Historically, mathematical research has been a paper-and-pencil
affair, usually consisting of long periods of thought, in which only
minor results are obtained, followed (when lucky) by short spurts of
inspiration that lead to more substantial conclusions, and ultimately
to publication. This is still the primary method of research in
mathematics today; but the introduction of the computer has made
other, more experimental, modes possible, while the growth of computer
networks has opened new paths for disseminating research.
My own mathematical work falls into three main categories: first, I
pursue a traditional research program in polyhedral geometry; second,
I develop computer-based tools for mathematics research and education;
and finally, I work on new methods to present mathematics via
hypertext and the internet. All three of these areas are described
more fully below. Since the latter two are somewhat non-standard, I
present them with more detail than may be usual.