What does it feel like to invent math?

The video explores the concept of infinite sums, starting with the surprising result that an infinite sum can equal negative one. It delves into the process of defining and understanding convergent infinite sums, illustrating how early mathematicians might have approached these concepts. The video generalizes these ideas, introducing the 2-adic metric, a new way to understand distance between numbers, and discusses its implications in modern number theory. It concludes with a reflection on the nature of mathematical discovery and invention.

What challenges arise when trying to define infinite sums in a rigorous mathematical framework?

What is the 2-adic metric, and how does it relate to the sum of powers of 2?

Discuss the implications of defining new mathematical concepts based on fuzzy discoveries.

In what ways does the exploration of infinite sums illustrate the process of mathematical discovery?