In recent decades, an explosive synergy between biology and mathematics has greatly enriched and extended both fields. Indeed, given its ability to reveal otherwise invisible worlds in all kinds of biological systems, mathematics has been called the "new microscope in biology." In turn, biology has stimulated the creation of new realms of mathematics. Duke's Mathematics Department has a large group of mathematicians who work on specific biological and medical applications and as well as the development of new applied mathematical techniques and new mathematical theorems inspired by biological applications. The range of applications is large and the mathematical techniques diverse, including dynamical systems, partial differential equations, stochastic dynamics, fluid dynamics, geometry, topology, and algebra.