There is something right about the view of mathematics as "the language of science”. Thinking of mathematics as a language is useful in appreciating the significance of, and the difficulties encountered arriving at, a good notational system. Good notation is far from trivial. The development of differential geometry, for example, with its Ricci curvature tensors and the like, is intimately connected with the notation employed. But thinking of mathematics as merely language is to ignore the other roles mathematics can play in science. I will consider the role good notation can play in prompting new ideas and new developments in mathematics and science. I will look at the recent work on mathematical explanation and argue that there are genuinely mathematical explanations of empirical facts and, moreover, the transparency of some of these explanations is dependent upon good mathematical notation.