Formal Mathematical Proof & Conjecture Auditor
AI models hallucinate lemmas, divide by zero in disguised forms, and generalize from weak finite evidence. Audit machine-generated mathematical proofs, stress-test conjectures against brute-force counterexample search, and visualize deduction trees locally.
Verification Analysis
Finite-domain searches cannot prove universal claims, but immediately refute flawed AI assertions that rely on hasty inductive leaps.
Why Mathematical AI Needs Formal Checking
Recent benchmarks show Large Language Models generate plausible-looking proofs that contain "phantom lemmas", invalid quantifier swaps (∃ vs ∀), and boundary condition oversights. This workbench separates intuitive AI suggestions from rigorous formal validation.
Common AI Mathematical Failure Modes
Division by disguised zero
AI proofs often divide both sides by an algebraic term like (a - b) without proving that a ≠ b, silently creating pseudo-proofs that 1 = 2 or 0 = 1.
Small-sample inductive extrapolation
Observing that 2^3 - 1 = 7, 2^5 - 1 = 31, and 2^7 - 1 = 127 are prime leads unconstrained models to assert that 2^p - 1 is always prime for odd p. Testing n = 9 immediately reveals 511 = 7 × 73.
Circular reference traps
In multi-step theorem provers, an AI agent may use Lemma B to prove Lemma C, while Lemma B silently relies on Lemma C as an implicit premise. Our cycle detector flags any cyclic dependency graph.
Deductive Rules Enforced Here
Modus Ponens & Substitution
If premise P is true and P → Q is an established tautology or proven prior step, Q is legitimately verified.
Mathematical Induction
Requires both a verified base case (n = 1 or n = 0) and a rigorous inductive step proof showing P(k) → P(k+1).
Exhaustive Finite Counterexample Filtering
Evaluates discrete candidates up to N = 50,000 using high-speed local JavaScript evaluation without sending code to an external server.