[miki123211]

This is why I find e so fascinating, frustrating and puzzling.

The other constants fundamental to science, like the gravitational constant or the speed of light, can only be measured, not discovered from nothing. We aren't even sure how constant they actually are, there might be extremely tiny variations in either time or space that our instruments just can't measure yet. In theory, other universes could exist where these constants are "set" a little bit differently; whether we could live in such universes is another matter entirely.

E, on the other hand, comes from pure mathematics. As long as fractions, addition and exponentiation work the same way in another hypothetical universe, this strange E number is going to have the same strange value.

[empath75]

e isn't really a fundamental physical constant and doesn't show up very much in famous scientific formulas. It's a number that has very convenient properties for performing calculus operations and shows up in that context. pi isn't really an important physical constant, either, but it shows up a lot because of two things --- it's useful for calculations involving cycles, and because things being spherical or circular is a useful simplifying assumption (and also because things particularly in astronomy end up being spherical or circular (or nearly) quite often in reality).

Neither of those things are sort of empirically measured, and in any formula where they show up, you could theoretically absorb them into other constants -- and in fact the Einstein gravitational constant does exactly that -- it's defined as (8*pi*G)/c^4, absorbing pi into newton's gravitational constant (for historical reasons, when using plank units, they set G and c to 1, so it ends up just being 8pi -- _reduced_ planck units set the whole constant to 1). It's just frequently easier to separate out e and pi for the purposes of actually working out the math.

[saintradon]

That's the same with pi if you think about it, and in my eyes is what makes it a transcendental number, so to speak. The numbers themselves could be different if you used a different base instead of base 10, but they still just represent a particularly useful value for us.

[jerf]

There's a good number of constants, and some of them are quite fun: https://en.wikipedia.org/wiki/List_of_mathematical_constants

One of my favorites is https://en.wikipedia.org/wiki/Feigenbaum_constants . Pops up in many situations, and as I understand it, it is not even well-understood why it pops up in as many places as it does. Intuitively one would expect that many of the places it pops up ought to have their own local constant of some sort, but instead this one keeps popping up. 7-year-old Numberphile video on it: https://www.youtube.com/watch?v=ETrYE4MdoLQ