Rate My Professor Daniel Mathews

Associate Professor Daniel Mathews works in the School of Mathematics at Monash University, where his research focuses on geometry, topology, and mathematical physics. His interests include low-dimensional topology such as knots and polynomials, geometric structures on 3-manifolds, hyperbolic 3-manifolds, contact 3-manifolds, quantum topology, symplectic and contact topology, planar graphs, and topological quantum field theories. Mathews obtained his PhD in Mathematics from Stanford University in 2009 with a thesis entitled "Chord diagrams, contact-topological quantum field theory, and contact categories," supervised by Yakov Eliashberg and Steven Kerckhoff. He previously earned an MSc in Mathematics from the University of Melbourne in 2004, a BSc (Hons) in Mathematics, an LLB (Hons), and a Diploma in Modern Languages (Italian) from the University of Melbourne. As a high school student, he represented Australia at the International Mathematical Olympiad, winning a silver medal in 1997 and a bronze medal in 1996.

Mathews has been at Monash University since 2013, starting as a Lecturer, becoming Senior Lecturer in 2018, and Associate Professor in 2022. Earlier appointments include Visiting Assistant Professor at Boston College (2010–2012), Postdoctoral Fellow at Université de Nantes (2009–2010), and Research Member at the Mathematical Sciences Research Institute (2010). His recent breakthrough with PhD student Orion Zymaris extends the 380-year-old Descartes Circle Theorem using spinors to describe radii of mutually tangent circles, published in the Journal of Geometry and Physics (2025), earning him a commendation in the 2025 Researcher of the Year Award. Key publications include "Spinors and horospheres" (Advances in Mathematics, 2025), "Spinors and the Descartes circle theorem" with O. Zymaris (Journal of Geometry and Physics, 2025), "A-polynomials, Ptolemy equations and Dehn filling" with J. A. Howie and J. S. Purcell (Algebraic and Geometric Topology, 2025), "A symplectic basis for 3-manifold triangulations" with J. S. Purcell (Communications in Analysis and Geometry, 2025), and the textbook "Specialist Mathematics: VCE Units 3 & 4" (second edition, 2023). Mathews has supervised several PhD and honours students, received the 2023 Monash Student Association Teaching Award, 2022 Dean’s Excellence in Teaching Award, 2019 Dean’s Commendation for Honours Supervision, 2015 BH Neumann Award, and 2014 Tall Poppy Award. He serves on the School Executive Committee, coordinates pure mathematics, and organizes topology seminars and conferences.