Title: Mapping Early Human-AI Collaborative Patterns in Proof Formalization

Abstract:

While human mathematicians have relied on written proofs to validate their arguments for centuries, the automatic verification of these proofs has historically remained a significant hurdle. Recent breakthroughs in artificial intelligence—particularly in code generation and sophisticated mathematical reasoning—offer the potential to revolutionize how proofs are formalized and subsequently verified. Rather than concentrating on benchmarking the capabilities of current state-of-the-art models, this research investigates the practical application of these tools by users. We employ a mixed-methods approach to examine the initial effects of AI on formalization workflows, exploring users' stated objectives, perceived obstacles, and actual adaptation strategies in practice. Qualitative survey data reveals a diverse range of preferences, though there is a prevailing consensus for AI support that maintains substantial human oversight in the proof discovery phase. To evaluate real-world engagement with AI under these constraints, we executed a controlled user study wherein participants attempted to formalize informal mathematical problems and their corresponding proofs, both with and without AI assistance. This study spanned various domains and difficulty levels. Despite existing limitations in autoformalization technology, participants generally achieved higher accuracy when AI tools were available compared to working alone, and most users demonstrated flexibility by integrating multiple distinct AI tools into their processes. Collectively, our findings illuminate the nascent phase of AI integration into formalization, highlighting the complex and interactive dynamic between human and machine collaboration.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC