# Chapter9Proof techniques IV — Magic

*If you can keep your head when all about you are losing theirs, it's
just possible you haven't grasped the situation. –Jean Kerr*

The famous mathematician
Paul Erdös is said to have believed that
God has a Book in which all the really elegant proofs are written.
The greatest praise that a collaborator^{ 1 } could receive from Erdös
was that they had discovered a “Book proof.” It is not
easy or straightforward for a mere mortal to come up with a Book
proof but notice that, since the Book is inaccessible to the living,
all the Book proofs of which we are aware were constructed by ordinary
human beings. In other words, it's not impossible!

The title of this final chapter is intended to be whimsical — there is no real magic involved in any of the arguments that we'll look at. Nevertheless, if you reflect a bit on the mental processes that must have gone into the development of these elegant proofs, perhaps you'll agree that there is something magical there.

At a minimum
we hope that you'll agree that they are beautiful — they are proofs
from the Book^{ 2 } .

Acknowledgment: Several of the topics in this section were unknown to the author until he visited the excellent mathematics website maintained by Alexander Bogomolny at

`http://www.cut-the-knot.org/`