Photo credit:  Jeroen Van der Meeren
(Warning:  I now wear different glasses.)

Paul Shafer

School of Mathematics
University of Leeds
United Kingdom

email:  p [dot] e [dot] shafer [at] leeds [dot] ac [dot ] uk

Hello!  My name is Paul, and I am a lecturer in the Logic Group in the School of Mathematics at the University of Leeds.  Please enjoy the links at the top of the page.

When people who are logicians ask me about what I do, I tell them that I study computability theory.  Most of my work to date has been on reverse mathematics and the degrees of unsolvability of mass problems (i.e., the Medvedev and Muchnik degrees).

When people who are not logicians ask me about what I do, I usually resort to the following quaint analogy.  I describe calculus as the mathematics of change and geometry as the mathematics of shape, and then I say that I like to think of logic as the mathematics of mathematics.  Mathematicians like to write proofs and make computations.  Logicians take these ideas of proof and computation and formulate them as mathematical objects in their own right.  This formalization makes it possible to ask precise questions about what is and is not provable and what is and is not computable.  It also lets us describe the complexities of mathematical objects and arguments in a meaningful way, and this lets us compare these complexities with each other.