I'm aware of the names "Archimedes' constant" and "Euler's number" for $\pi$ and $e$ respectively, but these don't seem to be used very commonly. Even in school I remember $\pi$ and $e$ being almost always referred to as "pi" and "e", to the extent that some math students don't even understand what "Archimedes' constant" is despite using it every day.

By contrast, nearly all other mathematical concepts have descriptive names not associated with the symbols used to represent them. Think of the golden ratio $\varphi$, the imagimary unit $i$, Euler-Mascheroni constant $\gamma$, etc.

Are there any specific historical reasons why $\pi$ and $e$ are not named any better than the symbols used for them?

I asked myself this question after reading this joke. If the problem had been instead "Give an example of a transcendental number", then both "pi" and "e" would have been great answers.

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    $\begingroup$ $\pi$, $e$ $\endgroup$ – mrf Jan 14 '16 at 12:29
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    $\begingroup$ Perhaps this is due to the fact that $\pi$ and $e$ are so widely used - if one says $\pi$, everyone knows you're talking about the ratio between the diameter and the circumference of a circle. However, constants like $\gamma$ or $i$ are also used in other instances - $\gamma$ being a common name for an angle (if $\alpha$ and $\beta$ are used already) and $i$ is used a lot in number theory, specifically in summations. Thus, for those it is useful to give them an extra name to be sure people understand what you're talking about. $\endgroup$ – vrugtehagel Jan 14 '16 at 12:33
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    $\begingroup$ Can you imagine saying "Archimedes' constant" every time you mean $\pi$ when walking a class through a derivation? $\endgroup$ – Travis Willse Jan 14 '16 at 12:37
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    $\begingroup$ The letter π is a perfectly good name, since it is the first letter of the Greek word περίμετρος (perimeter). As to e, it is the initial letter of both Euler and exponent. $\endgroup$ – Bernard Jan 14 '16 at 12:40
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    $\begingroup$ some math students don't even understand what “Archimedes' constant” is, despite using it every day. - So what ? You yourself have no idea what Legendre's constant is, despite using it every day. $\endgroup$ – Lucian Jan 14 '16 at 12:47

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