The great theorem of this chapter is, essentially, that there are infinitely many primes. Dunham will give us Euclid’s
original proof. Our second reading is from a work called “Proofs from THE BOOK”. You should read the
introduction to this book to get a sense of what is meant by the title, but the idea is that a mathematician named
Paul Erd
s thought that God kept a book of so-called perfect proofs of mathematical theorems. Some
other mathematicians compiled proofs of various theorems that they thought could be candidates
for “The Book”. We’ll look only at the section dedicated to the proof that there are infinitely many
primes, but you should feel free to explore the work in relation to any other theorems that interest
you.
Readings
First reading: Dunham, Chapter 3, pages 73-83
Second reading: Proofs from THE BOOK
- Read Chapter 1 (pages 3-8) and choose one proof other than Euclid’s to familiarize yourself with.