Original title: AutoGraphForge: Towards Automated Graph Theory Discovery
Ján Pastorek · September 2026
Graph theory studies networks of connected points. Mathematicians want to discover new mathematical rules about these networks, but coming up with true, original ideas takes a lot of work. To help, researchers built a computer system named AutoGraphForge. The system proposes ideas called conjectures using a small list of sample networks. It checks each idea against known mathematical rules using an optimization program to filter out ideas that are already known. Next, it tests surviving candidates against a giant collection of about 348,000 networks, plus active search programs looking for counterexamples that disprove them. If a test disproves an idea, that counterexample joins the sample list to improve future guesses. Over several rounds, the system produced 6,522 surviving conjectures. The researchers proved by hand that some of these were true. Finally, the system writes these claims into code for computer programs that search for formal mathematical proofs.
Imagine you are inventing new cookie recipes by mixing ingredients and baking test batches. First, you have to check if the recipe is already in a cookbook to avoid copying. If it's new, you then have to bake many batches to ensure the cookies always turn out right, not just once. In this paper, the system is like a robot chef that generates recipe ideas (conjectures), checks them against a giant cookbook (known math), tests them on thousands of virtual cookies (graphs) to find failures, and then writes the successful ones in a computer-readable format that can be automatically verified.
This could speed up mathematical research by automating the discovery and verification of new theorems, affecting mathematicians and anyone using graph theory in fields like network analysis or computer science.
The system is ongoing and currently running on a cluster, so it's not fully complete or validated. Some conjectures were proved by hand, indicating automated proving isn't flawless yet. It relies on a specific dataset and graph types, which might not cover all mathematical scenarios.
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AutoGraphForge: Towards Automated Graph Theory Discovery — Ján Pastorek
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.