Short answers, pulled from the story.
Jacob Bernoulli discovered the mathematical constant e in the year 1683 while calculating the maximum amount of money one could earn by compounding interest continuously. He proved that this value lay somewhere between 2 and 3 but could not determine its exact value at that time.
Leonhard Euler standardized the notation in 1727 and 1728, choosing the letter e to represent the number. He first used the symbol in an unpublished paper about the explosive forces of cannons and later in a letter to Christian Goldbach on the 25th of November 1731.
The number e is the only base for which the rate of change is exactly equal to the function's current value. If you graph the function e to the power of x, the slope of the curve at any point is identical to the height of the curve at that same point.
Charles Hermite proved that e is transcendental in 1873, meaning it is not the solution to any non-zero polynomial equation with rational coefficients. This was the first number to be proven transcendental without being specifically constructed for that purpose.
By the 24th of December 2023, a record-breaking calculation by Jordan Ranous had determined 35 trillion digits of e. This feat was made possible by modern high-speed desktop computers and advanced algorithms like binary splitting.
Google announced an intention to raise 2,718,281,828 dollars in its 2004 initial public offering, a figure rounded to the nearest dollar from the first ten digits of e. The company also placed billboards in Silicon Valley and other tech hubs challenging solvers to find the first ten-digit prime number hidden within the consecutive digits of e.