Proof Coach
An AI tutor that walks university students through Lean-style formal proof exercises in cryptography and discrete math, giving step-by-step hints instead of just answers and grading their hand-written proofs.
CS and math undergrads taking cryptography, discrete math, or intro formal methods courses
- Interactive proof editor with a Lean's-tactics-style hint system that nudges without solving
- Auto-grader for short proof assignments (correctness property of OTP, XOR commutativity, etc.) with rubric feedback
- Curated problem sets aligned with Boneh-Shoup, VCV-io, and standard crypto courses
- Instructor dashboard where professors assign and track cohort progress
Universities are racing to add formal verification to crypto curricula and the HashCloak tutorial is the kind of resource instructors want — but there's still no student-facing tool that turns the Lean learning curve into something self-serve.
Springer paper confirms Lean is being adopted in undergraduate math classrooms, but the intersection of formal verification + cryptography + discrete math is still a narrow subset of CS curricula; no large student-facing product has yet proven out demand at scale.Using the proof assistant Lean in undergraduate mathematics classrooms ↗Courses using Lean ↗
LeanTutor (arXiv 2506.08321, accepted at ICML 2025) is essentially the same concept — an LLM-based Lean-verified tutor that autoformalizes, generates next feasible tactics, and gives guiding feedback; this directly competes with Proof Coach and was published before the idea was framed.LeanTutor: Towards a Verified AI Mathematical Proof Tutor ↗LeanTutor: A Lean-Verified Tutor for Mathematical Proofs (ICML 2025) ↗
B2B institutional edtech deals require curriculum alignment and admin dashboards; student-paid niche tools rarely reach meaningful revenue, and the target user base (CS/math undergrads in specific courses) is a very small TAM with low willingness-to-pay.7 Education App Monetization Models That Actually Work in 2026 ↗
Formal verification is a multi-decade trend accelerating with NIST post-quantum cryptography standardization and AI-assisted proof tooling (Lean 4, F*, EasyCrypt); curricula are being updated to include this, so the underlying tailwind is durable.Formal Verification of Cryptography and Protocols ↗
LeanTutor's three-module architecture (autoformalizer, next-step generator, NL feedback) shows the build is possible but requires non-trivial ML work, Lean 4 kernel integration, and proof-search infrastructure — well beyond a weekend prototype.LeanTutor paper (arXiv) ↗