This paper examines three ideas: First, the traditional relationship between a science, the mathematics it uses and the engineering based on it. Second, the nature of (software) computer science, which may not be a science at all, and its unusual use of mathematics. And finally, the nature of software engineering, its relationship with computer science, and its use of mathematics called ‘formal methods’. These three ideas turn on the first of them, since the scientific world view seems natural for the study of computing. The paper's thesis is that while software touches science in many ways, it does not itself have a significant scientific component. For understanding programming, for teaching it and for applying it in the world, science is the wrong model. Mathematics has found its own foundations apart from science, and computer science must do the same.