Geddes' primary research interest is to develop algorithms for the mechanization of mathematics. More specifically, he is interested in the computational aspects of algebra and analysis. Currently, he is focusing on designing hybrid symbolic-numeric algorithms to perform definite integration and solve ordinary and partial differential equations.
Geddes retired from teaching in December 2008.
Geddes taught a mixture of both senior-level symbolic computation courses, at both the undergraduate and graduate level, as well as introductory courses on the principles of computer science.