The connection between thought and its expression in symbolism is perhaps more important in mathematics than in any other subject, for the complexity of mathematical thinking soon makes reference to symbolism an indispensable method of learning and discovery This is true both in the historical development of the science and in the experience of the individual student. Without visible symbolism to act as a scaffolding, the sheer complexity of the subject matter results very soon in an incoherence and breakdown of the thinking process. While this is true to some extent of all subjects of any high degree of complexity, in mathematics a new and extremely interesting element enters into the situation.