In this paper, different schools of thought are discussed and compared to encourage lively classroom discussion and interest in mathematics for high achieving Form 12 students and first (or higher) year university students enrolled in a mathematics degree program. In particular the work and views of two mathematicians, Kurt Godel (1931) and Ian Stewart (1996), mathematician and professor Reuben Hersh (1998) and university lecturer, researcher and writer Robyn Arianrhod (2003) are used to illustrate different views of mathematics. Two documentaries are suggested for viewing by students: "Dangerous Knowledge," relating the work and place of Godel in the history and foundations of mathematics (Malone & Tanner, 2008), and "How Kevin Bacon Cured Cancer" (Jacques, 2008) which illustrates how mathematicians and scientists work together developing and applying mathematics. (Contains 1 table.)