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In terms of readability as well as correct syntax, what is more preferred in mathematical equations: e^{...} or \exp(...) -- and why?

For instance, e^{x^2/(4t)} or \exp(x^2/(4t)). The latter is easier in that I can directly convert this expression into Mathematica for instance and then manipulate it, whereas the former I must convert each instance of e manually to E. On paper, the former is easier to read.

Typographically, depending on the argument, when should one use e^{x^2/(4t)} or when should one use \exp(x^2/(4t))?

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    This would be better asked at math.stackexchange.com. However, as a retired Math Professor e^{2x} was preferred as the other is a programming language construct for computing the value of the exponential. – R. Schumacher Jul 11 '15 at 3:10
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    Both forms are "correct" from a syntactical point of view, i.e., TeX won't throw an error. Which form should be used, i.e., which form is preferable from a typographic point of view, depends strongly on (a) what's inside the ... part and (b) whether the material occurs in inline math mode or display math mode. – Mico Jul 11 '15 at 3:12
  • @Mico Hi Mico, I updated my question to cover your points. – Jun-Goo Kwak Jul 11 '15 at 3:15
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    I prefer \exp for every formula more complex than x^2. In general, I have the opinion that large expressions containing fractions, integrals, sums etc. should be avoided at all costs in exponents, square roots and fractions. It is almost always possible to rewrite the equation to avoid this kind of situation. – Gaussler Jul 11 '15 at 7:57
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Let's see what Ellen Swanson in page 20 of her classic Mathematics into Type has to say about this:

enter image description here

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    Since e is a constant, wouldn't it better to make it roman? As in {\rm e}^x. (See: tex.stackexchange.com/q/19488/11626) – ja72 Feb 22 '18 at 18:46
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    @ja72 It is exactly the same question that guided me to this post through your comment. – Noir Jun 12 '18 at 0:31

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