The Book (Erdős)

The Book was Paul Erdős's name for an imaginary volume he attributed to a God he did not otherwise believe in—a God he called the Supreme Fascist, the cosmic adversary who hides the elegant proofs and torments mathematicians by withholding them. The Book contains, for every theorem, the single most beautiful proof: the argument of maximal elegance, minimal length, total inevitability, the proof that makes you see why the theorem must be true rather than merely accept that it is. 'You don't have to believe in God,' Erdős said, 'but you should believe in The Book.' When he encountered a proof of surpassing elegance—a three-line argument that rearranged your understanding of a whole subject, an insight so luminous it seemed discovered rather than invented—his highest praise was simple: this one is from the Book. The standard the Book represents is the standard the age of machine-generated mathematics now puts under maximum pressure. We have built systems that produce proofs of staggering size and perfect validity that