Welcome to TxGraffiti

A machine that dreams in mathematics, scrawling conjectures on the walls of discovery.

TxGraffiti is a Python toolkit for automated mathematical conjecturing.

It empowers machines to explore mathematical structure—uncovering patterns, generating inequalities, and proposing candidate theorems backed by data. TxGraffiti blends symbolic logic, optimization, and heuristics into a unified system capable of operating across graph theory, number theory, combinatorics, and more.

Originally prototyped in 2016, TxGraffiti descends from a rich lineage of systems—from Fajtlowicz’s Graffiti and DeLaViña’s Graffiti.pc, to Melót’s GraPHedron—and has since powered dozens of research projects, produced open conjectures, and contributed to peer-reviewed theorems.

This modern version of TxGraffiti was designed and developed by Randy Davila, with contributions from Jillian Eddy, and introduces new capabilities for discovery and interaction:

• Symbolic logic for properties, predicates, and conjectures

• Linear and geometric inequality generation via LP and convex hulls

• Heuristic filtering and aesthetic ranking

• Interactive exploration, export to Lean 4, and educational demos

Let your machine dream. Let it write mathematics.

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Getting Started

• Installation
• Quickstart

Key Features

• Logic
• Generators
• Heuristics
• Playground

Automated Conjecturing

• History
• Wang’s Program II
• Fajtlowicz’s Graffiti
• DeLaViña’s Sophie Heuristic
• Melót’s GraPHedron

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API Reference

• txgraffiti.generators
• txgraffiti.heuristics
• txgraffiti.logic
• txgraffiti.playground
• txgraffiti.processing
• txgraffiti.export_utils package
• txgraffiti.example_data package

Learn More

• 🌐 Interactive Web App

• 📄 Papers on arXiv

Happy conjecturing.