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According to Internet (actually, Wikipedia and Wolfram MathWorld), I have two information: It was Euler who first introduced the symbol $e$ (before people used $b$); the symbol is to honor Euler.

I find this very strange. My theory is that $e$ is for "exponential" not for Euler.

So what is the evidence that Euler was using the symbol to "honor" himself?

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    $\begingroup$ See here for details. $\endgroup$ – Mauro ALLEGRANZA Jun 1 '16 at 9:30
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    $\begingroup$ And see Leonhard Euler, Introductio in analysin infinitorum (1748), page 90, for the definition: "Ponamus. autem brevitatis gratia pro numero hoc $2,718281828459$ etc. constanter litteram $e$, quae ergo denotabit basin Logarithmorum naturalium seu hyperbolicorum, cui respondet litterae $k=1$ [in the previous defined infinite sum]". $\endgroup$ – Mauro ALLEGRANZA Jun 1 '16 at 9:36
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On the The number e page, one can find the following:

As far as we know the first time the number e appears in its own right is in 1690. In that year Leibniz wrote a letter to Huygens and in this he used the notation b for what we now call e. [...] Retrospectively, the early developments on the logarithm became part of an understanding of the number e.

Later:

So much of our mathematical notation is due to Euler that it will come as no surprise to find that the notation e for this number is due to him. The claim which has sometimes been made, however, that Euler used the letter e because it was the first letter of his name is ridiculous. It is probably not even the case that the e comes from "exponential", but it may have just be the next vowel after "a" and Euler was already using the notation "a" in his work. Whatever the reason, the notation e made its first appearance in a letter Euler wrote to Goldbach in 1731

Some other details are given here:

Euler started to use the letter e for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and the first appearance of e in a publication was Euler's Mechanica (1736). While in the subsequent years some researchers used the letter c, e was more common and eventually became the standard.

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You are right and your Internet source is wrong. First, Euler introduced this notation himself. And clearly this stood for "exponential". Euler was a modest person, and I cannot imagine him naming anything for himself. Second, if someone wanted to name something after Euler, s/he would choose capital E.

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  • $\begingroup$ Someone needs to change the Wikipedia then ... $\endgroup$ – Hao Chen Jun 1 '16 at 20:30
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    $\begingroup$ I don't think it's "clear" that $e$ stood for "exponential". Do you have any evidence for this claim? $\endgroup$ – Danu Jun 2 '16 at 8:41
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It was common among mathematicians of the 17th century to use vowels; thus Fermat's writing on adequality is full of A's and E's. Since A is used much too often the choice of the next vowel, E, was all too natural. I don't think Euler used the symbol to honor himself. Possibly once he chose E, the symbol was retained by later mathematicians so as to honor Euler.

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