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Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
We present AutoformBot, a multi-agent system for building an Autoformalized Textbook Library At Scale (Atlas) in Lean 4. AutoformBot orchestrates thousands of LLM agents, equipped with formal verification tools, dependency-aware task…
Formalising informal mathematical reasoning into formally verifiable code is a significant challenge for large language models. In scientific fields such as physics, domain-specific machinery (\textit{e.g.} Dirac notation, vector calculus)…
Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…
Evaluating statement autoformalization, translating natural language mathematics into formal languages like Lean 4, remains a significant challenge, with few metrics, datasets, and standards to robustly measure progress. In this work, we…
Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to…
Efficient and accurate autoformalization methods, which leverage large-scale datasets of extensive natural language mathematical problems to construct formal language datasets, are key to advancing formal mathematical reasoning. In this…
Large Language Models (LLMs) have emerged as powerful tools for accelerating scientific discovery, yet their static knowledge and hallucination issues hinder autonomous research applications. Recent advances integrate LLMs into agentic…
Autoformalization, the conversion of natural language mathematics into formal languages, offers significant potential for advancing mathematical reasoning. However, existing efforts are limited to formal languages with substantial online…
Reliable autoformalization remains challenging even in the era of large language models (LLMs). The scarcity of high-quality training data is a major bottleneck. Expert annotation requires substantial time and deep expertise in both…
Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…
We present a case study where an automatic AI system formalizes a textbook with more than 500 pages of graduate-level algebraic combinatorics to Lean. The resulting formalization represents a new milestone in textbook formalization scale…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
Scientific and Technical Intelligence (S&TI) analysis requires verifying complex technical claims across rapidly growing literature, where existing approaches fail to bridge the verification gap between surface-level accuracy and deeper…
Automatic translation of natural language mathematics into faithful Lean 4 code is hindered by the fundamental dissonance between informal set-theoretic intuition and strict formal type theory. This gap often causes LLMs to hallucinate…
We present a complete Lean 4 formalization of the equilibrium characterization in the Vlasov-Maxwell-Landau (VML) system, which describes the motion of charged plasma. The project demonstrates the full AI-assisted mathematical research…
Recent advances in large language models (LLMs) offer promising potential for automating formal methods. However, applying them to formal verification remains challenging due to the complexity of specification languages, the risk of…
Autoformalization, the process of transforming informal mathematical language into formal specifications and proofs remains a difficult task for state-of-the-art (large) language models. Existing works point to competing explanations for…
Formal verification offers a path to provably correct software, but writing verified code remains expensive enough that the technique is rarely used in production. Recent large language models can accelerate this work, and recent benchmarks…