Abstract: Historically, the interactions between mathematics and biology have not been as broad or well-known as those between mathematics and the other natural sciences. In the last decade, however, it has increased dramatically to the benefit of both disciplines: on one hand, mathematics can help illuminate and answer fundamental questions in biology; on the other, biology has become a rich source for challenging mathematical problems. The talk will highlight aspects of this interplay and outline examples in which the framing of a biological question in mathematical terms can sometime provide critical insight for obtaining an answer. Specific examples will include the Luria-Delbrük fluctuation test, gene network dynamics, finite dynamical systems, and hidden Markov models. http://www.brynmawr.edu/math/colloquium.html