Click here to read my short essay explaining what is meant by the term foundations of mathematics.
My paper Logic and Mathematics is a survey of logic and foundations of mathematics, for the general reader. It was published in a volume distributed by the Book-of-the-Month Club. It is available in several formats: DVI (84K), PDF (362K), PS (1080K), HTML.
A key issue in foundations of mathematics is Hilbert's program of finitistic reductionism. My paper Partial Realizations of Hilbert's Program is available in several formats: LaTeX (55K), DVI (72K), PDF (264K), PS (772K), HTML.
One of my ongoing research projects is Reverse Mathematics, an attempt to answer the foundational question: ``Which set existence axioms are needed to prove specific mathematical theorems?'' I study this question in the context of subsystems of second order arithmetic. I have written a book on this subject. Many of my publications deal with Reverse Mathematics, and many of my Ph.D. students have written theses in this area.
I teach two courses on foundations of mathematics:
I founded and continue to be associated with FOM, an automated e-mail list for discussing foundations of mathematics.
email@example.com / 7 April 2006