Mathematical explanation. The best mathematical proofs tell us why some mathematical fact holds, not simply that it holds. However to understand how one piece of mathematics explains another piece of mathematics is poorly understood. This project will develop a philosophical account of mathematical explanation. In particular, it will show how mathematics can explain further mathematics as well as how it can explain physical phenomena.
Mathematical notation: a philosophical account. This project will explore philosophical issues associated with mathematical notation. In particular, it will provide an account of how mathematical notation is used in mathematical applications and how it facilitates analogical reasoning in science.