Why is it called "$e$"?

Question

So I'm sure you have all heard of the number $e$ which is approximately $2.71828...$ . But why is it called $e$? It isn't due to Leonhard Euler, since he didn't name the number after himself, the first letter of his last name being just a coincidence. So, why is it called $e$?

Answer 1

The Earliest Uses of Symbols for Constants page mentions that Leibniz used the symbol $b$ in the 1690s, but Euler introduced $e$ in 1727. (D'Alambert used $a$ in the late 1740s; Melandri used $c$ in 1787.) A number of commentaries are listed (via sources on this page):

[Maor (1994) in "$e$: The Story of a Number"] Why did [Euler] choose the letter e? There is no general consensus. According to one view, Euler chose it because it is the first letter of the word exponential. More likely, the choice came to him naturally as the first "unused" letter of the alphabet, since the letters a, b, c, and d frequently appear elsewhere in mathematics. It seems unlikely that Euler chose the letter because it is the initial of his own name, as occasionally been suggested: he was an extremely modest man and often delayed publication of his own work so that a colleague or student of his would get due credit. In any event, his choice of the symbol e, like so many other symbols of his, became universally accepted.

[Ball (1960 or 1987)] It is probable that the choice of e for a particular base was determined by its being the vowel consecutive to a.

[Boyer (1989)] [This notation was] suggested perhaps by the first letter of the word "exponential."

[Wei-hwa Huang (1995)] I believe that e was not named because it was the first letter in Euler's name, but rather because he was using vowels for constants in a proof of his and e happened to be the second one.

[Olivier Gerard (1999)] The hypothesis made by my friend Etienne Delacroix de La Valette was that e was for "ein" (one in German) or "Einheit" (unity), which would be matching the sentence Euler uses to define it (whose logarithm is unity). As always, many explanations may be true at the same time.

See @PaulFrost's comment below, casting doubt on Gerard's (friend's) "ein/Einheit" hypothesis.