Lean Proof Coach
A study companion for physics and math grad students learning to formalize theorems in Lean, with built-in scaffolding for quantum information proofs.
physics and math grad students learning interactive theorem proving
- Step-by-step template generator that scaffolds common Lean proof shapes (induction, operator monotonicity, convexity)
- Searchable library of reusable quantum-information lemmas pulled from Mathlib and Lean-Quantum
- 'Explain the gap' feedback on partial proofs that points to the missing tactic without solving it
- Instructor dashboard for assigning and grading formalization exercises
Lean-Quantum just dropped as a major open library, but the onboarding curve for physics grad students is brutal — there's no AI tutor that understands both Lean tactics and the physics context.
Lean-Quantum library (arXiv:2607.05492) and Generalized Quantum Stein's Lemma formalization (arXiv:2510.08672) confirm an active, growing niche, but the addressable population of physics/math grad students learning to formalize quantum proofs is small.Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information ↗Quantum Formal Initiative (QFormal) ↗
LeanTutor (arXiv:2506.08321) is a direct LLM+Lean tutoring research system with the PeanoBench benchmark; though it focuses on math (Peano arithmetic) rather than physics/quantum, it is a credible near-term competitor and the surrounding ecosystem is academic/open-source, making commercial 'whitespace' modest.LeanTutor: Towards a Verified AI Mathematical Proof Tutor ↗PeanoBench: Dataset for Math Proof Evaluation ↗
No pricing, paid courses, or B2B buyer signals found; Lean-prover community is deeply open-source (leanprover-community courses list is free), and the target users (physics/math grad students) typically have very low discretionary budgets — weak WTP.Courses using Lean ↗Quantum Formal Initiative (QFormal) ↗
AI-assisted theorem proving is a multi-year macro trend (LeanTutor, Mathlib growth, ongoing Quantum Formal publications through 2025), and 'why now' is reinforced by the recent Lean-Quantum drop — durable demand likely.Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information ↗
LeanTutor's published proof-of-concept demonstrates the LLM ↔ Lean verification loop is buildable; physics-specific scaffolding and tactic coaching add complexity but don't introduce novel infrastructure risk.LeanTutor: Towards a Verified AI Mathematical Proof Tutor ↗