The paper reports an AI-assisted Lean 4 formalization of the Poincaré conjecture, beginning with limited reusable formal infrastructure for the geometric analysis. The authors combined a mathematician-prepared proof blueprint with explicit milestone statements, enabling parallel agent work and clear points for identifying blockers and providing guidance. Their analysis highlights the human interventions and organizational choices that shaped this workflow, and suggests that developing reusable infrastructure could reduce the cost of verifying future mathematical results in geometric analysis.
arXiv:2605. 22763v2 Announce Type: replace Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.
arXiv:2603. 02668v2 Announce Type: replace Abstract: We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub.
arXiv:2607. 07779v1 Announce Type: cross Abstract: Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages.
arXiv:2608.28433v2 Announce Type: replace Abstract: Proof assistants such as Lean 4 promise the paradigm of formally verified mathematics, but large-scale formalization projects have faced major barr...
arXiv:2610.33860v1 Announce Type: new Abstract: Numina Fuse is an agent-native application for formalizing mathematics in Lean 4. Since Lean can compile while not representing its intended informal m...
Artificial intelligence (AI) systems have ushered in a new age of proof abundance, but helping humans understand these proofs requires new attention to the differences in how AI agents and humans purs...
arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.
arXiv:2607. 09217v1 Announce Type: new Abstract: In this system paper, we present OpenProver, an open-source system for LLM-driven automated theorem proving (ATP) with integrated Lean 4 formal verification.
arXiv:2607. 19374v1 Announce Type: new Abstract: Recent formal reasoning systems have reached IMO-level performance, yet they leave a fragmented landscape: algebra and number theory are handled in Lean, while geometry still relies on domain-specific languages with limited formal guarantees.
arXiv:2610.18301v1 Announce Type: new Abstract: Recent progress in autoformalisation of mathematics using AI has been impressive. Measuring this progress requires datasets of formal statements that a...
The paper investigates how autonomous AI agents differ from humans in proof formalization tasks. Using a method called "simulated collaboration," the authors analyze nine major Lean collaborations involving 4.7 million definitions. They find that AI agents focus more on explicitly marked gaps, avoid densely connected proof centers and complex or surprising goals, yet are attracted to surprising proof bodies, which they tend to regularize toward a baseline.
arXiv:2604. 24021v4 Announce Type: replace Abstract: We present QED, an open-source multi-agent system that turns human-provided research questions into complete mathematical proofs without further human guidance.