Abstract: The computer has become an indispensable tool of mathematical discovery. While this claim hardly needs defending, results obtained by computer calculations are often considered less worthy than discoveries made by more traditional means. In this talk I will present some families of finite incidence geometries and theorems about these structures that were originally discovered by constructing small examples on a computer. I will also present a software package for the construction of combinatorial objects with prescribed automorphism groups that we are developing for the computer algebra system GAP.
