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AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
In AI-rich higher education, polished written mathematics has become easier to produce than trustworthy evidence of understanding. This article develops a human-scale methodology for service mathematics, with informatics as its main running…
Recent advances in Generative AI have transformed how users interact with data analysis through natural language interfaces. However, many systems rely too heavily on LLMs, creating risks of hallucination, opaque reasoning, and reduced user…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
Autoformalization, the automatic translation of mathematical content from natural language into machine-verifiable formal languages, has seen significant progress driven by advances in large language models (LLMs). Nonetheless, a primary…
We introduce MerLean, a fully automated agentic framework for autoformalization in quantum computation. MerLean extracts mathematical statements from \LaTeX{} source files, formalizes them into verified Lean~4 code built on Mathlib, and…
Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem…
The combination of LLM agents with external tools enables models to solve complex tasks beyond their knowledge base. Human-designed tools are inflexible and restricted to solutions within the scope of pre-existing tools created by experts.…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
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…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
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…
AI agents have shown initial promise in automating mathematical theorem proving in proof assistants such as Lean. The same proof assistants can be used to verify the correctness of code by pairing code with specifications and proofs that…
Artificial intelligence (AI) tools are being incorporated into scientific research workflows with the potential to enhance efficiency in tasks such as document analysis, question answering (Q&A), and literature search. However, system…
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and…
The widespread integration of Large Language Models (LLMs) necessitates rigorous and systematic safety evaluation. Existing paradigms either rely on constructed benchmarks to assess safety from predefined perspectives, or employ dynamic…
Exact scientific discovery requires more than heuristic search: candidate constructions must be turned into exact objects and checked independently. We address this gap by extending TeXRA with an independent Lean 4 verification layer,…
The interactive theorem prover Lean enables the verification of formal mathematical proofs and is backed by an expanding community. Central to this ecosystem is its mathematical library, mathlib4, which lays the groundwork for the…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
We present Lean Refactor, a plug-and-play retrieval-augmented agentic framework for multi-objective, controllable, and version-robust refactoring of Lean proofs. LLM-generated proofs are notoriously correct-but-verbose and brittle across…