Formalize and solve mathematical problems using ITPs (Lean 4/Mathlib, Coq, Isabelle/HOL), Automated Theorem Provers (Prover9/FOL), SMT solvers (Z3), SAT/Combinatorial solvers (PySAT, MiniZinc), and Specialized CAS (GAP, PARI/GP, Singular/M2). Use when Gemini CLI needs to formalize proofs, find counterexamples, or perform specialized computations across analysis, topology, algebra, and number theory.
A comprehensive framework for Interactive Theorem Proving (ITP), Automated Theorem Proving (ATP), model finding, and specialized algebraic computation.
| Tool | Domain / Strength | Use Case |
|---|---|---|
| Lean 4 / Mathlib | Formalization of Modern Math | Analysis, topology, PFR conjecture, Liquid Tensor. |
| Coq (Rocq) | Foundational Proofs / CS | Four Color Theorem, Feit-Thompson (Odd Order). |
| Isabelle/HOL | Math & Verification | Kepler Conjecture (Flyspeck), Prime Number Theorem. |
| Prover9 / Mace4 | FOL / Equational | Human-readable proofs, finite models, lattices. |
| Arithmetic / Optimization |
| Number theory, additive combinatorics, knots. |
| PySAT / MiniZinc | Combinatorial Solvers | SAT-encoding, Latin squares, extremal set theory. |
| GAP / PARI / M2 | Specialized CAS | Group theory, Number theory, Algebraic geometry. |
lake build (Lean 4)prover9 -f problem.inpython script_using_z3.pygap script.g