Mathematicians are forced to resort to the use of written symbols and images to describe their world - even among themselves. However, the symbols are not their world, just as musical notation is not music.

Over the centuries, the collective intellect of mathematicians has created their own universe. I do not know if it exists somewhere - I do not believe there is a "somewhere," in any usual sense of the word - but I can assure you that this mathematical universe feels quite real when you are inside it.

I intend to guide you through this mathematical universe. I will try to make you see through the eyes of a mathematician; and at the same time, to change your own way of seeing the world around you.

[Excerpt from the text of the preface]