This article focuses on the philosophy of creativity and its enhancement through an undergraduate research experience. In this paper we offer suggestions for infusing the undergraduate mathematics and science curriculum with research experiences as a way of fostering creativity in our students. We refer to the term "research" broadly, offering suggestions to accommodate students from various backgrounds and with different goals. We posit that creativity is a necessary component of scientific thinking, producing students that are motivated, passionate, skilled, adaptable, and responsible. Research experiences at the undergraduate level instill a deep sense of personalized education and learning that can make the entire university experience extremely pleasurable and of lasting value.