E (mathematical constant)

“Euler wrote... in 1748 his Introductio in Analysin Infinitorum, which was intended to serve as an introduction to pure analytical mathematics. ...He ...shewed that the trigonometrical and exponential functions were connected by the relation”

“The natural exponential function is identical with its derivative. This is the source of all the properties of the exponential function and the basic reason for its importance in applications.”

“The number e has an established place in mathematics alongside the Archimedian number π ever since the publication in 1748 of Euler's Introductio in Analysin Infinitorum. It provides an excellent illustration of how the principle of monotone sequences can serve to define a new real number.”

“To Euler is due the very remarkable formula”

“The exponential function, y e, is the instrument used, in one form or another, to describe the behavior of growing things. For this it is uniquely suited: it is the only function of x with a rate of change with respect to x equal to the function itself.”

“There is a familiar formula—perhaps the most compact and famous of all formulas—developed by Euler from a discovery of De Moivre: . ...It appeals equally to the mystic, the scientist, the philosopher, the mathematician.”

“Think of it: of the infinity of real numbers, those that are most important to mathematics—0, 1, √2, e and π—are located within less than four units on the number line. A remarkable coincidence? A mere detail in the Creator's grand design? I let the reader decide.”