-produced proofs that claim to disprove the Exponential Time Hypothesis

OpenAI says internal models produced manuscripts including a claimed disproof of the Exponential Time Hypothesis (ETH) and a partial result related to a Millennium Prize Problem. The company published the raw writeups and Lean formalizations, is funding independent review, and has asked outside experts (including a Nobel laureate) to act as "shepherds" to check and interpret the proofs.

9.0

2026-10-12

RESEARCH · 1 SOURCE · The Decoder

DeepMind's AlphaProof Nexus (using Gemini 3.1 Pro) solved dozens of open math problems, Science paper

A DeepMind system called AlphaProof Nexus, built around Gemini 3.1 Pro and using the Lean proof assistant (and optionally the specialized AlphaProof tool), produced formal proofs that the authors report solved dozens of open problems: nine of 353 open Erdős problems (two unsolved for 56 years), 44 conjectures from the OEIS, an open question in algebraic geometry, and an improved bound in min-max optimization; the team shared solutions online and published a peer-reviewed paper in Science. DeepMind says the nine Erdős solutions were found even without the AlphaProof specialist tool.

9.0

2026-10-07

RESEARCH · 3 SOURCES · OpenAI · The Verge AI · The Decoder

OpenAI publishes mathematics results from internal frontier model and posts Lean formalizations on GitHub

OpenAI published new results on open problems in mathematics obtained using an internal frontier model, and released Lean proof formalizations and related research details on GitHub. The release shares artifacts and documentation intended to enable verification and follow-up by the research community.

8.0

2026-09-24

RESEARCH · 1 SOURCE · arXiv cs.AI

GPT-5.6‑Sol generates provably complete generalized plans with Lean proofs

The arXiv preprint (arXiv:2609.27105v1) presents a pipeline that converts PDDL domain specifications into Lean, then uses GPT-5.6‑Sol to generate generalized plans and formal completeness proofs checked by Lean's kernel. Evaluated on 13 standard benchmark domains, the approach produced generalized plans with valid completeness proofs for 12 domains.

8.0

2026-09-08

RESEARCH · 1 SOURCE · OpenAI

OpenAI shares an AI-generated writeup and Lean formalization claiming a solution to the Navier–Stokes Millennium Prize Problem

OpenAI has shared an AI-generated writeup that claims a solution to the Navier–Stokes Millennium Prize Problem and published a formal proof encoded in the Lean theorem prover. The correctness and community acceptance of the claim remain to be independently verified.

9.0