Prime numbers are the "building blocks" of arithmetic, and one of the oldest results in mathematics is that there are infinitely many of them. While most proofs of this fact use number-theoretic arguments, there is a beautifully unexpected proof that comes from topology, the study of shapes and spaces. In 1955, Hillel Furstenberg showed that by looking at the integers through the lens of a special topology built from arithmetic progressions, one can prove the infinitude of primes in a completely new way.
This talk will introduce the basic ideas behind Furstenberg’s construction, explain why it works without requiring technical background, and highlight how it reveals surprising connections between two very different areas of mathematics.
