Characterizing initial human-AI proof formalization workflows

Researchers conducted mixed-methods studies on how mathematicians use AI tools to formalize proofs, finding that users prefer AI assistance while maintaining high-level control over proof discovery. A controlled user study showed participants achieved higher formalization accuracy with AI access than without, despite current tool limitations.

This research addresses a critical intersection of human capability and artificial intelligence by examining how mathematicians practically integrate AI into formal proof workflows. Rather than focusing solely on benchmarking AI performance, the study prioritizes understanding actual user behavior and preferences, revealing that mathematicians value AI as a collaborative partner rather than a replacement for human mathematical reasoning.

The research builds on decades of challenges in automated proof verification and recent AI advances in code generation and mathematical reasoning. As formal verification becomes increasingly important for software correctness and mathematical rigor, understanding human-AI collaboration workflows provides essential insights for tool designers and educators. The finding that users flexibly employ multiple AI tools suggests that different systems offer complementary strengths.

For the broader AI and mathematics communities, this work demonstrates that AI's impact on specialized domains like formal mathematics depends critically on how tools integrate with existing human practices. The improved accuracy rates when using AI indicate genuine productivity gains, though the study acknowledges current tool limitations. This suggests the trajectory toward more capable AI assistance is meeting real user demand.

Looking forward, the research indicates that successful AI integration in mathematics will require tools designed around human preferences for control and transparency rather than full automation. As AI capabilities advance, understanding these early-stage workflows becomes increasingly valuable for developing next-generation systems that enhance rather than undermine human mathematical thinking. The diverse user preferences documented suggest that one-size-fits-all approaches will likely fail.

• →Mathematicians prefer AI assistance in formalization while maintaining human control over proof discovery processes.
• →Users with AI access achieved higher formalization accuracy than those working without AI tools across varying difficulty levels.
• →Participants employed multiple different AI tools flexibly, indicating complementary strengths across systems.
• →Current AI tool limitations still exist but did not prevent productivity gains in controlled user studies.
• →Early-stage human-AI formalization workflows show promising integration patterns for broader mathematical practice.