Review of proofs from THE BOOK (4th edition) by Martin Aigner and Günter M. Ziegler

Paul Erdős, the most prolific mathematician of the twentieth century, had his own way of judging the beauty of various proofs. He said that there was a book somewhere, possibly in heaven, and that book contained the nicest and most elucidating proof of every theorem in mathematics. When somebody showed him a new proof, he either said, “this is the Book proof” or “this is not the Book proof”. Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdős. The theorems are so fundamental, their proofs so elegant, and the remaining open questions so intriguing that every mathematician, regardless of specialty, can benefit from reading this book. The book has five parts of roughly equal length.