I like the idea of "The Book". There's a lot of very elegant proofs in mathematics. One of my favorite is the proof that there is no greatest prime number. Assume there were a biggest prime, P. Now make the number 1 x 2 x 3 x 4 x 5 x .... x P plus 1. This number cannot be evenly divided by 2 or 3 or 4 or any number up to P because there will always be a remainder of 1 (that's the plus 1 on the end of the expression). That means the number must itself be prime or it must have a prime factor that is greater than P. Either way, we've shown that there must exist a prime greater than P, and we started by saying that P is the greatest prime. Therefore there is no greatest prime number. For example, if you suppose the greatest prime number is 5, make a new number 1 x 2 x 3 x 4 x 5 + 1 = 121. Try dividing 121 by 2, 3, 4, and 5. There will always be a remainder of 1. That means 121's prime factors must be greater that 5 (they are: 11 and 11). So 5 is not the greatest prime.