Automated Conjecturing VII: The Graph Brain Project & Big Mathematics

TL;DR

The paper presents the Graph Brain Project, demonstrating how automated discovery software and large-scale collaboration can revolutionize mathematical research, especially in graph theory, by generating novel conjectures and fostering systematic, collective investigation.

Contribution

It introduces a new approach using automated software for conjecture generation and advocates for large-scale collaborative research models in mathematics.

Findings

Automated software can generate non-trivial conjectures in graph theory.

Large-scale collaboration enhances mathematical discovery and research efficiency.

The approach can be applied to various mathematical fields beyond graph theory.

Abstract

The Graph Brain Project is an experiment in how the use of automated mathematical discovery software, databases, large collaboration, and systematic investigation provide a model for how mathematical research might proceed in the future. Our Project began with the development of a program that can be used to generate invariant-relation and property-relation conjectures in many areas of mathematics. This program can produce conjectures which are not implied by existing (published) theorems. Here we propose a new approach to push forward existing mathematical research goals---using automated mathematical discovery software. We suggest how to initiate and harness large-scale collaborative mathematics. We envision mathematical research labs similar to what exist in other sciences, new avenues for funding, new opportunities for training students, and a more efficient and effective use of published mathematical research. And our experiment in graph theory can be imitated in many other areas of mathematical research. Big Mathematics is the idea of large, systematic, collaborative research on problems of existing mathematical interest. What is possible when we put our skills, tools, and results together systematically?