\indent We discuss two topics that I have worked on at Lawrence Livermore National Laboratory, which give a sense of the breadth of the mathematical work that is done at a national lab. The first of these involves using optimization techniques to assess policy options for downsizing the US nuclear weapons stockpile. We discuss consolidation of the weapons complex in general, and our implementation of a mixed-integer linear programming model that is currently being used to evaluate policy alternatives. The second topic addresses mathematical methods for modeling an intelligent adversary, and how techniques from the field of artificial intelligence can be used to solve such problems. Using the crime of money laundering as a motivating example, we specifically seek to address the gap between the theory and practical application of such methods.