I explore the strange story of Euler’s number e, from a simple compound interest problem to one of the most important constants in mathematics.
This math documentary follows Jacob Bernoulli, Leonhard Euler, infinite series, exponential growth, logarithms, and Euler’s identity to show why e = 2.71828... appears everywhere.
_______
Time stamps:
00:00 The Compound Interest Problem
00:49 The Mysterious Number Mathematicians Couldn’t Explain
01:32 Jacob Bernoulli and the Banking Problem
02:07 Leonhard Euler Enters the Story
02:55 Euler Finds e in the Power Series
03:42 Euler’s Letter to Christian Goldbach
04:18 How Euler Understood e
06:45 How e Became a Mathematical Constant
07:32 The Many Faces of e
08:32 Euler Proves That e Is Irrational
09:49 Mathematicians Are Still Finding e Today
10:23 Euler’s Formula and Euler’s Identity
Music: Epidemic Sound
Public domain images: Wikimedia Commons
Additional licensed images: Envato Elements
Math Animations: I use Python Manim to create the math visualizations in this video
If you enjoy story-driven documentaries about mathematical breakthroughs, scientific ideas, and the people behind them, consider subscribing for future episodes.
And feel free to leave a comment if there’s another scientific breakthrough, idea, or genius you’d like me to explore.
