Automated Conjecturing VII: The Graph Brain Project & Big Mathematics

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?