Research Field: Geometry, Topology, Mathematical Physics.
If you want to understand how the world works at the most fundamental level, you need to understand mathematics. All known laws of physics are written in mathematics, but some current physics theories are written in terms of mathematical models that don’t quite make sense. That’s where mathematicians like Dr. Mathews are required.
In his research he builds mathematical models of physical interactions, known as “topological quantum field theories”. While these theories are simplified models of reality, they are perfect, abstract mathematical representations of processes happening in the universe. These theories are mathematically profound and use ideas from a vast range of mathematics and physics – algebra, geometry, topology, dynamics, string theory and information theory. By developing creative mathematical ideas and building elegant mathematical theories, we improve our understanding of both mathematics and physics, and hence our fundamental understanding of the universe in which we live.
Dr. Mathews has co-authored a book for talented secondary students called “Problem solving tactics”. He has also assisted with developing modules for 11-12 teachers for the Australian Mathematical Institute for the National Curriculum. He is involved in the International Mathematical Olympiad and co-authoring classroom materials and maths problems for 2013 Planet Earth. (http://mathsofplanetearth.org.au/schools)