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In the Homeric epic that is mathematics, e gets a choice epithet. It is “the natural base.”
I inventoried the reasons last year (for the historic once-in-a-century e Day). And I later stumbled across an even more delicious “naturalness” argument for e.
But that’s hardly exhaustive. Here’s another thing I dig about e, an easy fact for any first-year calculus student to verify:
Also, an addendum: a fun observation from Twitter…
Addendum #2, on March 4, 2019: the inimitable Sam Shah asks how we can introduce e to algebra students, and then delivers a delightful post rounding up more lovely e facts.