How does the natural logarithm e come from and what is its use?

Euler's formula for the base of natural logarithm

(approximately equal to the base of natural logarithm of 2.71828-e)

Euler is known as Shakespeare in the number field, and he is the most prolific mathematician in history. He is also a scholar with the most works in various fields (including all branches of theory and application in mathematics, mechanics, optics, acoustics, water conservancy, astronomy, chemistry, medicine, etc.). In the history of mathematics, the 18th century is called the "Euler era".

Born in Switzerland, Euler lost his right eye sight at the age of 31 and lost his eyes at the age of 59, but he is optimistic and has amazing memory and concentration. So that he can still think complex problems accurately in the noisy environment of 13 children.

Euler was humble all his life and never named what he found with his own name. Only the bottom of the natural logarithm, which is about 2.71828, was named E. But because of his extensive contribution to mathematics, in many branches of mathematics, On the contrary, we often see important constants, formulas and theorems named after him.

Many mathematical symbols that we are used to now are invented and introduced by Euler, such as function symbols f(x), π, e, ∑, logx, sinx, cosx, imaginary number I, etc. Senior high school teachers often use a joke about the base e of natural logarithm to help students remember a very special differential formula: in a mental illness. A patient said to others all day, "I differentiate you, I differentiate you." I don't know why. These patients all have a simple concept of calculus. They always think that one day they will be differentiated into zero and disappear like a general polynomial function, so they avoid him. However, one day he met an unmoved person, who was surprised, and this person simply said to him, "I am the x power of E. No wonder math students use e as a metaphor for unswerving love!

compared with π, which is the first letter of a circle in Greek characters, the origin of e is not well known. Some people even think that Euler takes the first letter of his name as the natural logarithm.

There are two more acceptable reasons for Euler's choice of e: one is that after four commonly used letters, such as A, B, C and D, the first letter that has not been frequently used is E, so he is natural. One is that e is the first letter of the index. Although you may suspect that the native language of Swiss Euler is not English, in fact, it is the index in French and German.