Researcher(s)
- Aiden Marly, Statistics, University of Delaware
Faculty Mentor(s)
- Sebastian Cioaba, Mathematical Sciences, University of Delaware
Abstract
Pure mathematics focuses on developing theories and investigating principles with the goal of expanding the boundaries of mathematical knowledge. Theories are developed by creating conjectures, which is a statement that is believed to be true but a formal proof or a counterexample has yet to be found. In graph theory, finding a counterexample to a problem involves finding a graph that violates the statement. When the counterexample to a problem is a small graph, it may seem fairly trivial to do so by hand. However, this is hardly the case and oftentimes the solution is a much more complex structure that humans can’t efficiently analyze. Therefore, artificial intelligence (AI) has emerged as a very useful tool for a pure mathematician. Recent research has shown success in using machines to find counterexamples to several open conjectures in graph theory and combinatorics. Notably, Adam Zsolt Wagner developed a reinforcement learning algorithm which involves training an agent to develop graphs by rewarding it based on how close a graph is to being a counterexample. The goal is for the rewards that the graph receives to continuously improve until a counterexample is found if one exists. Using his approach, we explore several open conjectures in spectral graph theory.