Proofs from THE BOOK

Paul Erdos liked to talk about The Book, in which God maintains the perfect proofs for mathematical theorems, following the dictum of GH Hardy that
there is no permanent place for ugly mathematics. Erdos also said that you don't need to believe in God but, as a mathematician, you should believe in
The Book. In this seminar, we will discuss chapters from "Proofs from THE BOOK", sixth edition, 2018. The book is available through the university library. The seminar will be held in English.

We have no definition or characterization of what constitutes a proof from The Book: all we [the authors] offer here is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations. We also hope that our readers will enjoy this despite the imperfections of our exposition. The selection is to a great extent influenced by Paul Erdos himself. A large number of the topics were suggested by him, and many of the proofs trace directly back to him, or were initiated by his supreme insight in asking the right question or in making the right conjecture. So to a large extent this book reflects the views of Paul Erdos as to what should be considered a proof from The Book.

A limiting factor for our selection of topics was that everything in this book is supposed to be accessible to readers whose backgrounds include only a modest amount of technique from undergraduate mathematics. A little linear algebra, some basic analysis and number theory, and a healthy dollop of elementary concepts and reasonings from discrete mathematics should be sufficient to understand and enjoy everything in this book.