formalization

This paper rethinks the linguistic notion of 'state' as a systemic morphosyntactic mechanism across synthetic languages, formalizing it as a set-valued function over grammatical templates within a Template-Based Modular Cognitive framework and offering a unified computational learning theory account.

AI systems, including ChatGPT and OpenAI's Sol, have disproved and fully formalized the Erdős Unit Distance conjecture, marking a milestone in AI-assisted mathematics. The article discusses the process and implications for the future of mathematical proof verification.

A formalization of combinatorial game theory in Lean 4, covering games, nimbers, and surreal numbers, based on Conway's work.

This paper introduces the MELD dataset for evaluating whether text embedding models capture mathematical equivalence across different terminologies, and finds that current models fail. It proposes a contrastive learning approach to align informal and formal mathematical statements, improving retrieval on both informal-formal and natural language tasks.

Terence Tao demonstrates how to use Claude Code as a red teaming tool to align Lean code style with Mathlib's official style guide, using the Riemann–Stieltjes integral formalization project as an example. The demonstration showcases the practical value of AI in code auditing and style alignment.