I am the O'Hara Professor of Philosophy and Mathematics at the University of Notre Dame. Until recently I was Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College Oxford, and before that affiliated for many years with the City University of New York.
My research is mostly in logic, broadly construed, especially mathematical logic and set theory, with connections to other areas.
I try to engage with any question that I find interesting. I strive for self-contained answers with clear explanations. I post answers to questions that I know how to answer or which I am able to figure out. I try to express my mathematical ideas in plain language when possible, preferring to avoid technical notation or terminology when I find that these obscure the idea of an argument. When clarity is enhanced by technical precision, however, I do try to provide it. I am less concerned with whether a question or answer conforms with various rules, as long as it leads to interesting mathematical ideas. For example, I feel free to make posts answering not the actual question that was asked but a related question, provided that this is interesting. In my view, answers on MathOverflow are mainly for the benefit of the broader community, rather than for the particular person who asked the question.
Contemplating a mathematical puzzle on MathOverflow has been one of the routine enjoyments in my life. Read my remarks on MathOverflow: the eternal fountain of mathematics.
I strongly prefer answers that explain a mathematical idea to answers that provide a reference for where that idea might be explained elsewhere. Similarly, I find questions that ask for a mathematical explanation to be more interesting than questions that ask for a reference.