Walter Dean, Associate Professor and Course Director, BSc Mathematics and Philosophy
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My name is Walter Dean, and I convene the Mathematics and Philosophy degree at Warwick. I originally became interested in the intersection between the subjects when I was in school via the "Mathematical Recreations" column in Scientific American. It was there that I first learned about topics the Fibonacci numbers, cellular automata (like Conway's Game of Life), fractals (with the Mandelbrot set), and Monte Carlo algorithms (e.g. for estimating the value of pi). As many of the columns also featured programing problems, this was also how I first came to appreciate the role of computers in mathematics.
This route also led me to popular books about the foundations of mathematics such as Abott's Flatland, Davis and Hersh's The Mathematical Experience, and Smullyan's To Mock a Mockingbird. This was how I first learned about topics like algorithmically undecidable problems and the impossibility of providing a set of axioms which correctly decides the answer to all problems of elementary number theory. This lead me to wonder about the nature of mathematics itself -- e.g. is it possible to know all mathematical truths? what are mathematical objects like natural numbers or real numbers? how is it that we are able come in contact with them?
At university, I discovered that not only have such questions about the nature of mathematics and its relation to the empirical world been discussed by philosophers since antiquity, but they were still be debated today. I was also inspired to study mathematical logic further after encountering "real life" instances of incompleteness and computational universality in algebra -- e.g. quintic equations which can't be solved by radicals, or of Diophantine equations which can simulate the operation of an arbitrary computer program.
My teaching and research are still engaged with many of the same topics. For instance I am interested in the scope of incompleteness phenomenon both in regard to paradoxes (like the Liar) traditionally studied by philosophers and also in regard to "weak" mathematical theories originating in computer science. I am also interested in foundational questions about computation -- e.g. what makes a mathematical formalism (such as a Turing machine) an accurate model of concretely embodied computation? what makes one problem harder to solve than another (e.g. primality testing versus factorization)? why has the P vs NP problem proven so hard to resolve and what does this tell us about the nature of mathematical problem solving itself?
The Warwick Maths-Phil degree is designed to help you develop and explore your own interests as quickly as possible. The first year covers common mathematical background together with elementary logic and a survey of contemporary themes in philosophy. After this there is a wide range of options available in both departments. For instance, there is the chance to study additional topics in logic and the foundations of mathematics such as Gödel's completeness and incompleteness theorems. Other options in Philosophy range from Metaphysics, to Political Philosophy, to Philosophy through Film, to Feminism. And within Maths, options includes Fluid Dynamics, Knot Theory, Fractal Geometry, and Topics in Mathematical Biology. Many of our students also elect to take options in other departments such as Computer Science or Economics. There is also the option of staying for a fourth year in which you may elect to do a research project in either maths or philosophy. In the past, this route has often inspired our students to go on to post-graduate work in both subjects.