lean-4

OpenAI announced a formal proof for the Navier-Stokes equations using Lean 4, reducing the cost of formal verification from tens of thousands of person-hours to just 17 hours, highlighting AI's transformative role in mathematics and verification.

StochBench introduces a domain-specific benchmark of 450 graduate stochastic processes problems in Lean 4, evaluated with an AI agent achieving a 34.9% proof rate, to advance formal theorem proving in applied mathematics.

This paper introduces AViD Journal, a pipeline for automated novelty verification of mathematical theorems using Lean 4, evaluating it on withdrawn arXiv papers and highlighting challenges in formal verification.

MathCode is an AI-powered coding assistant that converts mathematical problems into Lean 4 theorems and attempts formal proofs, featuring a persistent REPL, theorem libraries, and agent-mode proving.

A research paper introducing a failure-triggered cascade approach to safely integrate machine learning into Lean 4's grind tactic, achieving improved efficiency and solving previously unsolvable proofs without regressions.

This paper presents FVSpec, a benchmark for AI-assisted formal verification that translates real-world property-based tests from Python into Lean 4 specifications using a multi-agent LLM pipeline, aiming to drive progress on formal verification of real-world software.

Aleph Prover has formalized OpenAI's disproof of Paul Erdős' planar unit problem in Lean 4 and released it as open source for independent validation, demonstrating AI's role in accelerating mathematical research with verifiable proof data.

This paper evaluates Claude Code in an agentic proving framework on the Clever benchmark for program verification, achieving over 98% success in specification generation and end-to-end verification, revealing that existing benchmarks may be insufficient for evaluating modern agentic provers.

OProver is a unified framework for agentic formal theorem proving in Lean 4 that iteratively improves proof generation through training with verified proofs and compiler feedback, achieving state-of-the-art results on multiple benchmarks.

TorchLean is a newly released Lean 4 framework that enables formal verification of neural network software, featuring typed tensors, verified autograd, PyTorch interoperability, and GPU execution. The release expands support to modern architectures like diffusion models, GPT-style transformers, and state-space models, bridging practical ML workflows with mathematical proof checking.

This paper introduces Discover and Prove (DAP), an open-source agentic framework for automated theorem proving in Lean 4 that tackles 'Hard Mode' problems where the answer must be discovered independently before formal proof construction. The work releases new Hard Mode benchmark variants and achieves state-of-the-art results while revealing a significant gap between LLM answer accuracy (>80%) and formal prover success (<10%).