An automated mathematical proof system that utilizes a producer-reviewer agent loop to generate and verify rigorous theorems.
Install & Download
1. ClawHub CLI
The fastest way to install a skill directly from the registry.
npx clawhub@latest install math-proof
2. Manual Installation
Copy the skill folder to one of these locations
~/.openclaw/skills/ <project>/skills/ Priority: Workspace > Local > Bundled
3. Prompt Installation
Copy this prompt to OpenClaw to install it automatically.
Help me install math-proof using Clawhub. If Clawhub is not installed, install it first (npm i -g clawhub).
Prefer to download?
Get the raw skill files in a ZIP archive.
What is Math Proof & Review Loop?
The math-proof skill is a specialized workflow designed for Openclaw Skills that automates the generation and verification of complex mathematical proofs. By utilizing a multi-agent architecture, it creates a self-correcting environment where one agent (Producer A) drafts a proof while a second agent (Reviewer B) rigorously audits the logic for gaps, circular reasoning, or constraint violations.
This skill is particularly valuable for researchers, educators, and students who require high-fidelity, step-by-step mathematical derivations in LaTeX format. By enforcing a feedback loop that can run for up to 50 iterations, it ensures that the final output is not just a statistical guess from an LLM, but a logically sound demonstration that adheres to specific pedagogical or technical constraints.
Math Proof & Review Loop Use Cases
- Proving complex geometric theorems using specific Euclidean or algebraic methods.
- Validating student or peer-drafted lemmas for logical consistency.
- Generating rigorous LaTeX documentation for mathematical research papers.
- Deriving formulas while strictly avoiding prohibited tools like vectors or calculus.
- Automated peer-reviewing of mathematical propositions to identify hidden assumptions.
How Math Proof & Review Loop Works
- The user provides a theorem statement and optional constraints (e.g., 'no vectors', 'use LaTeX').
- The system requests pre-loop configuration, including feedback mode (Hint-only, History, or Full Disclosure) and reference materials.
- Agent A is spawned to produce a comprehensive, step-by-step proof based on the initial prompt and constraints.
- Agent B is spawned to review the proof, checking for logical errors, missing justifications, and constraint adherence.
- If Agent B rejects the proof, the feedback is passed back to Agent A (based on the chosen feedback mode) for revision.
- This cycle repeats until Agent B marks the proof as passed or the retry limit (default 50) is reached.
Math Proof & Review Loop Setup
To activate the math-proof skill within the Openclaw Skills framework, ensure your environment is configured for sub-agent spawning. No specific external math libraries are required as the agents handle LaTeX string generation natively.
# Trigger the skill by asking a math-related question in your agent interface
# Example query: "Prove that the sum of angles in a triangle is 180 degrees using only elementary geometry."
Math Proof & Review Loop Data Schema & Taxonomy
The skill organizes its workflow and data using the following taxonomy:
| Component | Description |
|---|---|
| Theorem Statement | The core mathematical proposition to be proved. |
| Feedback Modes | Hint-only (default), With history (previous draft included), Full disclosure (B's raw audit). |
| Constraints | User-defined rules (e.g., method restrictions, tool prohibitions, language requirements). |
| Trace Logs | A round-by-round summary of A's actions, B's critiques, and the current status. |
| Final Output | A validated, self-contained LaTeX proof with a success badge. |
Math Proof & Review Loop Advanced Features
- Multi-Agent A/B Loop: Implements a producer-reviewer pattern to eliminate hallucinations.
- Configurable Feedback Granularity: Allows users to control how much information the Proving Agent receives during failure cycles.
- Contextual Reference Injection: Supports including local textbook chapters or lecture notes in the prompt context for both agents.
- Constraint Enforcement: Strictly adheres to prohibited methodology (e.g., 'synthetic geometry only') throughout the loop.
- Auto-Correction: Automatically fixes trivial formatting errors without consuming retry quotas.
SKILL.md
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