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A Purdue paper introduces a bounded, online step-level repair module for Lean 4 theorem provers that feeds compiler error messages to a pretrained repair model instead of discarding failed tactics, achieving up to a 32% relative gain in solve rate on the LeanDojo benchmark and nearly doubling performance on Lean Workbook.
A collection of 100+ short reactions from mathematicians to OpenAI's October 6 announcement that its models solved over 100 open mathematical problems, ranging from astonishment at results like the Quasi-Riemann hypothesis to reflections on the future role of human mathematicians.
UT Austin Math Chair Francesco Maggi says OpenAI appears to be preparing to release around 400 AI-generated mathematical proofs at once, signaling that mathematical discovery may no longer be the scarce resource — human understanding is.
This paper introduces an approach for automatically generating generalized plans in Lean with formal proofs of completeness using LLMs, evaluated on benchmark domains showing significant advancements in automatic plan verification.
Verus is an open-source automated program verifier for Rust that helps ensure code correctness through mathematical proofs, and is used at Amazon for projects like the Nitro Isolation Engine.
ProofEvolve is a neuro-symbolic framework that evolves formally verified proof structures using neural models to enhance automated theorem proving, achieving high solve rates on Lean benchmarks by preserving verified knowledge from incomplete attempts.
The paper introduces FAR, a human-AI discovery paradigm that automates the search for mathematical problems from literature, with a pilot in combinatorics demonstrating its effectiveness in identifying conjectures and resolutions.
An AI system called Theo Conjecture, leveraging a large language model, solved a 35-year-old graph theory problem originally posed by mathematician Paul Erdős, discovering an unexpected term. The system works by proposing, testing, and revising mathematical ideas in a loop.
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.
OpenProver is an open-source system for LLM-driven automated theorem proving using Lean 4, featuring a Planner-Worker-Verifier architecture and both autonomous and interactive modes. It enables reproducible evaluation and human-AI synergy in mathematical proof search.
Research Math Agents (RMA) is an agentic framework for automated reasoning on research-level mathematical problems, achieving state-of-the-art results on the First Proof benchmark by solving 8 out of 10 problems, outperforming strong baselines like GPT-5.2R and Aletheia.
This paper introduces Formal Conjectures, an evolving benchmark of 2615 mathematical statements formalized in Lean 4, including open research conjectures for proof discovery and solved problems for auto-formalization, designed to evaluate automated reasoning systems with zero contamination.