# Six Ways to Prove that there are Infinitely Many Prime Numbers

## How mathematicians come at problems from different angles

7 min readFeb 12, 2024

One of the first things most mathematics undergraduates learn (and maybe even some smart and enthusiastic high school students) is a proof that there are infinitely many primes. In most cases the proof taught is the classic one developed by the Greek mathematician Euclid around 300BC and presented in Book 9 of his 13-volume *Elements *treatise.