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:

- MATH 558, Foundations of Mathematics I. This is an introductory
graduate course on foundations of mathematics. A course announcement and lecture
notes are available.
- MATH 565, Foundations of Mathematics II. This is an advanced graduate course on subsystems of second order arithmetic and Reverse Mathematics. A course announcement is available. I have published a book on this subject.

I founded and continue to be associated with FOM, an automated e-mail list for discussing foundations of mathematics.

t20@psu.edu / 7 April 2006