Digital computers have enabled mathematicians to pursue new approaches to discovering ideas, developing conjectures, and validating proofs. This emerging project focuses, in part, on the implications of novel computer use for the practice of mathematics. Furthermore, acknowledging the central role of computation in applied science demands a different understanding of the structure of scientific theories. The Institute has hosted conferences in the last two years on this theme. Rob Corless is developing a project, working with computational scientists, mathematicians and philosophers, extending into these more philosophical topics from his expertise in mathematical and scientific computing.