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Euler is usually credited with denoting this number with the letter $\mathrm e$. But

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 (Maor, 1994).

So, who first called this number "Euler's number"?

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    $\begingroup$ Checking English, French, and German sources, the earliest instance I could find dates to 1896. This is an entry in a German encyclopedia in which the term appears as "Eulersche Zahl". Given that the term was used in an encyclopedia, it stands to reason that it must have occurred in print earlier elsewhere. Note that there are also Euler numbers $E_n$ (an entirely different kettle of fish), and these pop up in literature from the 1800s. $\endgroup$
    – njuffa
    Jun 5, 2023 at 9:28
  • $\begingroup$ @njuffa: Could you link to that entry? $\endgroup$
    – user18522
    Jun 6, 2023 at 4:19
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    $\begingroup$ Meyers Conversations-Lexikon, 5. Auflage, 11. Band, Leipzig: Bibliographisches Institut 1896, p. 449 (online): " Logarithmische Spirale [...] Ist $r$ der Radius, $\phi$ der winkelmessende Bogen, $e$ die Eulersche Zahl, so ist die Gleichung der auch dem Ingenieur wichtigen Kurve $r=e^{a\phi}$." $\endgroup$
    – njuffa
    Jun 6, 2023 at 4:45

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Google Ngram does not show any use of "Euler's number" before 1880s, and early sources typically call "Euler's number" what is now called the Euler–Mascheroni constant $0.57721...$, see e.g. Sylvester's Constructive Theory of Partitions (1882), p. 298. Some other numbers associated with Euler are also called "Euler's", but not $e$.

"Euler's number $e$" is probably the creation of modern textbooks. The earliest one I found is the influential What is Mathematics by Courant and Robbins, p. 297. Whether it was the first or not, it must have contributed to its spread. For example, the curriculum of the geometry seminar at Regis College published in American Mathematical Monthly in 1950, recommends it as primary reading and copies "Euler's number $e$" from it (p. 256).

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