It’s not what you’d expect to find on the first page of a book titled “An Introduction to Mathematics”. There, immediately, the ghost from Shakespeare’s Hamlet makes his dramatic entrance. Whitehead is known for the frequent literary references in his writings even when the topic is as dry as maths or theoretical physics.
Perhaps Whitehead means to make a point that maths can be as fascinating and drama-filled as any historical saga of princes and villains and threatened kingdoms.
“The ghost in Hamlet no doubt performs an important dramatic function. Whatever may have been Shakespeare’s belief about ghosts he utilizes the popular conception to render objective what is in the minds of his characters.”
The key idea here is “render objective”. A belief, which is an internal subjective thing, is rendered objective when it is thrust “outside” as a ghostly figure in a story. And this is also what happens every time we put pen to paper or text to a web page. We render what is inside into a form that is visible outside.
Which is, of course, what I’ve just done!