Examining 4.7 million definitions in Lean: AI agents move away from proof depth toward explicit gaps

The abundance of automatically generated mathematical proofs opens a wide window for scrutinising AI agents' ability to emulate human reasoning, as a research paper by Balint Giffnar and Simon Dideo shows that these agents systematically and consistently deviate from human preferences when constructing formal proofs. The study, posted on arXiv in the fields of artificial intelligence and human-computer interaction, employed an experimental methodology called “cooperative simulation” to examine model behaviour across nine large human collaborative projects written in the interactive proof language Lean. The analysis covered more than 4.7 million mathematical definitions spread over more than six thousand software submissions, aiming to answer two core questions: whether agents attend to superficial syntactic structure or delve into deep semantics, and how their choices for the next step differ from those of a human mathematician.

The results showed a fundamental divergence in problem tracking, as AI agents are attracted far more strongly than humans to explicitly labelled gaps.While a human researcher balances the proof’s structure with its objective priorities, independent models rush to address gaps that have been clearly marked, ignoring the broader logical trajectory of the problem. The deviation does not stop there; the researchers also observed a relative aversion by agents toward densely connected proof nodes and toward complex or surprising proof goals, which are the central knots that underpin mathematical coherence and advanced reasoning.

The study also reveals a striking paradox in handling unfamiliar proof texts: agents tend to gravitate toward surprising proof passages, but they quickly move to smooth them out and revert them to the prevailing statistical baseline. This pattern-matching behaviour eliminates innovative routes or unconventional methods that the human mind employs to bypass logical bottlenecks. The findings highlight critical blind spots in the design of autonomous models and confirm that a profusion of outputs does not necessarily reflect a semantic understanding capable of driving mathematical knowledge construction without careful human guidance.

Full reliance on automated proof generation carries the risk of hiding logical flaws behind a veil of superficial achievements.When an agent avoids dense knots and rushes to close explicit gaps, it gives a misleading impression of rapid progress through completing partial tasks, while the core nucleus of the problem remains unsolved. This behaviour demonstrates that current agents act as tools for smoothing expected procedures and lack the architectural vision that sets priorities for building complex conceptual structures.

This shift directly affects engineers and technology leaders in the Gulf, Egypt and the Levant, especially teams building formal software verification systems or auditing the safety of smart contracts and critical infrastructures in banking, aviation and energy. If you rely on smart agents to examine precise code or prove the safety of critical algorithms, leaving the path to the agent represents a high-risk choice, because the model will naturally avoid the most tangled knots and gravitate toward smoothing easy steps. This reality calls for a reallocation of tasks within development teams, with human engineers managing central knots and defining unconventional proof goals, while restricting the agent’s assistance to precisely defined sub-gap filling, to avoid wasting compute resources and missing structural errors that might otherwise go unnoticed.