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Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
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…
AI-driven autoformalization of mathematics is advancing rapidly. However, the type checker of a proof assistant guarantees only the logical correctness of proofs; it does not verify whether propositions and definitions faithfully capture…
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…
Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
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,…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
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…
Autoformalization aims to convert informal mathematical proofs into machine-verifiable formats, bridging the gap between natural and formal languages. However, ensuring semantic alignment between the informal and formalized statements…
Autoformalisation, the task of expressing informal mathematical statements in formal language, is often viewed as a direct translation process. This, however, disregards a critical preceding step: conjecturing. Many mathematical problems…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…
Interactive theorem provers (ITPs) require manual formalization, which is labor-intensive and demands expert knowledge. While automated formalization offers a potential solution, it faces two major challenges: model hallucination (e.g.,…
Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…
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…