Lean 4

Evidence (19)

• 4Hacker News·10/8/2026research
  OpenAI Preprint Draws Criticism Over Partition Principle Claim

  A mathematician criticizes an OpenAI preprint claiming that the Partition Principle does not imply the Axiom of Choice, arguing that the paper is unclear, poorly structured, and not presented at a standard expected for serious mathematical work. The post also raises broader concerns about how AI-assisted mathematics should be evaluated, cited, and disclosed in academic publishing.

• 3Hacker News·10/8/2026research
  OpenAI withdraws three formalized mathematical results

  OpenAI updated its GitHub math repository with six new Lean formalizations, 19 modifications, and three withdrawals. The repository now reports about 42% of its top-line results formalized, and the team said it will continue adding formalizations and correcting errata.

• 10Hacker News·10/7/2026breakthrough
  OpenAI-Reported Math Breakthroughs Include a Proof of the Unique Games Conjecture

  The post discusses a set of major mathematics results reportedly released by OpenAI, including a proof of the Unique Games Conjecture and other long-standing problems in complexity theory and algorithms. The author notes that the proofs appear formally certified in Lean, but that humans have not yet fully understood them and are beginning to verify the details.

• 6Hacker News·9/27/2026research
  TLA+ Gets Attention as a Tool for Agentic Coding

  This article explains TLA+ after a viral post highlighted its use in modeling and verifying parts of an AI coding agent workflow. It argues that TLA+ is a useful starting point for specifying system behavior, but that proof systems such as Verus and automated pipelines can extend verification from models to real programs.

• 7Hacker News·9/18/2026research
  AI-assisted proof of Conway's refinement conjecture

  A Hacker News post describes how the author used a frontier AI model and Lean to produce a proof of Conway’s refinement conjecture in surreal number theory. The proof has passed mechanical checks in the Palomar registry, but it has not yet been independently verified by mathematicians.

• 6Hacker News·9/17/2026open_source
  Bend language promises proof-checked AI code on CPU and GPU

  Bend is a new programming language and runtime that emphasizes fast compilation, parallel execution on CPUs and GPUs, and proof-based checks to prevent rule-breaking changes. The post highlights AGENTS.md guidance, a law/proof workflow, and claims that AI-generated code can be constrained to satisfy declared invariants before commit.

• 7Hacker News·9/10/2026research
  OpenAI Navier-Stokes release includes a Lean 4 proof

  The article says OpenAI’s Navier-Stokes release included a formal proof written in Lean 4, highlighting the use of theorem proving in a high-profile research release. The Hacker News discussion centers on the significance of combining AI research with machine-checked mathematical verification.

• 7Hacker News·9/6/2026research
  AI-assisted proof of the Spherical Hadwiger Theorem

  A preprint by Wang and Wu claims to prove the long-open Spherical Hadwiger Conjecture with AI assistance, specifically noting OpenAI Codex helped develop proof details, find gaps, and prepare the manuscript. The post frames this as another sign that AI is starting to affect research mathematics, even in niche areas with limited economic value and sparse training data.

• 6Hacker News·9/4/2026open_source
  Formalizing Fermat's Last Theorem in Lean 4

  A GitHub project presents a Lean 4 formalization of Fermat's Last Theorem, showing how the theorem can be represented and checked in a proof assistant. The item is notable mainly as an open-source mathematics and software verification effort rather than a new theorem result.

• 10Hacker News·9/4/2026breakthrough
  Claude Formalizes Fermat’s Last Theorem

  Anthropic says Claude autonomously produced the first end-to-end, computer-checked formal proof of Fermat’s Last Theorem in 11 days. The proof was written in Lean and involved millions of lines of code and tens of thousands of intermediate theorems, highlighting progress in AI-assisted formal verification for mathematics.

• 6Hacker News·8/19/2026research
  Terence Tao launches Palomar for Lean-verified mathematics

  Terence Tao announced Palomar, a registry for Lean-verified mathematics that accepts snapshots of external GitHub repositories. The system checks both the formal Lean proof and the informal description of the result, with mechanical validation via Lean and an LLM-based consistency check for the written summary.

• 6Hacker News·8/11/2026open_source
  Lean 4 faithfulness checker for theorem statements

  Leanscreen is an open-source faithfulness screen for Lean 4 that checks theorem statements for vacuity, misleading docstrings, and other defects the compiler accepts. It offers fast local linting as well as deeper checks with independent judges and counterexample probing, and it was benchmarked against 886 human verdicts.

• 4Hacker News·8/7/2026open_source
  Wyzer, a new resource-oriented programming language

  Wyzer is an early-stage statically typed, compiled programming language focused on resource-oriented programming and distributed safety. Its author says it aims to address distributed deadlocks, cross-service correctness, and protocol mismatches using choreographic programming, linear and affine types, and a Perceus-style reference counting model.

• 8The New Stack·8/1/2026breakthrough
  OpenAI Claims Ten Math Proofs with Astra

  OpenAI says an internal version of its next major model, Astra, solved ten long-standing mathematical problems with less than $2,000 in token cost per problem. The work includes Lean 4 formalizations, a paper describing the proofs, and an LLM-generated reconstruction of the reasoning process. The announcement has drawn attention from mathematicians and follows earlier reports of AI systems finding cryptographic weaknesses.

• 8Hacker News·8/1/2026security
  Lean kernel soundness bug #14576 fixed

  A soundness bug in the Lean kernel was reported after an AI-assisted claim of a Collatz disproof exposed a flaw in nested inductive type handling. The Lean team shipped a fix quickly, added regression tests, and noted that independent checking still works when both the main kernel and the external checker are up to date. The issue affected only a metaprogramming path and is described as an implementation bug rather than a flaw in Lean's theory.

• 4Hacker News·7/30/2026research
  Discussion on whether Lean has become the default proof assistant

  The Hacker News discussion links to a MathOverflow post asking whether the theorem prover Lean is becoming the standard choice for formal proof work. The thread focuses on Lean's ecosystem, adoption, and whether the field is converging around a single tool. It is a community discussion rather than a product announcement or technical release.

• 7Hacker News·7/28/2026research
  Formally Verified 3D CSG Mesh Intersection in Lean 4

  This project presents what is claimed to be the first formally verified implementation of a 3D constructive solid geometry mesh intersection kernel, built in Lean 4 and checked against a short formal specification. It is also positioned as a way to rely on machine-checked proofs rather than trusting AI-generated implementation code, with a browser demo running the verified kernel in WebAssembly.

• 6Hacker News·7/26/2026research
  LLMs May Automate Proofs in Dependently Typed Languages

  The article argues that large language models, combined with proof irrelevance, could significantly reduce the manual effort required in dependently typed languages. It describes a Lean-based experiment building a Zstandard decompressor to test whether LLMs can make proof automation more practical and lessen proof engineering overhead.

• 5Hacker News·7/18/2026research
  The Rekursiv: a 1980s hardware object store ahead of its time

  This article revisits the Rekursiv, a custom computer built by Linn in the 1980s that enforced memory type and bounds checks in hardware, garbage-collected its own heap, and treated memory and disk as a persistent object store. The piece argues that ideas once seen as impractical have since appeared in modern Arm silicon, while the economics that helped kill the project have changed significantly.