For millennia, the Pythagorean theorem has provided a simple yet profound formula for computing distances between points. Remarkably, this timeless concept continues to captivate mathematicians, inspiring new discoveries and posing challenging open questions.

A central theme in this journey involves distance sets: collections of distances determined by points in a set. How large can a distance set be if the set of points it comes from is “large”? How does the structure of a set shape the distances it contains? These questions bridge classical geometry and modern mathematics, with applications reaching far beyond disciplinary boundaries.

This two-part series explores the surprising depth of these problems. The first talk introduces key ideas and landmark results in a way accessible to a general audience, requiring no advanced mathematical background. The second talk delves into analytical perspectives, uncovering deeper mathematical mysteries for those eager to explore the intricate beauty of this field.