Lecturer in Mathematics
Department of Mathematics and Statistics
University of Canterbury
Private Bag 4800
Christchurch, NEW ZEALAND
Room 703, Erskine Building
Telephone: +64 3 364 2987 ext 8878
Fax: +64 3 364 2587
"There is nothing like looking, if you want to find something. You certainly usually find something, if you look, but it is not always quite the something you were after."
- Thorin Oakenshield, from J. R. R. Tolkien's The Hobbit, or There and Back Again.
From 2013-2016, I am Principal Investigator on the Marsden-funded project Non-Classical Foundations of Analysis.
Mathematics is an inherently human activity, perhaps the most human activity possible. Our reasoning underpins it, our experiences inform it, our creativity causes it to flourish and our direction as a species - both social and technological - guides it. I mean, of course, mathematics in the broad sense: an appreciation for and study of number, pattern, emerging and inherent behaviour of regularities and irregularities in and about our world.
Being a human discipline, and humans being disposed to categorize (philosophically contentious though that claim may be), there is a certain societal need and duty to name a few topics in which I study. I list some of my current research interests, in no particular order:
- Non-classical mathematics: mathematics developed with a paraconsistent or intuitionistic ambient logic, and related foundational and philosophical issues.
- Analysis: non-classical analysis, functional analysis & extremal problems, partial differential equations, notions of continuity, compactness and separability.
- Logic, proof theory, and computability theory.
- Interdisciplinary: the interaction of mathematics with philosophy, physics, biology, engineering, economics and other disciplines.